<?xml version="1.0" encoding="UTF-8"?>
 <rdf:RDF xmlns="http://purl.org/rss/1.0/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:taxo="http://purl.org/rss/1.0/modules/taxonomy/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://web.resource.org/cc/" xmlns:syn="http://purl.org/rss/1.0/modules/syndication/" xmlns:admin="http://webns.net/mvcb/">
  <channel rdf:about="http://pinboard.in">
    <title>Pinboard (Vaguery)</title>
    <link>https://pinboard.in/u:Vaguery/public/</link>
    <description>recent bookmarks from Vaguery</description>
    <items>
      <rdf:Seq>	<rdf:li rdf:resource="https://arxiv.org/abs/2401.17720"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2603.21852v2"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2605.22129"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2309.16100"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2411.19864"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2301.01624"/>
	<rdf:li rdf:resource="https://personal.math.ubc.ca/~gerg/index.shtml?abstract=UECFE"/>
	<rdf:li rdf:resource="https://vadim.sdsu.edu/cf21.pdf"/>
	<rdf:li rdf:resource="https://www.researchgate.net/publication/392901951_A_NOTE_ON_HYPERGEOMETRIC_REPRESENTATION_OF_A_NEW_MATHEMATICAL_CONSTANT"/>
	<rdf:li rdf:resource="https://www.researchgate.net/publication/392282754_ON_A_GENERALIZATION_OF_THE_PERFECT_SQUARE_SEQUENCE_AND_ITS_POLYNOMIAL?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSJ9fQ"/>
	<rdf:li rdf:resource="https://users.mccme.ru/smirnoff/papers/friezes-eng.pdf"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2303.13253"/>
	<rdf:li rdf:resource="https://aperiodical.com/2022/03/john-conway-and-his-fruitful-fractions/"/>
	<rdf:li rdf:resource="https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf"/>
	<rdf:li rdf:resource="https://mathenchant.wordpress.com/2023/10/17/marvelous-arithmetics-of-distance/"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2307.04704"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2110.09511"/>
	<rdf:li rdf:resource="https://www.mathvalues.org/masterblog/my-mathematical-journey-the-stamp-problem"/>
	<rdf:li rdf:resource="https://publications.mfo.de/handle/mfo/1415"/>
	<rdf:li rdf:resource="https://publications.mfo.de/handle/mfo/1413"/>
	<rdf:li rdf:resource="https://whystartat.xyz/wiki/Main_Page"/>
	<rdf:li rdf:resource="http://www.openproblemgarden.org/"/>
	<rdf:li rdf:resource="https://johncarlosbaez.wordpress.com/2020/10/10/decimal-digits-of-1-%cf%80%c2%b2/"/>
	<rdf:li rdf:resource="https://blog.mrmeyer.com/2019/real-world-math-is-everywhere-or-its-nowhere/"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2103.09623"/>
	<rdf:li rdf:resource="https://imaginary.org/texts?page=1"/>
	<rdf:li rdf:resource="https://dl.acm.org/doi/abs/10.1145/3385412.3386037"/>
	<rdf:li rdf:resource="https://mathlesstraveled.com/2019/12/23/a-simple-proof-of-the-quadratic-formula/"/>
	<rdf:li rdf:resource="https://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts"/>
	<rdf:li rdf:resource="https://twitter.com/AndresECaicedo1/status/1302697810446483456"/>
	<rdf:li rdf:resource="https://divisbyzero.com/2019/11/12/tales-of-impossibility-now-released/"/>
	<rdf:li rdf:resource="https://www.math3ma.com/blog/topology-book"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1809.05923"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1902.07404"/>
	<rdf:li rdf:resource="https://mathenchant.wordpress.com/2020/01/24/what-proof-is-best/"/>
	<rdf:li rdf:resource="https://www.quantamagazine.org/the-numbers-and-geometry-behind-a-math-coloring-puzzle-20180618/"/>
	<rdf:li rdf:resource="https://mathenchant.wordpress.com/2019/02/16/who-mourns-the-tenth-heegner-number/"/>
	<rdf:li rdf:resource="http://arminstraub.com/math/what-is-column"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1809.08483"/>
	<rdf:li rdf:resource="https://math-frolic.blogspot.com/2018/04/math-and-understanding.html"/>
	<rdf:li rdf:resource="https://www.redblobgames.com/articles/curved-paths/"/>
	<rdf:li rdf:resource="https://samjshah.com/2018/02/09/alone-with-starry-night/"/>
	<rdf:li rdf:resource="http://library.msri.org/books/Book29/files/unsolved.pdf"/>
	<rdf:li rdf:resource="http://tonysmaths.blogspot.com/2018/05/mathematical-discoveries.html"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/math/9404236"/>
	<rdf:li rdf:resource="http://jdh.hamkins.org/alan-turing-on-computable-numbers/"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1610.02247"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/math/0408099"/>
	<rdf:li rdf:resource="https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1808.02841"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1808.07006"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1810.00173"/>
	<rdf:li rdf:resource="http://graphics.berkeley.edu/papers/Karpenko-EVD-2010-00/index.html"/>
	<rdf:li rdf:resource="https://twitter.com/jhnhw/status/1031829726757900288"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1808.03172"/>
	<rdf:li rdf:resource="https://www.theoremoftheday.org/Theorems.html#209"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1803.06824"/>
	<rdf:li rdf:resource="https://en.wikipedia.org/wiki/Generating_function"/>
	<rdf:li rdf:resource="https://en.wikipedia.org/wiki/Homotopy_type_theory"/>
	<rdf:li rdf:resource="https://www.smithsonianmag.com/history/the-woman-who-bested-the-men-at-math-120480965/"/>
	<rdf:li rdf:resource="http://www.openproblemgarden.org/home"/>
	<rdf:li rdf:resource="https://pdfs.semanticscholar.org/7efd/0c0bcbde96fed232069e1015df7fe2ccd8aa.pdf"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1802.06712"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1801.02602"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1612.01093"/>
	<rdf:li rdf:resource="https://press.princeton.edu/math/subjects/mgen.html"/>
	<rdf:li rdf:resource="https://www.youtube.com/watch?v=YCXmUi56rao"/>
	<rdf:li rdf:resource="http://parrt.cs.usfca.edu/doc/matrix-calculus/index.html"/>
	<rdf:li rdf:resource="http://www.theoremoftheday.org/Resources/RelatedSites.htm#magazines"/>
	<rdf:li rdf:resource="https://medium.com/q-e-d"/>
      </rdf:Seq>
    </items>
  </channel><item rdf:about="https://arxiv.org/abs/2401.17720">
    <title>[2401.17720] Apéry Acceleration of Continued Fractions</title>
    <dc:date>2026-05-25T12:10:58+00:00</dc:date>
    <link>https://arxiv.org/abs/2401.17720</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Apéry in his proof of the irrationality of ζ(3). We show in particular that this can be applied to a large number of continued fractions which can be found in the literature, thus providing a large number of new continued fractions. As examples, we give a new continued fraction for log(2) and for ζ(3), as well as a simple proof of one due to Ramanujan.
]]></description>
<dc:subject>continued-fractions representation rather-interesting heuristics mathematics performance-measure to-write-about to-simulate consider:evolutionary-search consider:accuracy-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:aaaab8b3e49a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:evolutionary-search"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:accuracy-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2603.21852v2">
    <title>[2603.21852v2] All elementary functions from a single binary operator</title>
    <dc:date>2026-05-22T10:46:58+00:00</dc:date>
    <link>https://arxiv.org/abs/2603.21852v2</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as e, pi, and i; arithmetic operations including addition, subtraction, multiplication, division, and exponentiation as well as the usual transcendental and algebraic functions. For example, exp(x)=eml(x,1), ln(x)=eml(1,eml(eml(1,x),1)), and likewise for all other operations. That such an operator exists was not anticipated; I found it by systematic exhaustive search and established constructively that it suffices for the concrete scientific-calculator basis. In EML (Exp-Minus-Log) form, every such expression becomes a binary tree of identical nodes, yielding a grammar as simple as S -> 1 | eml(S,S). This uniform structure also enables gradient-based symbolic regression: using EML trees as trainable circuits with standard optimizers (Adam), I demonstrate the feasibility of exact recovery of closed-form elementary functions from numerical data at shallow tree depths up to 4. The same architecture can fit arbitrary data, but when the generating law is elementary, it may recover the exact formula.
]]></description>
<dc:subject>mathematics representation rather-interesting amusing-also to-write-about consider:genetic-programming consider:alternatives</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0c232cea7a85/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:amusing-also"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:alternatives"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2605.22129">
    <title>[2605.22129] On Isotopies and hyperbolicity of weaves</title>
    <dc:date>2026-05-22T10:22:03+00:00</dc:date>
    <link>https://arxiv.org/abs/2605.22129</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A weave is a type of textile that consists of vertical and horizontal threads, and typically it has a periodic structure. In this paper, we regard a weave as a link in the thickened torus with a diagram consisting of closed geodesics. As main results, we characterize isotopies and hyperbolicity of weaves to determine them from diagrams. Moreover, we show that there does not exist an essential Conway sphere for a weave. We use normal positions of essential surfaces of weave complements to describe them.
]]></description>
<dc:subject>topology combinatorics mathematical-recreations mathematics knot-theory to-understand enumeration consider:structural-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:67c9f5ce3c4c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:knot-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:structural-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2309.16100">
    <title>[2309.16100] Generating functions of substitutions</title>
    <dc:date>2026-04-20T11:43:03+00:00</dc:date>
    <link>https://arxiv.org/abs/2309.16100</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We prove that a substitution is aperiodic if and only if some of its associated generating functions are transcendental. These generating functions have a recursive structure arising from the substitution which we use to study their roots in the case of the Fibonacci substitution.
]]></description>
<dc:subject>rewriting-systems strings nonlinear-dynamics mathematical-recreations mathematics to-understand consider:feature-discovery consider:inverse-problem</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:90c29aada2bb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:inverse-problem"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2411.19864">
    <title>[2411.19864] An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate</title>
    <dc:date>2025-11-03T17:54:39+00:00</dc:date>
    <link>https://arxiv.org/abs/2411.19864</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It is well known that there is a somewhat mysterious relation between the area of the quartic Fermat curve x4+y4=1, aka squircle, and the arc length of the lemniscate (x2+y2)2=x2−y2. The standardproof of this fact uses relations between elliptic integrals and the gamma function. In this article we generalize this result to relate areas of sectors of the squircle to arc lengths of segments of the lemniscate. We provide a geometric interpretation of this relation and an elementary proof of the relation, which only uses basic integral calculus. We also discuss an alternate version of this kind of relation, which is implicit in a calculation of Siegel.
]]></description>
<dc:subject>geometry mathematical-recreations mathematics polynomials plane-geometry rather-interesting amusing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:22e1e557fd59/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:polynomials"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:amusing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2301.01624">
    <title>[2301.01624] Pattern Recognition Experiments on Mathematical Expressions</title>
    <dc:date>2025-08-01T13:14:00+00:00</dc:date>
    <link>https://arxiv.org/abs/2301.01624</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We provide the results of pattern recognition experiments on mathematical expressions.
We give a few examples of conjectured results. None of which was thoroughly checked for novelty. We did not attempt to prove all the relations found and focused on their generation.
]]></description>
<dc:subject>mathematics rather-interesting number-theory generative-models formal-languages exploration to-write-about to-simulate consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3d4aa24f0e81/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:exploration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://personal.math.ubc.ca/~gerg/index.shtml?abstract=UECFE">
    <title>The unreasonable effectualness of continued function expansions</title>
    <dc:date>2025-07-23T22:28:20+00:00</dc:date>
    <link>https://personal.math.ubc.ca/~gerg/index.shtml?abstract=UECFE</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we might ask that algebraic numbers of a given degree have periodic expansions, just as quadratic irrationals have periodic continued fractions; or we might ask that familiar transcendental constants such as e or π have periodic or terminating expansions. In this paper, we show that there exist such generalized continued function expansions with essentially any desired behavior.
]]></description>
<dc:subject>continued-fractions mathematics number-theory representation oh-no-attractive-nuisance to-write-about to-simulate consider:genetic-programming consider:convergence consider:rewriting-systems dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:66aba79cd93c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:oh-no-attractive-nuisance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:convergence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://vadim.sdsu.edu/cf21.pdf">
    <title>Continued Fractions in the 21st Century [PDF]</title>
    <dc:date>2025-07-14T15:33:00+00:00</dc:date>
    <link>https://vadim.sdsu.edu/cf21.pdf</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Abstract. We present useful (though largely not original) continued fraction tools, that deserve
to be more widely known to a broad mathematical audience]]></description>
<dc:subject>mathematics continued-fractions number-theory algorithms rather-interesting review representation to-write-about to-simulate consider:general-CFs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b45d19fc41b4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:general-CFs"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.researchgate.net/publication/392901951_A_NOTE_ON_HYPERGEOMETRIC_REPRESENTATION_OF_A_NEW_MATHEMATICAL_CONSTANT">
    <title>(PDF) A NOTE ON HYPERGEOMETRIC REPRESENTATION OF A NEW MATHEMATICAL CONSTANT</title>
    <dc:date>2025-06-29T14:11:59+00:00</dc:date>
    <link>https://www.researchgate.net/publication/392901951_A_NOTE_ON_HYPERGEOMETRIC_REPRESENTATION_OF_A_NEW_MATHEMATICAL_CONSTANT</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The main objective of this note is to introduce a new mathematical constant which has been expressed as a sum of two Gauss's hyper-geometric functions. The newly introduced mathematical constant which upon specialisation reduces to a large number of mathematical constants (including the well-known Gelfond's constant e π and Ramanujan's constant e π √ 163) available in the literature]]></description>
<dc:subject>mathematics representation rather-interesting construction to-write-about number-theory continued-fractions to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:77dd59d8e07f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.researchgate.net/publication/392282754_ON_A_GENERALIZATION_OF_THE_PERFECT_SQUARE_SEQUENCE_AND_ITS_POLYNOMIAL?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSJ9fQ">
    <title>(PDF) ON A GENERALIZATION OF THE PERFECT SQUARE SEQUENCE AND ITS POLYNOMIAL</title>
    <dc:date>2025-06-25T19:26:07+00:00</dc:date>
    <link>https://www.researchgate.net/publication/392282754_ON_A_GENERALIZATION_OF_THE_PERFECT_SQUARE_SEQUENCE_AND_ITS_POLYNOMIAL?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSJ9fQ</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this study, we introduce a new recurrence relation of the perfect square sequence. We establish the relationship of perfect square sequence concerned with Fibonacci and Lucas sequences. We compute some important identities such as Catalan, Cassini, and special summation formula for this sequence. We associate the perfect square sequence with Lucas sequence and we call it the perfect square Lucas sequence. In addition, the Binet formula, generating function and summation formula of this sequence is obtained, as well as some properties are satisfied. Furthermore, we present the relationship of perfect square Lucas sequence with Fibonacci and Lucas sequences. Also, we obtain the relationship of perfect square Lucas sequence with perfect square sequence and we present matrix representation of this sequence. Besides, we described polynomials of perfect square and perfect square Lucas sequences. We get Binet formulas, generating functions, and Simpson formula for these polynomials. Eventually, satisfied some intriguing relations between these two polynomials, as well as we give the matrix representation of them.]]></description>
<dc:subject>mathematics Fibonacci number-theory matrices to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:cb725c391fc9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Fibonacci"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://users.mccme.ru/smirnoff/papers/friezes-eng.pdf">
    <title>FRIEZES AND CONTINUED FRACTIONS [PDF]</title>
    <dc:date>2025-06-25T19:22:27+00:00</dc:date>
    <link>https://users.mccme.ru/smirnoff/papers/friezes-eng.pdf</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Abstract. Notes from a mini-course given at the 19th Summer School “Modern Mathematics”, Dubna, July 18–29, 2019.]]></description>
<dc:subject>mathematical-recreations mathematics John-Conway combinatorics rather-interesting to-understand number-theory enumeration</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:561a22e0c563/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:John-Conway"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2303.13253">
    <title>[2303.13253] What is a degree of freedom? Configuration spaces and their topology</title>
    <dc:date>2024-09-28T15:37:42+00:00</dc:date>
    <link>https://arxiv.org/abs/2303.13253</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Understanding degrees of freedom in classical mechanics is fundamental to characterizing physical systems. Counting them is usually easy, especially if we can assign them a clear meaning. However, the precise definition of a degree of freedom is not usually presented in first-year physics courses since it requires mathematical knowledge only learned in more advanced courses. In this paper, we use a pedagogical approach motivated by simple but non-trivial mechanical examples to define degrees of freedom and configuration spaces. We highlight the role that topology plays in understanding these ideas.
]]></description>
<dc:subject>define-your-terms mathematics philosophy-of-science explanation physics statistics to-write-about rather-interesting topology dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:446c6a5e7624/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:define-your-terms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://aperiodical.com/2022/03/john-conway-and-his-fruitful-fractions/">
    <title>John Conway and his fruitful fractions | The Aperiodical</title>
    <dc:date>2024-09-09T15:32:16+00:00</dc:date>
    <link>https://aperiodical.com/2022/03/john-conway-and-his-fruitful-fractions/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The first time I encountered this set of fractions was in the wonderful book, The Book of Numbers, by Conway and Guy. I was so intrigued as to how Conway came up with his idea, I emailed him to ask. I was delighted to receive an outline of an explanation and even a second set of fractions, neither of which I can now find – it was 1996 and pre-cloud storage! But no worries… Conway explains everything in this lecture, which also demonstrates his passion for mathematics and his ability to express his ideas in a relaxed and humorous way, even when he searches for an error in his proof on 26 minutes. The lecture also includes an introduction to Conway’s computer language, FRACTRAN, which includes the statement:

