MetaFilter posts tagged with Math and maths
http://www.metafilter.com/tags/Math+maths
Posts tagged with 'Math' and 'maths' at MetaFilter.Sun, 26 Jul 2015 13:54:00 -0800Sun, 26 Jul 2015 13:54:00 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Loop - Pool on an elliptical table
http://www.metafilter.com/151559/Loop%2DPool%2Don%2Dan%2Delliptical%2Dtable
<a href="http://www.loop-the-game.com">Loop - Pool on an elliptical table.</a> <i>The ellipse has two significant points, called focuses, which have a remarkable geometrical property that is almost always explained using the example of an imaginary pool table.
"If a pool table is the shape of an ellipse, then a ball shot from one focus will always rebound to the other focus no matter in which direction the ball is shot."
That sounded interesting! Wouldn't it be fun, I thought, if I could build one of these imaginary tables?
<a href="http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jul/16/loop-new-cue-sport-pool-ellipse-elliptical">So I did</a>.</i> tag:metafilter.com,2015:site.151559Sun, 26 Jul 2015 13:54:00 -0800dngHoTT Coq
http://www.metafilter.com/150345/HoTT%2DCoq
<a href="https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/">Univalent Foundations Redefines Mathematics</a> - "When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to <a href="http://homotopytypetheory.org/book/">rewrite the century-old rules</a> underlying all of mathematics." (<a href="http://www.metafilter.com/126041/Computerized-Math-Formal-Proofs-andamp-Alternative-Logic">previously</a>) <a href="http://www.ams.org/notices/201309/rnoti-p1164.pdf">Voevodsky's Univalence Axiom in Homotopy Type Theory</a>
<blockquote>One of Voevodsky's goals (<a href="https://intelligence.org/2014/02/21/john-baez-on-research-tactics/">as we understand it</a>) is that, in a not too distant future, mathematicians will be able to verify the correctness of their own papers by working <a href="http://math.andrej.com/2014/01/13/univalent-foundations-subsume-classical-mathematics/">within the system of univalent foundations</a> formalized in a proof assistant and that doing so will become natural even for pure mathematicians (the same way that most mathematicians now typeset their own papers in TeX). We believe that this aspect of the <a href="http://ncatlab.org/nlab/show/univalence+axiom">univalent foundations program</a> distinguishes it from other approaches to foundations by providing a practical utility for the working mathematician.</blockquote>
-<a href="http://www.science4all.org/le-nguyen-hoang/type-theory/">Type Theory: A Modern Computable Paradigm for Math</a>
-<a href="http://www.science4all.org/le-nguyen-hoang/homotopy-type-theory/">Homotopy Type Theory and Higher Inductive Types</a>
-<a href="http://www.science4all.org/le-nguyen-hoang/univalence/">Univalent Foundations of Mathematics</a>
also btw...
-<a href="https://www.youtube.com/watch?v=QNznD9hMEh0">James Simons interview</a>
-<a href="https://mathematicswithoutapologies.wordpress.com/2015/05/13/univalent-foundations-no-comment/">Univalent Foundations: "No Comment."</a> (<a href="http://math-frolic.blogspot.com/2015/05/set-theory-type-theory-hott-univalent.html">via</a>)
-<a href="https://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/">There's more to mathematics than rigour and proofs</a> tag:metafilter.com,2015:site.150345Tue, 09 Jun 2015 22:40:35 -0800kliuless3Blue1Brown: Reminding the world that math makes sense
http://www.metafilter.com/150242/3Blue1Brown%2DReminding%2Dthe%2Dworld%2Dthat%2Dmath%2Dmakes%2Dsense
<a href="https://www.youtube.com/watch?v=F_0yfvm0UoU">Understanding e to the pi i</a> - "<a href="http://www.3blue1brown.com/s/HowToThinkAboutExponentials.pdf">An intuitive explanation</a> as to why <a href="http://www.bbc.co.uk/programmes/b04hz49f" title="Melvyn Bragg and his guests discuss Euler's number, also known as e. First discovered in the seventeenth century by the Swiss mathematician Jacob Bernoulli when he was studying compound interest, e is now recognised as one of the most important and interesting numbers in mathematics. Roughly equal to 2.718, e is useful in studying many everyday situations, from personal savings to epidemics. It also features in Euler's Identity, sometimes described as the most beautiful equation ever written. With: Colva Roney-Dougal, Reader in Pure Mathematics at the University of St Andrews; June Barrow-Green, Senior Lecturer in the History of Maths at the Open University; and Vicky Neale, Whitehead Lecturer at the Mathematical Institute and Balliol College at the University of Oxford.">e</a> to the <a href="http://www.bbc.co.uk/programmes/p004y291" title="Melvyn Bragg and guests discuss the history of the most detailed number in nature. In the Bible's description of Solomon's temple it comes out as three, Archimedes calculated it to the equivalent of 14 decimal places and today's super computers have defined it with an extraordinary degree of accuracy to its first 1.4 trillion digits. It is the longest number in nature and we only need its first 32 figures to calculate the size of the known universe within the accuracy of one proton. We are talking about Pi, 3.14159 etc, the number which describes the ratio of a circle's diameter to its circumference. How has something so commonplace in nature been such a challenge for maths? And what does the oddly ubiquitous nature of Pi tell us about the hidden complexities of our world? With: Robert Kaplan, co-founder of the Maths Circle at Harvard University; Eleanor Robson, Lecturer in the Department of History and Philosophy of Science at Cambridge University; and Ian Stewart, Professor of Mathematics at the University of Warwick.">pi</a> <a