MetaFilter posts tagged with Math and logic
http://www.metafilter.com/tags/Math+logic
Posts tagged with 'Math' and 'logic' at MetaFilter.Tue, 09 Jun 2015 22:40:35 -0800Tue, 09 Jun 2015 22:40:35 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60HoTT 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 -0800kliulessThe roads ahead are long and winding...
http://www.metafilter.com/149311/The%2Droads%2Dahead%2Dare%2Dlong%2Dand%2Dwinding
<a href="http://www.theincrediblecompany.com/try-alcazar" title="In-browser, playable version">Alcazar is a neat little path-finding logic game.</a> There are also <a href="http://www.theincrediblecompany.com/alcazar-1/" title="pencil and paper is best">printable puzzles, strategy tips and metapuzzles</a> to be had. The author has a two-part post (<a href="http://edderiofer.blogspot.com/2014/11/on-subject-of-parity-when-we-refer-to.html">Part 1</a>,<a href="http://edderiofer.blogspot.com/2014/11/parity-in-alcazar-and-other-such-loop.html"> Part 2</a>) on the use of parity in the puzzle, and another author writes briefly about <a href="http://ravensoft.tumblr.com/post/105861925602/alcazar-is-an-amazing-puzzle-game-that-can-teach">programming and problem-solving skills.</a> tag:metafilter.com,2015:site.149311Sat, 02 May 2015 05:07:38 -0800WolfdogStill Combining Numbers On A Grid To Get Bigger Numbers, But Different
http://www.metafilter.com/145164/Still%2DCombining%2DNumbers%2DOn%2DA%2DGrid%2DTo%2DGet%2DBigger%2DNumbers%2DBut%2DDifferent
<a href="http://www.veewo.com/games/get10/">Get 10</a> is a new browser game from veewo, creators of <em>1024</em>. tag:metafilter.com,2014:site.145164Tue, 09 Dec 2014 00:12:41 -0800RinkuA 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 -0800kliulessComputerized 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 -0800kliulessMaking Math Fun
http://www.metafilter.com/119620/Making%2DMath%2DFun
Is your elementary school youngster struggling with math? Are they a visual person? Would math games and videos help them learn? Enter <a href="http://www.mathplayground.com/">Math Playground</a>, to assist with problem solving and real world math. Try the enticing logic game <a href="http://www.mathplayground.com/logic_sugarsugar.html">Sugar, Sugar</a> or beef up your <a href="http://www.mathplayground.com/wpdatabase/wpindex.html">math word problem</a> skills. There are plenty of <a href="http://www.mathplayground.com/games.html">games</a> to help educate while entertaining. tag:metafilter.com,2012:site.119620Tue, 04 Sep 2012 16:34:21 -0800netbrosbons mots, poems, math, knitting and logic
http://www.metafilter.com/119002/bon%2Dmots%2Dpoems%2Dmath%2Dknitting%2Dand%2Dlogic
<a href="https://www.dpmms.cam.ac.uk/~tf/liszt.html">Entertaining, collected bon mots</a> and<a href="https://www.dpmms.cam.ac.uk/~tf/poem10.html"> surprisingly interesting, collected poems</a> by various authors. From <a href="https://www.dpmms.cam.ac.uk/~tf/">a likable math brainiac's site</a>, Dr T.E. Forster, a Cambridge University lecturer. He also<a href="https://www.dpmms.cam.ac.uk/~tf/squarenew.html"> knits</a> and writes <a href="https://www.dpmms.cam.ac.uk/~tf/BILAPintro.pdf">about Buddhist logic</a> [pdf]. Bonus, there's<a href="https://www.dpmms.cam.ac.uk/~tf/louisesbrain.gif"> a fun gif</a>. tag:metafilter.com,2012:site.119002Thu, 16 Aug 2012 20:00:52 -0800nickyskyeG.H. Hardy reviews Principia Mathematica
http://www.metafilter.com/107360/GH%2DHardy%2Dreviews%2DPrincipia%2DMathematica
<a href="http://www.cl.cam.ac.uk/~ns441/files/hardy-principia.pdf">"Perhaps twenty or thirty people in England may be expected to read this book."</a> G.H. Hardy's review of Whitehead and Russell's <em>Principia Mathematica</em>, published in the Times Literary Supplement 100 years ago last week. "The time has passed when a philosopher can afford to be ignorant of mathematics, and a little perseverance will be well rewarded. It will be something to learn how many of the spectres that have haunted philosophers modern mathematics has finally laid to rest." tag:metafilter.com,2011:site.107360Mon, 12 Sep 2011 14:37:37 -0800escabecheKill Math
http://www.metafilter.com/105839/Kill%2DMath
<a href="http://worrydream.com/KillMath/">Bret Victor on WorryDream</a> The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols.