]]></description>
<dc:subject>mathematics number-theory primes innovation rather-interesting to-write-about to-simulate consider:optimization consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a158d0064e38/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:primes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:innovation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf">
    <title>[untitled]</title>
    <dc:date>2024-07-23T12:31:38+00:00</dc:date>
    <link>https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This collection of open problems has been circulated since 2018 when, encouraged by Sean Prendiville, I prepared a draft for the Arithmetic Ramsey Theory workshop in Manchester. That document was itself an expanded version of a manuscript I circulated among students starting in 2013.
The choice of problems is personal. Many are connected with topics I have worked on, but by no means all. For the most part I have avoided particularly notorious open problems (the Riemann Hypothesis, twin prime conjecture, and so on), although many of the problems are very well-known to people in the relevant field. I would like this document to stimulate further research, rather than be simply a compendium of things we do not know. For that reason I have also tried to steer clear of problems which are ‘obviously hopeless’, though progress on a number of entries does currently look a rather distant prospect.
To keep the bibliography to a reasonable length I have not given a full history
for each problem, but hopefully there is sufficient information for anyone interested
in a problem to follow up in more detail.]]></description>
<dc:subject>open-problems mathematical-recreations mathematics to-write-about consider:benchmarks number-theory combinatorics review collection</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6079ad3d87f0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:benchmarks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:collection"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://mathenchant.wordpress.com/2023/10/17/marvelous-arithmetics-of-distance/">
    <title>Marvelous Arithmetics of Distance |</title>
    <dc:date>2024-07-08T12:41:52+00:00</dc:date>
    <link>https://mathenchant.wordpress.com/2023/10/17/marvelous-arithmetics-of-distance/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Near the start of this article, I quoted Paul Garrett’s warning against ignoring the p-adics. But perhaps I should have mentioned the peril that awaits those who, far from ignoring p-adic numbers, become seduced by them. Mathematician Peter Scholze, whose work on p-adic numbers had much to do with his winning a Fields Medal, writes: “Now I find real numbers much, much more confusing than p-adic numbers. I’ve gotten so used to them that now real numbers feel very strange.”