href="http://www.bbc.co.uk/programmes/b00tt6b2" title="Melvyn Bragg and his guests discuss imaginary numbers. In the sixteenth century, a group of mathematicians in Bologna found a solution to a problem that had puzzled generations before them: a completely new kind of number. For more than a century this discovery was greeted with such scepticism that the great French thinker Rene Descartes dismissed it as an 'imaginary' number. The name stuck - but so did the numbers. Long dismissed as useless or even fictitious, the imaginary number i and its properties were first explored seriously in the eighteenth century. Today the imaginary numbers are in daily use by engineers, and are vital to our understanding of phenomena including electricity and radio waves. With: Marcus du Sautoy, Professor of Mathematics at Oxford University; Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick; and Caroline Series, Professor of Mathematics at the University of Warwick.">i</a> equals -1 <a href="https://www.youtube.com/watch?v=1rVHLZm5Aho">without a hint</a> of calculus. This is <a href="https://www.youtube.com/watch?v=zLzLxVeqdQg">not your usual</a> Taylor series nonsense." (<a href="https://twitter.com/stevenstrogatz/status/604653212214292481" title="''A star is born.''">via</a> <a href="https://twitter.com/Noahpinion/status/604679198259580928" title="''Best geek video I've seen all week.''">via</a>; <a href="http://www.reddit.com/r/math/comments/2xzzk0/nontaylorseries_explanation_for_eulers_formula/">reddit</a>; <a href="http://www.metafilter.com/89918/Math-is-beautiful">previously</a>) <a href="https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw">More videos from 3Blue1Brown</a>: "<a href="http://www.3blue1brown.com/">3Blue1Brown</a> is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be <a href="http://www.3blue1brown.com/about/" title="''When the tool I am building for animations becomes something besides a jumble of Python and Duct tape, I'll make it publicly available so that anyone can use it to easily illustrate their own explanations.''">driven by animations</a>, for difficult problems to be made simple with changes in perspective, and for philosophizing to be limited to the brevity and semantic constraints of silly poetry. Basically, math sits in <a href="https://plus.google.com/117663015413546257905/posts/QAhMH35LThk">an ivory tower it built itself out of</a> jargon and impossibly long sequences of (seemingly) logical steps, and I would like to take it out for a walk to <a href="http://wordplay.blogs.nytimes.com/2015/03/09/%CF%80/">meet everyone</a>." tag:metafilter.com,2015:site.150242Sat, 06 Jun 2015 11:42:18 -0800kliulessArithmeticfilter
http://www.metafilter.com/146474/Arithmeticfilter
<a href="http://www.momonix.com/calc/">Nothing but an endless supply of mental arithmetic problems.</a> Five levels of difficulty, from "10 - 6" to "√370881." You can find slightly more granular training <a href="http://windhoff.net/mental_arithmetic/#Addition">here</a>. See <a href="http://en.wikipedia.org/wiki/Mental_calculation">Wikipedia</a> for a survey of mental methods, or read <a href="http://www-history.mcs.st-and.ac.uk/HistTopics/Mental_arithmetic.html">A.C. Aitken's</a> <a href="http://stepanov.lk.net/mnemo/aitkene.html">explanation</a> of his Art of Calculation. tag:metafilter.com,2015:site.146474Mon, 26 Jan 2015 08:41:53 -0800IridicNo Pentagons
http://www.metafilter.com/146120/No%2DPentagons
<a href="http://gruze.org/tilings/">Imperfect Congruence</a> - <i>It is a curious fact that no edge-to-edge regular polygon tiling of the plane can include a pentagon ... This website explains the basic mathematics of a particular class of tilings of the plane, those involving regular polygons such as triangles or hexagons. As will be shown, certain combinations of regular polygons cannot be extended to a full tiling of the plane without involving additional shapes, such as rhombs. The site contains some commentary on Renaissance research on this subject carried out by two renowned figures, the mathematician-astronomer Johannes Kepler and the artist Albrecht Dürer.</i> Bonus link: <a href="http://plus.maths.org/content/trouble-five">The Trouble with Five</a> (by Craig Kaplan, at Plus magazine - a short, tantalizing article suitable for school-age readers...) tag:metafilter.com,2015:site.146120Wed, 14 Jan 2015 11:58:51 -0800Wolfdog"Science is when you think a lot."
http://www.metafilter.com/145704/Science%2Dis%2Dwhen%2Dyou%2Dthink%2Da%2Dlot
<a href="http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf">Two enjoyable chapters</a> [PDF, 33 pages] from the book <i><a href="http://www.ams.org/bookstore-getitem/item=MCL-5">Math from Three to Seven</a>: The Story of a Mathematical Circle for Preschoolers.</i> "This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children." tag:metafilter.com,2014:site.145704Mon, 29 Dec 2014 10:43:09 -0800Wolfdog√2N
http://www.metafilter.com/143992/2N
<a href="http://www.quantamagazine.org/20141015-at-the-far-ends-of-a-new-universal-law/">At the Far Ends of a New Universal Law</a> <blockquote>The law appeared in full form two decades later, when the mathematicians Craig Tracy and Harold Widom proved that the critical point in the kind of model May used was the peak of a statistical distribution. Then, in 1999, Jinho Baik, Percy Deift and Kurt Johansson discovered that the same statistical distribution also describes variations in sequences of shuffled integers — a completely unrelated mathematical abstraction. Soon the distribution appeared in models of the wriggling perimeter of a bacterial colony and other kinds of random growth. Before long, it was showing up all over physics and mathematics.