]]></description>
<dc:subject>mathematical-recreations mathematics number-theory p-adic-numbers to-understand to-write-about consider:continued-fractions</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6ccc9d1f58bc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:p-adic-numbers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:continued-fractions"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2307.04704">
    <title>[2307.04704] Argumentation in Mathematical Practice</title>
    <dc:date>2023-08-22T13:25:21+00:00</dc:date>
    <link>https://arxiv.org/abs/2307.04704</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of mathematical reasoning closely resemble patterns of reasoning in nonmathematical domains. Hence the tools developed to understand informal reasoning, collectively known as argumentation theory, are also applicable to much mathematical argumentation. This chapter investigates some of the details of that application. Consideration is given to the many contrasting meanings of the word ``argument''; to some of the specific argumentation-theoretic tools that have been applied to mathematics, notably Toulmin layouts and argumentation schemes; to some of the different ways that argumentation is implicated in mathematical practices; and to the social aspects of mathematical argumentation.
]]></description>
<dc:subject>argumentation mathematics social-norms philosophy-of-science rather-interesting logic cultural-norms</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b6feed7913d6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:argumentation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:social-norms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:logic"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cultural-norms"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2110.09511">
    <title>[2110.09511] Automated Generation of Triangle Geometry Theorems</title>
    <dc:date>2023-05-07T13:43:41+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.09511</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this article, we introduce an algorithm for automatic generation and categorization of triangle geometry theorems.
]]></description>
<dc:subject>code-generation mathematics plane-geometry search-algorithms rather-interesting representation formal-languages</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d576ecb55060/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:code-generation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:search-algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.mathvalues.org/masterblog/my-mathematical-journey-the-stamp-problem">
    <title>MAA Blog: The Stamp Problem — MATH VALUES</title>
    <dc:date>2022-05-28T11:43:56+00:00</dc:date>
    <link>https://www.mathvalues.org/masterblog/my-mathematical-journey-the-stamp-problem</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The term intellectual need was introduced by Guershon Harel. It refers to a problematic situation that necessitates the development of a particular piece of mathematics. Harel illustrates this with reference to A Radical Approach to Real Analysis in which I draw on Fourier’s solution of Laplace’s equation and the problems it created for the then current understandings of infinite series. The intellectual need for a better comprehension of infinite series would give rise to the real analysis of the 19th century. The emphasis is on the necessity of the piece of mathematics. If you really want students to be engaged, you have to pique their natural curiosity.

I have never been satisfied with the introduction of modular arithmetic as “clock arithmetic”: what happens when you add nine hours to 7:00 pm? The problem is just not sufficiently engaging. In contrast, students find the stamp problem intriguing and challenging. By the time they are done they comprehend how modular arithmetic works 

]]></description>
<dc:subject>pedagogy intellectual-need rather-interesting autobiography mathematical-recreations mathematics education</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ec3f7e36380a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pedagogy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:intellectual-need"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:autobiography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:education"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://publications.mfo.de/handle/mfo/1415">
    <title>Algebra, matrices, and computers</title>
    <dc:date>2021-10-07T10:22:23+00:00</dc:date>
    <link>https://publications.mfo.de/handle/mfo/1415</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[What part does algebra play in representing the real
 world abstractly? How can algebra be used to solve
 hard mathematical problems with the aid of modern
 computing technology? We provide answers to these
 questions that rely on the theory of matrix groups
 and new methods for handling matrix groups in a
 computer.
]]></description>
<dc:subject>matrices mathematics rather-interesting review mathematical-programming group-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:de7584db8d80/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://publications.mfo.de/handle/mfo/1413">
    <title>Diophantine equations and why they are hard</title>
    <dc:date>2021-09-12T12:50:46+00:00</dc:date>
    <link>https://publications.mfo.de/handle/mfo/1413</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Diophantine equations are polynomial equations whose
 solutions are required to be integer numbers. They
 have captured the attention of mathematicians during
 millennia and are at the center of much of contemporary
 research. Some Diophantine equations are easy,
 while some others are truly difficult. After some time
 spent with these equations, it might seem that no
 matter what powerful methods we learn or develop,
 there will always be a Diophantine equation immune
 to them, which requires a new trick, a better idea, or
 a refined technique. In this snapshot we explain why.
]]></description>
<dc:subject>mathematics Diophantine-equations constraint-satisfaction explanation computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b0b1ee7fbd9b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Diophantine-equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://whystartat.xyz/wiki/Main_Page">
    <title>Why start at x, y, z</title>
    <dc:date>2021-07-31T11:06:31+00:00</dc:date>
    <link>https://whystartat.xyz/wiki/Main_Page</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This is a collection of ambiguous, inconsistent, or just unpleasant conventions in mathematical notation, started by Christian Lawson-Perfect.