"The big question was why," said Satya Majumdar, a statistical physicist at the University of Paris-Sud. "Why does it pop up everywhere?"</blockquote> tag:metafilter.com,2014:site.143992Tue, 28 Oct 2014 12:59:35 -0800the man of twists and turnsTake that, Keanu Reeves.
http://www.metafilter.com/143228/Take%2Dthat%2DKeanu%2DReeves
<a href="http://www.autostraddle.com/rebel-girls-mapping-power-privilege-and-oppression-254794/">Privilege and oppression explained through math</a> - specifically, matrices and Venn diagrams. tag:metafilter.com,2014:site.143228Wed, 01 Oct 2014 10:05:31 -0800divabatCalculus without limits
http://www.metafilter.com/142845/Calculus%2Dwithout%2Dlimits
<a href="https://plus.google.com/u/0/117663015413546257905/posts/14b9fdM62un">Hyperreal numbers: infinities and infinitesimals</a> - "In 1976, <a href="https://www.math.wisc.edu/~keisler/">Jerome Keisler</a>, a student of the famous logician <a href="http://johncarlosbaez.wordpress.com/2013/03/31/probability-theory-and-the-undefinability-of-truth/">Tarski</a>, published this <a href="http://www.vias.org/calculus/">elementary textbook</a> that <a href="http://en.wikipedia.org/wiki/Infinitesimal#History_of_the_infinitesimal">teaches calculus</a> using <a href="http://en.wikipedia.org/wiki/Hyperreal_number">hyperreal numbers</a>. <a href="https://www.math.wisc.edu/~keisler/calc.html">Now it's free</a>, with a Creative Commons copyright!" (pdf—<a href="https://www.math.wisc.edu/~keisler/keislercalc-12-27-13.pdf">25mb</a> :) also btw :P
<ul><li><a href="https://plus.google.com/u/0/117663015413546257905/posts/JHAku2S1KFw">The logic of real and complex numbers</a> - "The cool part is that in some ways the complex numbers are <i>simpler</i> than the real numbers! The <a href="http://johncarlosbaez.wordpress.com/2014/09/08/the-logic-of-real-and-complex-numbers/">ultimate reason</a> is that you can't talk about one complex number being greater than another. This avoids some nonstandard number systems where you have a number that's greater than all the ones you wanted to talk about."</li>
<li><a href="https://plus.google.com/u/0/117663015413546257905/posts/dZcXuyHj7LH">Science, models, and machine learning</a> - "<a href="http://johncarlosbaez.wordpress.com/2014/09/03/science-models-and-machine-learning/">Machine learning</a> is the art of <a href="http://www.newscientist.com/article/mg22329832.700-googles-factchecking-bots-build-vast-knowledge-bank.html?full=true">getting computers to learn, so you don't have to</a> explicitly tell them what to do. People use it in spam filters, search engines that guess what you're trying to find, optical character recognition, <a href="https://medium.com/aspen-ideas/robots-with-their-heads-in-the-clouds-e88ac44def8a">cars that drive themselves</a>, and <a href="https://plus.google.com/u/0/117663015413546257905/posts/SrQe3Bsd9kp">many other</a> things. <a href="http://www.metafilter.com/135046/Things-Dont-Make-Sense-Till-They-Make-Sense-to-a-Stupid-Robot">But how does it work?</a>"</li>
<li><a href="http://infoproc.blogspot.com/2014/08/neural-networks-and-deep-learning-2.html">Neural Networks and Deep Learning</a> - "Inspired by the topics discussed in this <a href="http://infoproc.blogspot.com/2014/08/neural-networks-and-deep-learning.html">earlier post</a>, I've been reading <a href="http://neuralnetworksanddeeplearning.com/">Michael Nielsen's online book</a> on neural nets and deep learning."</li>
<li><a href="http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/cat_statcomp.html">Introduction to Statistical Computing</a> - "At an intersection of <a href="http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/cat_enigmas_of_chance.html">Enigmas of Chance</a> and <a href="http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/cat_corrupting_the_young.html">Corrupting the Young</a>."</li>
<li><a href="http://www.math.columbia.edu/~woit/wordpress/?p=7172">Higher Algebra & Topos Theory</a> - "<a href="http://www.macfound.org/fellows/921/">Mathematician Jacob Lurie</a>, who was honored for redefining models in algebraic geometry, negotiated with his publisher to make his book on <a href="https://plus.google.com/u/0/117663015413546257905/posts/LX52bzbuWgH">math principles</a> available for <a href="http://www.math.harvard.edu/~lurie/">free download</a> on his personal website. While academics sometimes place papers online free, putting a whole book online isn't yet standard practice, according to the 36-year-old Harvard University professor. 'From my point of view, the benefit of writing a book is for people to look at it. I would like as many people as possible to look at it', he said."</li></ul> tag:metafilter.com,2014:site.142845Wed, 17 Sep 2014 17:23:34 -0800kliuless21st Century Wiener
http://www.metafilter.com/140806/21st%2DCentury%2DWiener
<a href="http://www.theatlantic.com/technology/archive/2014/06/norbert-wiener-the-eccentric-genius-whose-time-may-have-finally-come-again/372607/">Norbert Wiener: The Eccentric Genius Whose Time May Have Finally Come (Again)</a> - "The most direct reason for Wiener's fall to relative obscurity was the breakthrough of a young mathematician and engineer named <a href="http://www.metafilter.com/6138/The-passing-of-a-giant">Claude Shannon</a>." <a href="http://tikalon.com/blog/blog.php?article=2014/Norbert_Wiener">Norbert Wiener</a>:
<blockquote>In his 1950 book, "<a href="http://en.wikipedia.org/wiki/The_Human_Use_of_Human_Beings">The Human Use of Human Beings</a>," [<a href="http://21stcenturywiener.org/wp-content/uploads/2013/11/The-Human-Use-of-Human-Beings-by-N.-Wiener.pdf">PDF</a>] Wiener <a href="http://www.forbes.com/sites/christopherhelman/2014/07/02/dean-kamen-thinks-his-new-stirling-engine-could-power-the-world/print/">envisioned</a> a <a href="https://medium.com/@AdamThierer/muddling-through-how-we-learn-to-cope-with-technological-change-6282d0d342a6">utopia</a> in which <a href="http://www.bloombergview.com/articles/2014-07-07/larry-page-s-slacker-utopia">automation</a> would relieve humanity of <a href="http://marginalrevolution.com/marginalrevolution/2014/07/the-decline-of-drudgery-and-the-paradox-of-hard-work.html">manual</a> <a href="http://crookedtimber.org/2014/07/10/in-search-of-search-theory/">labor</a> to allow more <a href="http://continuations.com/post/91111911845/more-on-basic-income-and-robots">creative</a> pursuits. Sixty years later, we have much automation, but <a href="http://www.economist.com/blogs/freeexchange/2014/07/thomas-piketty-history-money">income</a> <a href="http://boingboing.net/2014/06/24/thomas-pikettys-capital-in-t.html">inequality</a> rather than utopia. Wiener died in Stockholm, Sweden, at age 69.
The crater, <a href="http://en.wikipedia.org/wiki/Wiener_%28crater%29">Wiener</a>, on the far side of the Moon is named after him. I've always believed in "Wiener's Law of Libraries," "<a href="http://en.wikiquote.org/wiki/Norbert_Wiener">There are no answers, only cross references</a>". The IEEE is sponsoring a conference, <a href="http://21stcenturywiener.org/">Norbert Wiener in the 21st Century</a>, commemorating Norbert Wiener. </blockquote>
also btw...
<ul><li><a href="http://www.nytimes.com/2013/05/21/science/mit-scholars-1949-essay-on-machine-age-is-found.html?pagewanted=all">In 1949, He Imagined an Age of Robots</a>: " 'The Machine Age' (<a href="http://libraries.mit.edu/archives/mithistory/pdf/MC0022_MachineAgeV3_1949.pdf">pdf</a>) an essay written for <i>The New York Times</i> by Norbert Wiener, a visionary mathematician, languished for six decades in the M.I.T. archives, and now excerpts are being published."</li>
<li><a href="http://infoproc.blogspot.com/2014/06/theoreticians-as-professional-outsiders.html">Theoreticians as Professional Outsiders</a>: The Modeling Strategies of John von Neumann and Norbert Wiener (<a href="http://www.ehudlamm.com/outsiders.pdf">pdf</a>)</li>
<blockquote>Both von Neumann and Wiener were outsiders to biology. Both were inspired by biology and both proposed models and generalizations that proved inspirational for biologists. Around the same time in the 1940s von Neumann developed the notion of self reproducing automata and Wiener suggested an explication of teleology using the notion of negative feedback. These efforts were similar in spirit. Both von Neumann and Wiener used mathematical ideas to attack foundational issues in biology, and the concepts they articulated had lasting effect. But there were significant differences as well. Von Neumann presented a how-possibly model, which sparked interest by mathematicians and computer scientists, while Wiener collaborated more directly with biologists, and his proposal influenced the philosophy of biology. The two cases illustrate different strategies by which mathematicians, the "professional outsiders" of science, can choose to guide their engagement with biological questions and with the biological community, and <a href="http://www.metafilter.com/137105/John-Baez-on-the-maths-of-connecting-everyone-and-everything-on-earth">illustrate different kinds of generalizations</a> that mathematization can contribute to biology. The different strategies employed by von Neumann and Wiener and the types of models they constructed may have affected the fate of von Neumann's and Wiener's ideas – as well as the reputation, in biology, of von Neumann and Wiener themselves.</blockquote>
<li><a href="http://www.nytimes.com/2014/07/08/science/a-billionaire-mathematicians-life-of-ferocious-curiosity.html">A Billionaire Mathematician's Life of Ferocious Curiosity</a>: "Dr. Simons received his doctorate at 23; advanced code breaking for the National Security Agency at 26; led a university math department at 30; won geometry's top prize at 37; <a href="http://infoproc.blogspot.com/2014/07/james-simons-mathematics-common-sense.html">founded Renaissance Technologies</a>, one of the world's most successful hedge funds, at 44; and began setting up <a href="http://www.simonsfoundation.org/quanta/">charitable foundations</a> at 56."</li>
<li><a href="http://infoproc.blogspot.com/2014/07/physics-and-horizons-of-truth.html">Physics and the Horizons of Truth</a>: "mathematics without something like the 'axiom of infinity' might be well-defined..." [<a href="http://infoproc.blogspot.com/2013/06/horizons-of-truth.html">Horizons of Truth</a>: Kurt Gödel and the Foundations of Mathematics (<a href="http://f3.tiera.ru/2/M_Mathematics/MA_Algebra/MAml_Mathematical%20logic/Baaz%20M.,%20et%20al.%20(eds.)%20Kurt%20Goedel%20and%20the%20foundations%20of%20mathematics.%20Horizons%20of%20truth%20(CUP,%202011)(ISBN%200521761441)(O)(541s)_MAml_.pdf">pdf</a>)]</li>
<li><a href="https://www.youtube.com/watch?v=uh6GCY9i6tY">Sentences you never thought you'd hear in Congress</a>: "Madame Speaker, I would like to talk about <a href="http://www.metafilter.com/134338/binding-the-andat">twin prime numbers</a>..."</li></ul> tag:metafilter.com,2014:site.140806Fri, 11 Jul 2014 07:11:08 -0800kliulessMath or Maths?