For each bit of notation, I want to collect examples, alternatives, and references to discussions about them.

Like all language, mathematical notation is just something we make up to help express our ideas, and opinions, abuses of notation, lapses in memory and convenience all work against consistency and clarity.

The site's name is a reference to the question about why we start naming variables at 𝑥. The logo is a drawing of the stacked fraction 
 
Ξ
¯
Ξ
.

]]></description>
<dc:subject>mathematics notation cultural-norms community typography clarity-of-communication I-remember-Freddie-Way veteran-of-the-infix-wars</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e9c60f4960ee/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:notation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cultural-norms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:community"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:typography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:clarity-of-communication"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:I-remember-Freddie-Way"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:veteran-of-the-infix-wars"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.openproblemgarden.org/">
    <title>Home | Open Problem Garden</title>
    <dc:date>2021-06-25T11:51:06+00:00</dc:date>
    <link>http://www.openproblemgarden.org/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Welcome to the Open Problem Garden, a collection of unsolved problems in mathematics. Here you may:

Read descriptions of open problems.
Post comments on them.
Create and edit open problems pages (please contact us and we will set you up an account. Unfortunately, the automatic process is too prone to spammers at this moment.)
]]></description>
<dc:subject>open-questions unsolved-problems mathematics to-write-about consider:impossible-benchmarks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:620344db406c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unsolved-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:impossible-benchmarks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://johncarlosbaez.wordpress.com/2020/10/10/decimal-digits-of-1-%cf%80%c2%b2/">
    <title>Decimal Digits of 1/π² | Azimuth</title>
    <dc:date>2021-05-28T16:58:11+00:00</dc:date>
    <link>https://johncarlosbaez.wordpress.com/2020/10/10/decimal-digits-of-1-%cf%80%c2%b2/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This formula may let you compute a decimal digit of  without computing all the previous digits:

]]></description>
<dc:subject>mathematics number-theory rather-interesting novel-forms to-write-about consider:looking-to-see consider:training-data</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:45d9292e7c26/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:novel-forms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:training-data"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://blog.mrmeyer.com/2019/real-world-math-is-everywhere-or-its-nowhere/">
    <title>“Real-World” Math Is Everywhere or It’s Nowhere – dy/dan</title>
    <dc:date>2021-05-23T11:38:34+00:00</dc:date>
    <link>https://blog.mrmeyer.com/2019/real-world-math-is-everywhere-or-its-nowhere/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It makes the mathematical modeler’s job harder. The tasks mathematical modelers enjoy are not categorically different from Polygraph. The early ideas that teachers need to elicit, provoke, and develop in those tasks differ from Polygraph only in their degree of contextual complexity. Instead of telling teachers, “Here is how this task is similar to everything else you’ve done this year,” and benefiting from pedagogical coherence, they tell teachers, “This task is categorically different from everything else you’ve done this year and why aren’t you doing more of them?”

I’m trying to convince mathematical modelers that their process is the same one by which anyone learns anything, that they should spend much less time patrolling borders that don’t exist, and instead apply their processes to every area of the world, every last bit of which is “real.”

]]></description>
<dc:subject>philosophy-of-science mathematics pedagogy philosophy rather-interesting good-point models define-your-terms</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f271b56f664b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pedagogy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:good-point"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:define-your-terms"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2103.09623">
    <title>[2103.09623] Euclid After Computer Proof-checking</title>
    <dc:date>2021-05-07T14:09:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2103.09623</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Euclid pioneered the concept of a mathematical theory developed from axioms by a series of justified proof steps. From the outset there were critics and improvers. In this century the use of computers to check proofs for correctness sets a new standard of rigor. How does Euclid stand up under such an examination? And what does the exercise have to teach us about geometry, mathematical foundations, and the relation of logic to truth?
]]></description>
<dc:subject>mathematics logic-programming rather-interesting proof proof-systems looking-to-see symbolic-processing formal-languages</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6fd3c348ddd5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:logic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://imaginary.org/texts?page=1">
    <title>Texts | IMAGINARY</title>
    <dc:date>2020-11-13T23:41:13+00:00</dc:date>
    <link>https://imaginary.org/texts?page=1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Here you can find a variety of mathematical texts on many different topics. One section is related to the “snapshots of modern mathematics from Oberwolfach”, the other section offers general background material connected to our exhibits and projects. We hope you enjoy your read!

]]></description>
<dc:subject>mathematical-recreations mathematics rather-interesting archive to-read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f3b14298a7aa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:archive"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://dl.acm.org/doi/abs/10.1145/3385412.3386037">
    <title>Towards an API for the real numbers | Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation</title>
    <dc:date>2020-11-01T12:09:49+00:00</dc:date>
    <link>https://dl.acm.org/doi/abs/10.1145/3385412.3386037</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The real numbers are pervasive, both in daily life, and in mathematics. Students spend much time studying their properties. Yet computers and programming languages generally provide only an approximation geared towards performance, at the expense of many of the nice properties we were taught in high school.
Although this is entirely appropriate for many applications, particularly those that are sensitive to arithmetic performance in the usual sense, we argue that there are others where it is a poor choice. If arithmetic computations and result are directly exposed to human users who are not floating point experts, floating point approximations tend to be viewed as bugs. For applications such as calculators, spreadsheets, and various verification tasks, the cost of precision sacrifices is high, and the performance benefit is often not critical. We argue that previous attempts to provide accurate and understandable results for such applications using the recursive reals were great steps in the right direction, but they do not suffice. Comparing recursive reals diverges if they are equal. In many cases, comparison of numbers, including equal ones, is both important, particularly in simple cases, and intractable in the general case.
We propose an API for a real number type that explicitly provides decidable equality in the easy common cases, in which it is often unnatural not to. We describe a surprisingly compact and simple implementation in detail. The approach relies heavily on classical number theory results. We demonstrate the utility of such a facility in two applications: testing floating point functions, and to implement arithmetic in Google's Android calculator application.]]></description>
<dc:subject>computer-science representation number-theory rather-interesting API to-understand to-write-about mathematics philosophy-of-engineering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e018a87cf481/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computer-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:API"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-engineering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://mathlesstraveled.com/2019/12/23/a-simple-proof-of-the-quadratic-formula/">
    <title>A simple proof of the quadratic formula | The Math Less Traveled</title>
    <dc:date>2020-09-19T12:36:26+00:00</dc:date>
    <link>https://mathlesstraveled.com/2019/12/23/a-simple-proof-of-the-quadratic-formula/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[My colleague Gabe Ferrer recently brought to my attention a remarkable new paper by Po-Shen Loh, A Simple Proof of the Quadratic Formula. This paper is remarkable for several reasons: first of all, it’s remarkable that anyone could discover anything new about the quadratic formula; it’s also remarkable for a research mathematician to publish something about elementary mathematics. (But Po-Shen Loh is not your average research mathematician either; he does lots of really cool work making mathematics more accessible for all kinds of learners.) I’m going to explain the basic idea but I highly recommend actually reading the paper, which not only explains the ideas but also does a great job putting everything in proper historical context. Loh has also made a whole web page dedicated to explaining the ideas, with a video, worked examples, etc.; it’s definitely worth taking a look!

]]></description>
<dc:subject>algebra mathematics proof simple-things-revisited to-reread consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4097acec5c46/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simple-things-revisited"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-reread"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts">
    <title>soft question - Awfully sophisticated proof for simple facts - MathOverflow</title>
    <dc:date>2020-09-18T21:22:21+00:00</dc:date>
    <link>https://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It is sometimes the case that one can produce proofs of simple facts that are of disproportionate sophistication which, however, do not involve any circularity. For example, (I think) I gave an example in this M.SE answer (the title of this question comes from Pete's comment there) If I recall correctly, another example is proving Wedderburn's theorem on the commutativity of finite division rings by computing the Brauer group of their centers.