http://www.metafilter.com/138740/Math%2Dor%2DMaths
<a href="http://www.numberphile.com/videos/math_maths.html">Math or Maths?</a> A few minutes with Dr Lynne Murphy (an American linguist in England) should clear this right up. Via <a href="http://www.numberphile.com/index.html">Numberphile</a>. tag:metafilter.com,2014:site.138740Wed, 30 Apr 2014 17:39:24 -0800R. MuttA SAT Attack on the Erdos Discrepancy Conjecture
http://www.metafilter.com/138247/A%2DSAT%2DAttack%2Don%2Dthe%2DErdos%2DDiscrepancy%2DConjecture
<a href="http://io9.com/computers-are-providing-solutions-to-math-problems-that-1525261141">Computers are providing solutions to math problems that we can't check</a> - "A computer has solved the longstanding <a href="http://arxiv.org/abs/1402.2184">Erdős discrepancy</a> problem! Trouble is, we have no idea what it's talking about — because the solution, which is <a href="http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html">as long as all of Wikipedia</a>'s pages combined, is far too <a href="http://mathbabe.org/2013/07/30/the-stacks-project-gets-ever-awesomer-with-new-viz/">voluminous</a> for us <a href="http://oliviacaramello.com/Unification/Unification.htm">puny humans</a> to confirm." (<a href="http://marginalrevolution.com/marginalrevolution/2014/04/are-computer-coming-up-with-answers-we-cannot-understand.html">via</a>; <a href="http://www.metafilter.com/126041/Computerized-Math-Formal-Proofs-andamp-Alternative-Logic">previously</a> ;) tag:metafilter.com,2014:site.138247Sat, 12 Apr 2014 08:55:27 -0800kliulessthere is no soundtrack
http://www.metafilter.com/137347/there%2Dis%2Dno%2Dsoundtrack
<a href="https://www.simonsfoundation.org/quanta/20140224-a-fluid-new-path-in-grand-math-challenge/">Finite time blowup for an averaged three-dimensional Navier-Stokes equation</a> - "[<a href="http://terrytao.wordpress.com/">Terence Tao</a>] has shown that in an alternative abstract universe closely related to the one described by the <a href="http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations">Navier-Stokes</a> equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, <a href="http://www.drseussart.com/details/illustration/littlecats.html">like the Cat in the Hat</a>, keeps transferring its energy to smaller and smaller copies of itself until the fluid '<a href="http://terrytao.wordpress.com/2014/02/04/finite-time-blowup-for-an-averaged-three-dimensional-navier-stokes-equation/">blows up</a>.' " [<a href="http://terrytao.wordpress.com/2014/02/25/conserved-quantities-for-the-euler-equations/">1</a>,<a href="http://terrytao.wordpress.com/2014/03/02/noethers-theorem-and-the-conservation-laws-for-the-euler-equations/">2</a>,<a href="http://terrytao.wordpress.com/2014/03/06/conserved-quantities-for-the-surface-quasi-geostrophic-equation/">3</a>] (<a href="http://www.metafilter.com/55295/Another-Clay-Institute-Millenium-Prize-Problem-Solved">previously</a>) tag:metafilter.com,2014:site.137347Sun, 09 Mar 2014 13:49:39 -0800kliulessJohn Baez on the maths of connecting everyone (and everything) on earth
http://www.metafilter.com/137105/John%2DBaez%2Don%2Dthe%2Dmaths%2Dof%2Dconnecting%2Deveryone%2Dand%2Deverything%2Don%2Dearth
<a href="http://johncarlosbaez.wordpress.com/2014/02/22/network-theory-overview/">Network Theory Overview</a> - "<a href="http://johncarlosbaez.wordpress.com/2014/02/07/network-theory-talks-at-oxford/">The idea</a>: nature and the world of human technology are <a href="http://johncarlosbaez.wordpress.com/2013/04/23/network-theory-part-29/">full of networks</a>! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using <a href="http://math.ucr.edu/home/baez/irvine/">category theory</a>. But why should <a href="http://www.perimeterinstitute.ca/videos/energy-and-environment-what-physicists-can-do">physicists have all the fun</a>? This is the century of <i><a href="https://plus.google.com/117663015413546257905/posts/e6stQjMvm3y">understanding living systems and adapting to life on a finite planet</a></i>. Math isn't the main thing we need, but it's got to be <a href="https://plus.google.com/117663015413546257905/posts/5gt7pfibYMg">part of the solution</a>... <a href="http://johncarlosbaez.wordpress.com/2014/03/02/network-theory-i/">so one thing we should do</a> is develop a unified and powerful <a href="http://math.ucr.edu/home/baez/networks/">theory of networks</a>." (<a href="https://plus.google.com/117663015413546257905/posts/SmWyn8HcDyW">via</a> ;) tag:metafilter.com,2014:site.137105Sun, 02 Mar 2014 09:06:38 -0800kliulessWondering What to Get with That Gift Card?
http://www.metafilter.com/135164/Wondering%2DWhat%2Dto%2DGet%2Dwith%2DThat%2DGift%2DCard
It's a bit late for the holiday, but math(s) comedian Helen Arney <a href="http://www.bbc.co.uk/programmes/p01ns0wj">sings about her Christmas wish</a> -- the largest known Mersenne Prime, <a href="http://en.wikipedia.org/wiki/Mersenne_prime">Mersenne 48</a>. The song appeared on a recent edition of the BBC4 radio show/podcast <a href="http://www.bbc.co.uk/programmes/b006qshd">More or Less</a> which deals with numbers and especially statistics. Arney performs as part of <a href="http://festivalofthespokennerd.com/">The Festival of the Spoken Nerd</a> in the UK.