Do you know of other examples of nuking mosquitos like this?
]]></description>
<dc:subject>mathematics amusing math-jokes proof rather-interesting pragmatics to-write-about consider:genetic-programming consider:the-genie-problem</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:519c835717a6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:amusing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:math-jokes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pragmatics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:the-genie-problem"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://twitter.com/AndresECaicedo1/status/1302697810446483456">
    <title>Andrés E. Caicedo on Twitter: &quot;Is √17 irrational? A thread I learned recently of a cute, apparently open, problem that I think is interesting and merits some mention. 1/&quot; / Twitter</title>
    <dc:date>2020-09-09T23:50:07+00:00</dc:date>
    <link>https://twitter.com/AndresECaicedo1/status/1302697810446483456</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[thread on an interesting open question]]></description>
<dc:subject>mathematics history-of-mathematics proof looking-to-see rather-interesting to-write-about to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:bbce5651b731/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history-of-mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://divisbyzero.com/2019/11/12/tales-of-impossibility-now-released/">
    <title>Tales of Impossibility: Now Published! – David Richeson: Division by Zero</title>
    <dc:date>2020-05-05T22:43:53+00:00</dc:date>
    <link>https://divisbyzero.com/2019/11/12/tales-of-impossibility-now-released/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[I’m very excited to announce that my new book, Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (Princeton University Press, 2019), is now available! (OK. It was published about a month ago, but I am just now getting around to blogging about it.)
]]></description>
<dc:subject>mathematical-recreations mathematics history to-read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f68a38545a70/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.math3ma.com/blog/topology-book">
    <title>Topology: A Categorical Approach</title>
    <dc:date>2020-04-13T11:20:07+00:00</dc:date>
    <link>https://www.math3ma.com/blog/topology-book</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[I've been collaborating on an exciting project for quite some time now, and today I'm happy to share it with you. There is a new topology book on the market! Topology: A Categorical Approach is a graduate-level textbook that presents basic topology from the modern perspective of category theory. Coauthored with Tyler Bryson and John Terilla, Topology is published through MIT Press and will be released on August 18, 2020. But you can pre-order on Amazon now! 

]]></description>
<dc:subject>books topology to-read category-theory from-library via:several mathematics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a1448aaebe44/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:books"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:category-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:from-library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:several"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.05923">
    <title>[1809.05923] What is Applied Category Theory?</title>
    <dc:date>2020-03-19T15:52:13+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.05923</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and compositionality), two constructions (monoidal categories and decorated cospans) and two examples (chemical reaction networks and natural language processing) within the field.
]]></description>
<dc:subject>category-theory mathematics to-understand surveys formalization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c4bf5f6e07f7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:category-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:surveys"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formalization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1902.07404">
    <title>[1902.07404] The Provability of Consistency</title>
    <dc:date>2020-03-08T21:27:16+00:00</dc:date>
    <link>https://arxiv.org/abs/1902.07404</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Hilbert's program of establishing consistency of theories like Peano arithmetic PA using only finitary tools has long been considered impossible. The standard reference here is Goedel's Second Incompleteness Theorem by which a theory T, if consistent, cannot prove the arithmetical formula ConT, 'for all x, x is not a code of a proof of a contradiction in T.' We argue that such arithmetization of consistency distorts the problem. ConT is stronger than the original notion of consistency, hence Goedel's theorem does not yield impossibility of proving consistency by finitary tools. We consider consistency in its standard form 'no sequence of formulas S is a derivation of a contradiction.' Using partial truth definitions, for each derivation S in PA we construct a finitary proof that S does not contain 0=1. This establishes consistency for PA by finitary means and vindicates, to some extent, Hilbert's consistency program. This also suggests that in the arithmetical form, consistency, similar to induction, reflection, truth, should be represented by a scheme rather than by a single formula.
]]></description>
<dc:subject>formal-logic mathematics representation proof philosophy rather-interesting the-mangle-in-practice</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0655a0f645cc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-logic"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:the-mangle-in-practice"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://mathenchant.wordpress.com/2020/01/24/what-proof-is-best/">
    <title>What Proof Is Best? |</title>
    <dc:date>2020-02-18T22:37:51+00:00</dc:date>
    <link>https://mathenchant.wordpress.com/2020/01/24/what-proof-is-best/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A great illustration of this “Let a hundred proofs bloom” point of view is provided by an article by Stan Wagon called “Fourteen Proofs of a Result About Tiling a Rectangle”. Here’s the result his title refers to (a puzzle posed and solved by Nicolaas de Bruijn): Whenever a rectangle can be cut up into smaller rectangles each of which has at least one integer side, then the big rectangle has at least one integer side too. (Here “at least one integer side” is tantamount to “at least two integer sides”, since the opposite sides of a rectangle always have the same length.)

]]></description>
<dc:subject>mathematics philosophy solution-spaces diversity proof to-write-about to-simulate consider:surprise</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:080300918eb5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:solution-spaces"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diversity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:surprise"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.quantamagazine.org/the-numbers-and-geometry-behind-a-math-coloring-puzzle-20180618/">
    <title>The Numbers and Geometry Behind a Math Coloring Puzzle | Quanta Magazine</title>
    <dc:date>2020-01-10T16:16:43+00:00</dc:date>
    <link>https://www.quantamagazine.org/the-numbers-and-geometry-behind-a-math-coloring-puzzle-20180618/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Just as the Moser spindle creates intricate interdependencies among its seven points that cannot be satisfied using only three colors, the 1,581-point construction by de Grey shown above cannot be colored using only four colors without a pair of points 1 unit apart being colored the same. But unlike with the Moser spindle, it’s not easy to see this just by looking — in fact, it takes a computer search to verify that four colors really aren’t enough. Thanks to de Grey’s discovery, we now know that the chromatic number of the plane is at least 5. Combined with our previous knowledge, that means we know that the chromatic number of the plane is either 5, 6 or 7. We just don’t know which!

]]></description>
<dc:subject>mathematics tiling open-questions rather-interesting matchstick-graphs constraint-satisfaction to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e4020fdc672d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matchstick-graphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://mathenchant.wordpress.com/2019/02/16/who-mourns-the-tenth-heegner-number/">
    <title>Who Mourns the Tenth Heegner Number? |</title>
    <dc:date>2019-07-25T11:11:17+00:00</dc:date>
    <link>https://mathenchant.wordpress.com/2019/02/16/who-mourns-the-tenth-heegner-number/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[There’s an episode1 of a science-fiction television series in which space travelers land on a planet peopled by their own descendants. The descendants explain that the travelers will try to leave the planet and fail, accidentally stranding themselves several centuries in the past. Armed with this knowledge, the travelers can try to thwart their destiny; but are they willing to try if their successful escape would doom their descendants, leaving the travelers with the memory of descendants who, thanks to their escape, never were?

This is science fiction, but it’s also math. More specifically, it’s proof by contradiction. As Ben Blum-Smith recently wrote on Twitter: “Sufficiently long contradiction proofs *make me sad*! When you stick with the mathematical characters long enough, you start to get attached, and then they disappear, never to have existed in the first place.”

]]></description>
<dc:subject>mathematical-recreations mathematics number-theory the-mangle-in-practice exploration history-of-science rather-interesting to-write-about see-if-GP-makes-these-mistakes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:56e48772d536/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:the-mangle-in-practice"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:exploration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:see-if-GP-makes-these-mistakes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arminstraub.com/math/what-is-column">
    <title>arminstraub.com - The &quot;What Is...?&quot; column</title>
    <dc:date>2019-06-11T10:17:29+00:00</dc:date>
    <link>http://arminstraub.com/math/what-is-column</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[I very much enjoy reading the "What Is...?" column in the Notices of the AMS. Unfortunately, there seemed to be no index to this column. I have therefore created this one in the hope that it might be helpful to others as well.

]]></description>
<dc:subject>mathematics explanation mathematical-recreations to-read via:arthegall</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:34d980a540a0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:arthegall"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.08483">
    <title>[1809.08483] Symplectic Matroids, Circuits, and Signed Graphs</title>
    <dc:date>2019-04-24T14:00:16+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.08483</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[One generalization of ordinary matroids is symplectic matroids. While symplectic matroids were initially defined by their collections of bases, there has been no cryptomorphic definition of symplectic matroids in terms of circuits. We give a definition of symplectic matroids by collections of circuits. As an application, we construct a class of examples of symplectic matroids from graphs in terms of circuits.
]]></description>
<dc:subject>matroids to-understand mathematics graph-theory hypergraphs representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d43f96e3d785/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matroids"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://math-frolic.blogspot.com/2018/04/math-and-understanding.html">
    <title>Math-Frolic!: Math and Understanding</title>
    <dc:date>2019-04-24T13:44:54+00:00</dc:date>
    <link>https://math-frolic.blogspot.com/2018/04/math-and-understanding.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Physicists often remark that no one actually understands quantum mechanics (and those who say they do are lying), but they use it because it consistently works.
Similarly, polymath John von Neumann once famously said that , “…in mathematics you don’t understand things, you just get used to them.”
And in a similar vein David Wells quotes applied mathematician, Oliver Heaviside, thusly:

“The prevalent idea of mathematical works is that you must understand the reason why first, before you proceed to practise.  That is fudge and fiddlesticks. I know mathematical processes that I have used with success for a very long time, of which neither I nor anyone else understands the scholastic logic. I have grown into them, and so understood them that way.”

It seems to me that a lot of the emphasis these days from professional mathematicians, as well as in Common Core’s approach, is for students to develop a much deeper understanding of mathematical logic and connections first (and foremost), and for rote processes to follow thereafter. A change in perspective or outlook perhaps??? (or maybe math education has simply always been a mixture of both, in a sort of chicken-and-egg fashion).
]]></description>
<dc:subject>mathematics mathematical-recreations pedagogy the-mangle-in-practice learning-by-making-do</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c219e0997eff/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pedagogy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:the-mangle-in-practice"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:learning-by-making-do"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.redblobgames.com/articles/curved-paths/">
    <title>Curved Paths</title>
    <dc:date>2019-03-24T11:50:36+00:00</dc:date>
    <link>https://www.redblobgames.com/articles/curved-paths/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Piecewise circular curves are used in manufacturing, robotics, and highway engineering, but I haven’t found many online references for them. As with circular arcs, piecewise circular curves can handle offsets, distances, and interpolation. Here are some papers I used to learn about circular arcs, biarcs, and piecewise circular curves:

]]></description>
<dc:subject>game-design mathematics constraint-satisfaction engineering-design rather-interesting aesthetics the-mangle-in-practice representation plane-geometry parametrization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1d9267b8429a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:game-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aesthetics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:the-mangle-in-practice"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:parametrization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://samjshah.com/2018/02/09/alone-with-starry-night/">
    <title>Alone with “Starry Night” | Continuous Everywhere but Differentiable Nowhere</title>
    <dc:date>2019-03-12T11:01:20+00:00</dc:date>
    <link>https://samjshah.com/2018/02/09/alone-with-starry-night/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[So I wasn’t actually alone with Van Gogh’s Starry Night. But I went to MoMA this morning and got to tour the museum with other math teachers before the museum opened. Our sherpa? George Hart, mathematical artist. A few months ago, I got an email from two different teacher friends letting me know about this opportunity to take a master class on Geometric Sculpture put together by the Academy for Teachers. What an opportunity indeed!

I show up at 8:30 am and me and a gaggle of math teachers (a gaggle is eighteen, right?) are raring to go. We have fancy namecards and everything. (Note to self: at the book club I’m hosting in a bit over a month, create fancy namecards.)

]]></description>
<dc:subject>art mathematical-recreations mathematics rather-interesting creativity pedagogy</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6973b9acfded/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:art"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:creativity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pedagogy"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://library.msri.org/books/Book29/files/unsolved.pdf">
    <title>[PDF] Unsolved problems in combinatorial games</title>
    <dc:date>2019-02-26T13:52:30+00:00</dc:date>
    <link>http://library.msri.org/books/Book29/files/unsolved.pdf</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Abstract. This periodically updated reference resource is intended to put eager researchers on the path to fame and (perhaps) fortune.]]></description>
<dc:subject>game-theory open-questions mathematical-recreations mathematics nudge-targets to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0347066f71ab/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:game-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://tonysmaths.blogspot.com/2018/05/mathematical-discoveries.html">
    <title>Tony's Maths Blog: Mathematical discoveries</title>
    <dc:date>2019-02-24T12:01:25+00:00</dc:date>
    <link>http://tonysmaths.blogspot.com/2018/05/mathematical-discoveries.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[I think these stories shed some light on mathematical creativity.  It needs hard work, of course, but it also needs flexibility.  Cocks (by his modest account) had the advantage over his colleagues that his mind wasn't conditioned by an unproductive idea.  Rivest's solution came after a break from thinking about it.  Of course, there are many other examples - Poincaré's inspiration as he was getting on a bus is the standard one - but it is always interesting to hear how great mathematical discoveries came about, and to hear this story from Cocks himself was a wonderful privilege.
]]></description>
<dc:subject>mathematics the-mangle-in-practice discovery to-write-about the-case-for-GP exploration-and-exploitation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:35fa269b7823/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:the-mangle-in-practice"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:the-case-for-GP"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:exploration-and-exploitation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/9404236">
    <title>[math/9404236] On proof and progress in mathematics</title>
    <dc:date>2019-02-07T11:36:51+00:00</dc:date>
    <link>https://arxiv.org/abs/math/9404236</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.
]]></description>
<dc:subject>philosophy-of-science mathematics models-and-modes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:235a6a6a241c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models-and-modes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jdh.hamkins.org/alan-turing-on-computable-numbers/">
    <title>Alan Turing, On computable numbers | Joel David Hamkins</title>
    <dc:date>2018-12-09T12:54:15+00:00</dc:date>
    <link>http://jdh.hamkins.org/alan-turing-on-computable-numbers/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[What I was extremely surprised to find, however, and what I want to tell you about today, is that despite the title of the article, Turing adopts an incorrect approach to the theory of computable numbers. His central definition is what is now usually regarded as a mistaken way to proceed with this concept.

Let me explain. Turing defines that a computable real number is one whose decimal (or binary) expansion can be enumerated by a finite procedure, by what we now call a Turing machine. You can see this in the very first sentence of his paper, and he elaborates on and confirms this definition in detail later on in the paper.