Bonus Helen Arney -- <a href="http://www.youtube.com/watch?v=5JOAoiX1LHA&feature=c4-overview-vl&list=PLUQzg8K3BcJLmneP2TwqoEJvqr2_NvFIX">"The Google Song"</a> from Numberphile [<a href="http://www.metafilter.com/123329/Numberphile-videos-about-numbers-and-stuff">previously</a>] tag:metafilter.com,2013:site.135164Sat, 28 Dec 2013 07:20:05 -0800GenjiandProustbinding the andat
http://www.metafilter.com/134338/binding%2Dthe%2Dandat
<a href="http://www.wired.com/wiredscience/2013/11/prime/all/">Closing in on the twin prime conjecture</a> (<a href="https://www.simonsfoundation.org/quanta/20131119-together-and-alone-closing-the-prime-gap/">Quanta</a>) - "Just months after <a href="http://www.metafilter.com/128049/Quite-a-day-for-analytic-number-theory">Zhang</a> announced his result, <a href="http://arxiv.org/abs/1311.4600">Maynard</a> has presented an independent proof that pushes the gap down to 600. A <a href="http://terrytao.wordpress.com/tag/polymath8/">new Polymath project</a> is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." <a href="https://plus.google.com/u/0/117663015413546257905/posts/LxR23RdyvuF">also btw</a> :P (<a href="https://plus.google.com/u/0/117663015413546257905/posts/jd5K4jBKRYP">for fun</a>!)
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/Z4cUWGQp8Ar">Schröder–Hipparchus numbers</a> (<a href="http://golem.ph.utexas.edu/category/2013/04/permutations_polynomials_and_p.html">The Hipparchus Operad</a>)
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/WoXqXCzkc9S">Quasi</a>-<a href="http://golem.ph.utexas.edu/category/2013/06/quasicrystals_and_the_riemann.html">crystals</a> (<a href="https://plus.google.com/u/0/117663015413546257905/posts/j4Xxg44n1t6">quantum physics and number theory</a>)
-<a href="https://www.simonsfoundation.org/quanta/20131126-to-settle-infinity-question-a-new-law-of-logic/">To Settle Infinity Question, a New Law of Mathematics</a>
oh and <a href="https://www.simonsfoundation.org/quanta/20131107-physicists-eye-quantum-gravity-interface/">perhaps</a> more practically...
-<a href="http://www.thephysicsmill.com/2013/10/13/causal-dynamical-triangulations/">Quantum Geometry: Causal Dynamical Triangulations</a> (<a href="https://plus.google.com/u/0/117663015413546257905/posts/ATg9EwD5CJy">via</a>)
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/9HeN1sSQztA">Quantropy</a>
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/51Gd5adQZNM">Petri nets</a> (<a href="http://johncarlosbaez.wordpress.com/2013/04/19/petri-net-programming-part-3/">programming</a> <a href="http://www.metafilter.com/134300/ASCII-fluid-simulator">water</a>)
-<a href="http://johncarlosbaez.wordpress.com/2013/04/23/network-theory-part-29/">Network theory</a>
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/SrQe3Bsd9kp">The network of mathematics</a>
-<a href="http://math.ucr.edu/home/baez/irvine/">The Foundations of Applied Mathematics</a> (<a href="https://plus.google.com/u/0/117663015413546257905/posts/LX52bzbuWgH">topos theory</a>)
-<a href="http://www.wired.com/wiredscience/2013/10/topology-data-sets/all/">Topological Data Analysis</a> tag:metafilter.com,2013:site.134338Sun, 01 Dec 2013 16:19:50 -0800kliulessTwelve Tones
http://www.metafilter.com/129471/Twelve%2DTones
<i>"It's just one of those days where you wake up thinking that if you jazzed up Stravinsky's Owl And The Pussycat it'd be <a href="http://www.youtube.com/watch?v=4niz8TfY794">awesome</a>..."</i> [SLYT] <a href="http://www.youtube.com/watch?v=4niz8TfY794">Twelve Tones</a> is a new video essay by mathemusician <a href="https://www.khanacademy.org/math/recreational-math/vi-hart">Vi Hart</a>, using Schoenberg's <a href="https://en.wikipedia.org/wiki/Twelve-tone_technique">twelve tone technique</a> as the jumping off point for a meditation on the nature of art, meaning, and creativity, the tension between cliche and stuff people recognise, and pattern recognition.
Previous Vi Hart: <a href="http://www.metafilter.com/122117/Potatoes-and-Math">1</a>, <a href="http://www.metafilter.com/119511/I-Heart-Cardioids">2</a>, <a href="http://www.metafilter.com/112181/Pineapple-under-the-sea-Really">3</a>, <a href="http://www.metafilter.com/98150/Explorations-of-a-Recreational-Mathematician">4</a>. tag:metafilter.com,2013:site.129471Thu, 27 Jun 2013 14:54:10 -0800mottyIs there any point to the 12 times table?