]]></description>
<dc:subject>computability mathematics number-theory algorithms rather-interesting history-of-science representation to-write-about ReQ</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6fb3a8749162/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ReQ"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1610.02247">
    <title>[1610.02247] Logic as a distributive law</title>
    <dc:date>2018-11-27T12:40:16+00:00</dc:date>
    <link>https://arxiv.org/abs/1610.02247</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc: Catv→ Cat for the free calculus on a category of terms and rewrites and a 2-monad BoolAlg for the free Boolean algebra on a category, we get a 2-monad Form = BoolAlg + Calc for the free category of formulae and proofs. We also get the 2-monad BoolAlg ∘ Calc for subsets of terms. The interpretation of formulae is a natural transformation $\interp{-}$: Form ⇒ BoolAlg ∘ Calc defined by the units and multiplications of the monads and a distributive law transformation δ: Calc ∘ BoolAlg ⇒ BoolAlg ∘ Calc. This interpretation is consistent both with the Curry-Howard isomorphism and with realizability. We give an implementation of the "possibly" modal operator parametrized by a two-hole term context and show that, surprisingly, the arrow type constructor in the λ-calculus is a specific case. We also exhibit nontrivial formulae encoding confinement and liveness properties for a reflective higher-order variant of the π-calculus.
]]></description>
<dc:subject>representation higher-order mathematics category-theory to-understand π-calculus ReQ</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:685037dca425/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:higher-order"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:category-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:π-calculus"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ReQ"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/0408099">
    <title>[math/0408099] Tropical Mathematics</title>
    <dc:date>2018-10-16T10:35:57+00:00</dc:date>
    <link>https://arxiv.org/abs/math/0408099</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the ``tropical approach'' in mathematics, which has gotten a lot of attention recently in combinatorics, algebraic geometry and related fields. It offers an an elementary introduction to this subject, touching upon Arithmetic, Polynomials, Curves, Phylogenetics and Linear Spaces. Each section ends with a suggestion for further research. The bibliography contains numerousreferences for further reading in this field.]]></description>
<dc:subject>group-theory mathematics representation combinatorics rather-interesting to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7f81a1c52380/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/">
    <title>Patterns That Eventually Fail | Azimuth</title>
    <dc:date>2018-10-07T18:00:10+00:00</dc:date>
    <link>https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Sometimes patterns can lead you astray.]]></description>
<dc:subject>mathematical-recreations mathematics patterns rather-interesting to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ae5cca121c1c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:patterns"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1808.02841">
    <title>[1808.02841] On divergent Series</title>
    <dc:date>2018-10-07T16:03:13+00:00</dc:date>
    <link>https://arxiv.org/abs/1808.02841</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This is the translation of Leonhard Euler's paper "De Seriebus divergentibus" written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example 1!−2!+3!−etc. and uses different methods to sum it. He finds a value of about 0.59....
]]></description>
<dc:subject>mathematics history translation series to-write-about rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9bef961b0d14/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:translation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1808.07006">
    <title>[1808.07006] Observations on continued fractions</title>
    <dc:date>2018-10-07T16:01:44+00:00</dc:date>
    <link>https://arxiv.org/abs/1808.07006</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This is a translation of Euler's Latin paper "De fractionibus continuis observationes" into English. In this paper Euler describes his theory of continued fractions. He teaches, how to transform series into continued fractions, solves the Riccati-Differential equation by means of continued fractions and finds many other interesting formulas and results (e.g, the continued fraction for the quotient of two hypergeometric series usually attributed to Gau{\ss})
]]></description>
<dc:subject>continued-fractions translation mathematics history rather-interesting to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f87b0626bf5c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:translation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1810.00173">
    <title>[1810.00173] On solids whose (entire) surface can be unfolded onto a plane</title>
    <dc:date>2018-10-07T16:00:25+00:00</dc:date>
    <link>https://arxiv.org/abs/1810.00173</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This is the English translation of Leonhard Euler's Latin paper "De solidis quorum superficiem in planum explicare licet". Euler explains several methods to obtain equations for developable surfaces. Therefore, this paper might be interesting for anyone studying the history of Differential Geometry.
]]></description>
<dc:subject>geometry history mathematics translation rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:053eb3b6178d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:history"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:translation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://graphics.berkeley.edu/papers/Karpenko-EVD-2010-00/index.html">
    <title>Exploded View Diagrams of Mathematical Surfaces - U.C. Berkeley Computer Graphics Research</title>
    <dc:date>2018-08-27T12:08:12+00:00</dc:date>
    <link>http://graphics.berkeley.edu/papers/Karpenko-EVD-2010-00/index.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present a technique for visualizing complicated mathematical surfaces that is inspired by hand-designed topological illustrations. Our approach generates exploded views that expose the internal structure of such a surface by partitioning it into parallel slices, which are separated from each other along a single linear explosion axis. Our contributions include a set of simple, prescriptive design rules for choosing an explosion axis and placing cutting planes, as well as automatic algorithms for applying these rules. First we analyze the input shape to select the explosion axis based on the detected rotational and reflective symmetries of the input model. We then partition the shape into slices that are designed to help viewers better understand how the shape of the surface and its cross-sections vary along the explosion axis. Our algorithms work directly on triangle meshes, and do not depend on any specific parameterization of the surface. We generate exploded views for a variety of mathematical surfaces using our system.

]]></description>
<dc:subject>visualization mathematics topology rather-interesting algorithms to-do</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1f32ed09dbc4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-do"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://twitter.com/jhnhw/status/1031829726757900288">
    <title>John Williamson on Twitter: &quot;First 1e6 integers, represented as binary vectors indicating their prime factors, and laid out using the sparse matrix support in @leland_mcinnes's UMAP dimensionality reduction algorithm. This is from a 1000000x78628 (!) bina</title>
    <dc:date>2018-08-22T12:31:54+00:00</dc:date>
    <link>https://twitter.com/jhnhw/status/1031829726757900288</link>
    <dc:creator>Vaguery</dc:creator><dc:subject>mathematics number-theory visualization rather-interesting graph-theory graph-layout dimension-reduction to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0eb50a4ea912/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-layout"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dimension-reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1808.03172">
    <title>[1808.03172] An Invitation to Noncommutative Algebra</title>
    <dc:date>2018-08-14T01:15:15+00:00</dc:date>
    <link>https://arxiv.org/abs/1808.03172</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This is a brief introduction to the world of Noncommutative Algebra aimed for advanced undergraduate and beginning graduate students.
]]></description>
<dc:subject>mathematics to-read to-understand group-theory category-theory introduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c4fd73c58673/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:category-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:introduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.theoremoftheday.org/Theorems.html#209">
    <title>Theorem of the Day</title>
    <dc:date>2018-07-29T09:37:40+00:00</dc:date>
    <link>https://www.theoremoftheday.org/Theorems.html#209</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The list is presented here in reverse chronological order, so that new additions will appear at the top. This is not the order in which the theorem of the day is picked which is more designed to mix up the different areas of mathematics and the level of abstractness or technicality involved. The way that the list of theorems is indexed is described here.

]]></description>
<dc:subject>mathematics proof lists rather-interesting nudge-targets consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:395609febeae/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:lists"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1803.06824">
    <title>[1803.06824] Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?</title>
    <dc:date>2018-06-14T14:19:31+00:00</dc:date>
    <link>https://arxiv.org/abs/1803.06824</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. Since a finite volume of space can't contain more than a finite amount of information, I argue that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is "random numbers", as their series of bits are truly random. I propose an alternative classical mechanics, which is empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. I argue that it is more economical and natural to accept non-determinism with potentialities as a real mode of existence, both for classical and quantum physics.
]]></description>
<dc:subject>philosophy-of-science mathematics representation rather-interesting to-understand information-theory huh</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:02e8829cfcd9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy-of-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:huh"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://en.wikipedia.org/wiki/Generating_function">
    <title>Generating function - Wikipedia</title>
    <dc:date>2018-04-27T00:35:33+00:00</dc:date>
    <link>https://en.wikipedia.org/wiki/Generating_function</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series. The sum of this infinite series is the generating function. Unlike an ordinary series, this formal series is allowed to diverge, meaning that the generating function is not always a true function and the "variable" is actually an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem.[1] One can generalize to formal series in more than one indeterminate, to encode information about arrays of numbers indexed by several natural numbers.
There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require indices to start at 1 rather than 0), but the ease with which they can be handled may differ considerably. The particular generating function, if any, that is most useful in a given context will depend upon the nature of the sequence and the details of the problem being addressed.
Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations defined for formal series. These expressions in terms of the indeterminate x may involve arithmetic operations, differentiation with respect to x and composition with (i.e., substitution into) other generating functions; since these operations are also defined for functions, the result looks like a function of x. Indeed, the closed form expression can often be interpreted as a function that can be evaluated at (sufficiently small) concrete values of x, and which has the formal series as its series expansion; this explains the designation "generating functions". However such interpretation is not required to be possible, because formal series are not required to give a convergent series when a nonzero numeric value is substituted for x. Also, not all expressions that are meaningful as functions of x are meaningful as expressions designating formal series; for example, negative and fractional powers of x are examples of functions that do not have a corresponding formal power series.
Generating functions are not functions in the formal sense of a mapping from a domain to a codomain. Generating functions are sometimes called generating series,[2] in that a series of terms can be said to be the generator of its sequence of term coefficients.
]]></description>
<dc:subject>mathematics via:arthegall to-understand rather-interesting to-write-about nudge-targets hmmmmmm</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a5f6252be6b1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:arthegall"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hmmmmmm"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://en.wikipedia.org/wiki/Homotopy_type_theory">
    <title>Homotopy type theory - Wikipedia</title>
    <dc:date>2018-04-27T00:16:00+00:00</dc:date>
    <link>https://en.wikipedia.org/wiki/Homotopy_type_theory</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In mathematical logic and computer science, homotopy type theory (HoTT /hɒt/) refers to various lines of development of intensional type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory applies.
This includes, among other lines of work, the construction of homotopical and higher-categorical models for such type theories; the use of type theory as a logic (or internal language) for abstract homotopy theory and higher category theory; the development of mathematics within a type-theoretic foundation (including both previously existing mathematics and new mathematics that homotopical types make possible); and the formalization of each of these in computer proof assistants.
There is a large overlap between the work referred to as homotopy type theory, and as the univalent foundations project. Although neither is precisely delineated, and the terms are sometimes used interchangeably, the choice of usage also sometimes corresponds to differences in viewpoint and emphasis.[1] As such, this article may not represent the views of all researchers in the fields equally.
]]></description>
<dc:subject>mathematics recommended-by-barista to-understand abstruse possibly-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2e3944ea061d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:recommended-by-barista"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:abstruse"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:possibly-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.smithsonianmag.com/history/the-woman-who-bested-the-men-at-math-120480965/">
    <title>The Woman Who Bested the Men at Math | History | Smithsonian</title>
    <dc:date>2018-04-06T13:56:32+00:00</dc:date>
    <link>https://www.smithsonianmag.com/history/the-woman-who-bested-the-men-at-math-120480965/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[To be a woman in the Victorian age was to be weak: the connection was that definite. To be female was also to be fragile, dependent, prone to nerves and—not least—possessed of a mind that was several degrees inferior to a man’s. For much of the 19th century, women were not expected to shine either academically or athletically, and those who attempted to do so were cautioned that they were taking an appalling risk. Mainstream medicine was clear on this point: to dream of studying at the university level was to chance madness or sterility, if not both.