http://www.metafilter.com/129457/Is%2Dthere%2Dany%2Dpoint%2Dto%2Dthe%2D12%2Dtimes%2Dtable
<a href="http://blog.wolfram.com/2013/06/26/is-there-any-point-to-the-12-time">Is there any point to the 12 times table?</a> Bonus: <a href="http://www.youtube.com/watch?v=vzXcI49jdV0">Times table song</a> tag:metafilter.com,2013:site.129457Thu, 27 Jun 2013 07:18:38 -0800Cat Pie HurtsProof and Community Standards
http://www.metafilter.com/127954/Proof%2Dand%2DCommunity%2DStandards
In August of last year, mathematician Shinichi Mochizuki reported that he had solved one of the great puzzles of number theory: the ABC conjecture (<a href="http://www.metafilter.com/119847/Mathematics-world-abuzz-with-a-proof-of-the-ABC-Conjecture">previously on Metafilter</a>). Almost a year later, no one else knows whether he has succeeded. <a href="http://projectwordsworth.com/the-paradox-of-the-proof/">No one can understand his proof.</a> tag:metafilter.com,2013:site.127954Fri, 10 May 2013 14:51:46 -0800painqualeComputerized Math, Formal Proofs and Alternative Logic
http://www.metafilter.com/126041/Computerized%2DMath%2DFormal%2DProofs%2Dandamp%2DAlternative%2DLogic
<a href="http://www.wired.com/wiredscience/2013/03/computers-and-math/all/">Using computer systems for doing mathematical proofs</a> - "With the proliferation of <a href="http://en.wikipedia.org/wiki/Computer-assisted_proof">computer-assisted proofs</a> that are all but impossible to check by hand, Hales thinks computers must become the judge." <blockquote>Three years ago, Vladimir Voevodsky, one of the organizers of a new program on the foundations of mathematics at the Institute for Advanced Study in Princeton, N.J., discovered that a formal logic system that was developed by computer scientists, called "<a href="http://en.wikipedia.org/wiki/Type_theory">type theory</a>" could be used to re-create the entire mathematical universe from scratch. Type theory is consistent with the mathematical axioms, but couched in the language of computers. Voevodsky believes this alternative way to formalize mathematics, which he has renamed the <a href="http://video.ias.edu/univalent/voevodsky">univalent foundations of mathematics</a>, will streamline the process of formal theorem proving. Voevodsky and his team are adapting a <a href="https://plus.google.com/u/0/117663015413546257905/posts/4BZRibN6iKQ">program named Coq</a>, which was designed to formally verify computer algorithms, for use in abstract mathematics.</blockquote>
also btw, speaking of mathematical revolutions, from a historical perspective, check out <a href="http://www.scientificamerican.com/article.cfm?id=the-man-of-numbers-fibona&print=true">The Man of Numbers: Fibonacci's Arithmetic Revolution</a> - "Before the 13th century Europeans used Roman numerals to do arithmetic. Leonardo of Pisa, better known today as Fibonacci, is largely responsible for the adoption of the Hindu–Arabic numeral system in Europe, which revolutionized not only mathematics but commerce and trade as well. How did the system spread from the Arab world to Europe, and what would our lives be without it?" tag:metafilter.com,2013:site.126041Sat, 16 Mar 2013 15:33:01 -0800kliulessthe power and beauty of mathematics
http://www.metafilter.com/124535/the%2Dpower%2Dand%2Dbeauty%2Dof%2Dmathematics
<a href="http://blogs.scientificamerican.com/the-curious-wavefunction/2013/01/22/an-eternity-of-infinities-the-power-and-beauty-of-mathematics/">An eternity of infinities</a> (<a href="http://economistsview.typepad.com/economistsview/2013/01/links-for-01-23-2013.html">via</a>) "The comparison of infinities is simple to understand and is a fantastic device for introducing children to the wonders of mathematics. It drives home the essential weirdness of the mathematical universe and raises penetrating questions not only about the nature of this universe but about the nature of the human mind that can comprehend it. One of the biggest questions concerns the nature of reality itself. Physics has also revealed counter-intuitive truths about the universe like the curvature of space-time, the duality of waves and particles and the spooky phenomenon of entanglement, but these truths undoubtedly have a real existence as observed through exhaustive experimentation. But what do the bizarre truths revealed by mathematics actually mean? Unlike the truths of physics they can't exactly be touched and seen. Can some of these such as the perceived differences between two kinds of infinities simply be a function of human perception, or do these truths point to an objective reality 'out there'? If they are only a function of human perception, what is it exactly in the structure of the brain that makes such wondrous creations possible? In the twenty-first century when neuroscience promises to reveal more of the brain than was ever possible, the investigation of mathematical understanding could prove to be profoundly significant." tag:metafilter.com,2013:site.124535Sat, 02 Feb 2013 09:14:26 -0800kliulessAn example of "order out of chaos"
http://www.metafilter.com/122470/An%2Dexample%2Dof%2Dorder%2Dout%2Dof%2Dchaos
<a href="http://blog.matthen.com/post/35993520930/draw-some-random-points-on-a-piece-of-paper-and">"Draw some random points</a> on a piece of paper and join them up to make a random polygon. Find all the midpoints and connecting them up to give a new shape, and repeat. The resulting shape will get smaller and smaller, and will tend towards an ellipse!" [<a href="http://pastebin.com/2JJ96L14" title="code to make this in Mathematica">code to make this in Mathematica</a>] [<a href="http://www.jasondavies.com/random-polygon-ellipse/">a version which allows you to watch the process step by step, with 10 vertices or 100</a>] tag:metafilter.com,2012:site.122470Mon, 03 Dec 2012 14:09:36 -0800ocherdracodirect realism
http://www.metafilter.com/122400/direct%2Drealism
<a href="http://dannyreviews.com/h/Nature_Computation.html">The Nature of Computation</a> - <a href="http://masi.cscs.lsa.umich.edu/~crshalizi/reviews/nature-of-computation.html">Intellects Vast and Warm and Sympathetic</a>: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/weblog/algae-2011-10.html">via</a>) <blockquote>This is, simply put, the best-written book on the theory of computation I have ever read; one of the best-written mathematical books I have ever read, period... from beginning to end, and all the 900+ pages in between, this was lucid, insightful, just rigorous enough, alive to how technical problems relate to larger issues, and above all, passionate and human.</blockquote>also btw...<ul><li><a href="http://infoproc.blogspot.com/2011/10/on-origin-of-probability-in-quantum.html">On the origin of probability in quantum mechanics</a> - "Because the wave function evolves entirely deterministically in <a href="http://infoproc.blogspot.com/2012/11/schwinger-on-quantum-foundations.html">many worlds</a>, all probabilities are necessarily subjective and the interpretation does not require <a href="http://www.metafilter.com/contribute/search.mefi?q=chaitin&tab=comments&site=mefi&sort=date">true</a> <a href="http://www.metafilter.com/122256/The-Royal-Society-Winton-Prize-2012">randomness</a>, thereby preserving Einstein's requirement that outcomes have causes."
<li><a href="http://johncarlosbaez.wordpress.com/2012/10/08/the-mathematical-origin-of-irreversibility/">The Mathematical Origin of Irreversibility</a> - "The key to this rather profound connection resides in a universal property of Markov processes discovered recently in the context of non-equilibrium statistical mechanics, and known as the '<a href="https://plus.google.com/u/0/117663015413546257905/posts/cLjAKybxWR8">fluctuation theorem</a>'. Typically stated in terms of '<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/notebooks/prigogine.html">dissipated work</a>' or '<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/notebooks/tsallis.html">entropy production</a>', this result can be seen as an extension of the Second Law of Thermodynamics to <i>small</i> systems, where thermal fluctuations cannot be neglected. But <i>it is actually much more than this</i>: it is the mathematical underpinning of irreversibility itself, be it thermodynamical, evolutionary, or else. To make this point clear, let me start by giving a general formulation of the fluctuation theorem that makes no reference to physics concepts such as 'heat' or 'work' "
<li><a href="https://plus.google.com/u/0/117663015413546257905/posts/jYw1fnVTFbY">A nice easy explanation</a> of the <a href="http://www.metafilter.com/119847/Mathematics-world-abuzz-with-a-proof-of-the-ABC-Conjecture">abc</a> <a href="https://plus.google.com/u/0/117663015413546257905/posts/Npu7xDniXMS">conjecture</a> [also btw <a href="http://www.metafilter.com/121668/Grahams-Number">1</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/VLkhD7NBAb3">2</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/6pbLR5Yyf8h">3</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/cqMha2Lz5gr">4</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/cLjAKybxWR8">5</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/4BZRibN6iKQ">6</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/DdA4HkKfMiL">7</a>,<a href="http://www.metafilter.com/107661/Counting">8</a>]
<li><a href="http://en.wikipedia.org/wiki/Hilary_Putnam">An argument for the reality of mathematical entities</a> [<a href="http://en.wikipedia.org/wiki/Max_Tegmark">1</a>,<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/reviews/ballard-natural/">2</a>,<a href="http://andrewsullivan.thedailybeast.com/2012/08/ask-jim-holt-anything-your-favorite-philosopher-and-why.html">3</a>]
<li><a href="http://blogs.discovermagazine.com/cosmicvariance/2012/10/22/from-particles-to-people-the-laws-of-nature-and-the-meaning-of-life/">From Particles to People: The Laws of Nature and the Meaning of Life</a> [<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/04/24/the-particle-at-the-end-of-the-universe/">1</a>,<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/11/13/a-book-full-of-particles/">2</a>,<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/10/11/moving-naturalism-forward/">3</a>,<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/10/18/feynman-on-initial-conditions-evolving-laws-and-what-we-consider-physics/">4</a>,<a href="http://science.slashdot.org/story/12/08/01/2127225/entangled-particles-break-classical-law-of-thermodynamics-say-physicists">5</a>]</li></li></li></li></li></ul><a href="http://www.hpcwire.com/hpcwire/2012-10-10/could_the_universe_reveal_itself_as_a_computer_simulation_.html">Could the Universe Reveal Itself as a Computer Simulation?</a> (<a href="http://www.metafilter.com/119883/WHOA-DUDE-ARE-WE-INSIDE-A-COMPUTER-RIGHT-NOW">previously</a>) tag:metafilter.com,2012:site.122400Sat, 01 Dec 2012 00:12:10 -0800kliulessnoncommutative balls in boxes
http://www.metafilter.com/118119/noncommutative%2Dballs%2Din%2Dboxes
<a href="http://golem.ph.utexas.edu/category/2012/07/morton_and_vicary_on_the_categ.html">Morton and Vicary on the Categorified Heisenberg Algebra</a> - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." <blockquote>This insight, that funny facts about quantum mechanics are related to simple facts about balls in boxes, allows us to 'categorify' a chunk of quantum mechanics—including the Heisenberg algebra, which is the algebra generated by the position and momentum operators. Now is not the time to explain what that means. The important thing is that Mikhail Khovanov figured out a seemingly quite different way to categorify the same chunk of quantum mechanics, so there was a big puzzle about how his approach relates to the one I just described. Jeffrey Morton and Jamie Vicary have solved that puzzle.
The big spinoff is this. Khovanov's approach showed that in categorified quantum mechanics, a bunch of new equations are true! These equations are 'higher analogues' of Heisenberg's famous formula
<center><i>pq − qp = −i</i></center>
So, these new equations should be important! ... Now Jeffrey and Jamie have shown how to get these equations just by thinking about balls in boxes... The important thing is this: those equations are not something we get to choose, or make up. They are what they are, and they're just sitting there waiting for us to discover them.</blockquote>btw <a href="https://plus.google.com/u/0/117663015413546257905/posts/7ovL7oxoV5Z">John Baez sez</a>: "<a href="http://arxiv.org/abs/1207.2054">Don't even look at it</a> unless you're an expert in mathematical physics, but it's important - and I think someday it could change our understanding of quantum mechanics." :P (I didn't; I know next to nothing about this stuff, but I found it interesting so I thought I'd share ;) tag:metafilter.com,2012:site.118119Sat, 21 Jul 2012 09:42:04 -0800kliulessThe Art of π, φ and e
http://www.metafilter.com/117319/The%2DArt%2Dof%2Dpi%2Dphi%2Dand%2De
<a href="http://mkweb.bcgsc.ca/pi/art/">The Art of π, φ and <em>e</em></a> The creator of <a href="http://circos.ca/">Circos</a> and <a href="http://www.metafilter.com/110081/Buzzing-about-network-graphs">hive plots</a> plays around with visualizing a few irrational numbers and their odd characteristics. tag:metafilter.com,2012:site.117319Tue, 26 Jun 2012 14:27:04 -0800Blazecock Pileon