It took generations to transform this received opinion; that, a long series of scientific studies, and the determination and hard work of many thousands of women. For all that, though, it is still possible to point to one single achievement, and one single day, and say: this is when everything began to change. That day was June 7, 1890, when—for the first and only time—a woman ranked first in the mathematical examinations held at the University of Cambridge. It was the day that Philippa Fawcett placed “above the Senior Wrangler.”

]]></description>
<dc:subject>nanohistory sexism biography mathematics academic-culture</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5b095674a808/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nanohistory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sexism"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:biography"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:academic-culture"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.openproblemgarden.org/home">
    <title>Home | Open Problem Garden</title>
    <dc:date>2018-03-24T11:37:00+00:00</dc:date>
    <link>http://www.openproblemgarden.org/home</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Welcome to the Open Problem Garden, a collection of unsolved problems in mathematics. Here you may:

Read descriptions of open problems.
Post comments on them.
Create and edit open problems pages (please contact us and we will set you up an account. Unfortunately, the automatic process is too prone to spammers at this moment.)]]></description>
<dc:subject>open-problems mathematical-recreations mathematics computer-science to-write-about nudge-targets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7ad233883a1d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computer-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://pdfs.semanticscholar.org/7efd/0c0bcbde96fed232069e1015df7fe2ccd8aa.pdf">
    <title>Varieties of Self-references (PDF)</title>
    <dc:date>2018-03-20T11:33:54+00:00</dc:date>
    <link>https://pdfs.semanticscholar.org/7efd/0c0bcbde96fed232069e1015df7fe2ccd8aa.pdf</link>
    <dc:creator>Vaguery</dc:creator><dc:subject>philosophy representation mathematics via:? ambiguity pragmatics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:72851cd94cf3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:philosophy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:?"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ambiguity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pragmatics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1802.06712">
    <title>[1802.06712] Multithreading for the expression-dag-based number type Real_algebraic</title>
    <dc:date>2018-03-10T13:23:34+00:00</dc:date>
    <link>https://arxiv.org/abs/1802.06712</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Many algorithms, especially in the field of computational geometry, are based on the premise that arithmetic operations are performed exactly. Real machines are based on inexact floating-point arithmetic. Various number types have been developed to close this gap by providing exact computation or ensuring exact decisions. In this report we describe the implementation of an extension to the exact-decisions number type Real_algebraic that enables us to take advantage of multiple processing units.
]]></description>
<dc:subject>representation programming-language algebra rather-interesting mathematics to-write-about to-try</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:47d5b64f7a98/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:programming-language"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-try"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1801.02602">
    <title>[1801.02602] Three Puzzles on Mathematics, Computation, and Games</title>
    <dc:date>2018-03-10T13:17:27+00:00</dc:date>
    <link>https://arxiv.org/abs/1801.02602</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?
]]></description>
<dc:subject>mathematics computational-complexity rather-interesting lecture to-write-about linear-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e51295766ebc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:lecture"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:linear-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1612.01093">
    <title>[1612.01093] Globular: an online proof assistant for higher-dimensional rewriting</title>
    <dc:date>2018-02-27T12:29:39+00:00</dc:date>
    <link>https://arxiv.org/abs/1612.01093</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their construction with a point-and- click interface, and performs type checking to prevent incorrect rewrites. Hosted on the web, it has a low barrier to use, and allows hyperlinking of formalized proofs directly from research papers. It allows the formalization of proofs from logic, topology and algebra which are not formalizable by other methods, and we give several examples.
]]></description>
<dc:subject>rewriting-systems mathematics proofs to-understand category-theory rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7d57292d0685/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proofs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:category-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://press.princeton.edu/math/subjects/mgen.html">
    <title>Browse Princeton Catalog in Popular Math | Princeton University Press</title>
    <dc:date>2018-02-21T23:03:56+00:00</dc:date>
    <link>https://press.princeton.edu/math/subjects/mgen.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Browse Princeton's Math Subject Area (by Title) in Popular Math]]></description>
<dc:subject>mathematics books to-read nudge-targets mathematical-recreations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8bb15ce4e38c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:books"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.youtube.com/watch?v=YCXmUi56rao">
    <title>Ham Sandwich Problem - Numberphile - YouTube</title>
    <dc:date>2018-02-03T18:08:19+00:00</dc:date>
    <link>https://www.youtube.com/watch?v=YCXmUi56rao</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Ham Sandwich Problem - Numberphile]]></description>
<dc:subject>mathematics topology mathematical-recreations nudge-targets consider:looking-to-see consider:prescriptive-algorithm</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6df06d0d75d9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:prescriptive-algorithm"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://parrt.cs.usfca.edu/doc/matrix-calculus/index.html">
    <title>[untitled]</title>
    <dc:date>2018-02-03T18:00:31+00:00</dc:date>
    <link>http://parrt.cs.usfca.edu/doc/matrix-calculus/index.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at forums.fast.ai. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here.

]]></description>
<dc:subject>via:numerous matrices mathematics review calculus deep-learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:289ee818876d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:numerous"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:review"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:calculus"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:deep-learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.theoremoftheday.org/Resources/RelatedSites.htm#magazines">
    <title>Theorem of the Day</title>
    <dc:date>2018-02-03T16:05:12+00:00</dc:date>
    <link>http://www.theoremoftheday.org/Resources/RelatedSites.htm#magazines</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The links below will bring you (in a new window) a superb collections of sites, blogs, online magazines etc, covering large parts of mathematics. Some subject-specific links are here.
]]></description>
<dc:subject>resources mathematical-recreations mathematics to-read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2cba312444c9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:resources"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://medium.com/q-e-d">
    <title>Q.E.D. – Medium</title>
    <dc:date>2018-01-26T13:24:05+00:00</dc:date>
    <link>https://medium.com/q-e-d</link>
    <dc:creator>Vaguery</dc:creator><dc:subject>mathematics education zine rather-interesting to-write-about pedagogy mathematical-recreations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d5c9a26bdbf5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:education"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:zine"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:pedagogy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>