When most people speak of Math, what they have in mind is more its mechanism than its essence. This "Math" consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result. The process is not unlike casting lots. tag:metafilter.com,2011:site.105839Sun, 24 Jul 2011 06:47:20 -0800naightOnline statistics textbook
http://www.metafilter.com/94566/Online%2Dstatistics%2Dtextbook
Interested in teaching yourself some statistics? Here is an excellent online and interactive <a href="http://statistics.berkeley.edu/~stark/SticiGui/">statistics textbook</a> developed at UC Berkeley, and also used at CUNY, UCSC, SJSU, and Bard. Here is the <a href="http://statistics.berkeley.edu/~stark/Teach/S21/Su10/">syllabus</a> for the course at Berkeley. And here are some insightful <a href="http://www.samefacts.com/2010/08/technology-and-society/online-education-notes-from-the-field/">reflections</a> from the professor on developing Berkeley's first fully approved online course. tag:metafilter.com,2010:site.94566Mon, 09 Aug 2010 09:23:30 -0800AceRockAll Gnytte Long
http://www.metafilter.com/88291/All%2DGnytte%2DLong
<a href="http://web.mit.edu/puzzle/www/09/puzzles/the_sexaholics_of_truthteller_planet/PUZZLE/">The Sexaholics of Truthteller Planet</a> - yes, it's one of those rotten logic problems, one of many that can be found at Tanya Khovanova's <a href="http://blog.tanyakhovanova.com/?p=181">Math Guide to the MIT Mystery Hunt</a>. tag:metafilter.com,2010:site.88291Wed, 13 Jan 2010 09:16:38 -0800WolfdogI am a strange loop.
http://www.metafilter.com/82063/I%2Dam%2Da%2Dstrange%2Dloop
<a href="http://prelectur.stanford.edu/lecturers/hofstadter/excerpts.html">Douglas Hofstadter's</a> <em><a href="http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach">Gödel, Escher, Bach: An Eternal Golden Braid</a></em> has been recorded as <a href="http://ocw.mit.edu/OcwWeb/hs/geb/VideoLectures/">a series of video lectures</a> for MIT's <a href="http://ocw.mit.edu/OcwWeb/web/home/home/index.htm">Open Courseware</a> project. tag:metafilter.com,2009:site.82063Sat, 30 May 2009 21:30:41 -0800loquaciousThe Mathemagician and Pied Puzzler, and others
http://www.metafilter.com/75321/The%2DMathemagician%2Dand%2DPied%2DPuzzler%2Dand%2Dothers
<a href="http://www.g4g4.com/paul/BOOK.pdf"><i>The Mathemagician and Pied Puzzler</i></a> <small>(PDF, rough table of contents <a href="http://www.worldcat.org/oclc/40338600?tab=details">here</a>)</small> is a collection of puzzles created by members of the <a href="http://www.g4g4.com/">Gathering 4 Gardner Foundation</a>, in tribute to <a href="http://www.csicop.org/si/9803/gardner.html">the man himself</a> <small>(<a href="http://www.metafilter.com/mefi/21286">previously</a>)</small>. Also freely available at the G4G site is <em><a href="http://www.g4g4.com/pc/pc92.pdf">Puzzle Craft</a></em> <small>(PDF)</small>, by Stewart Coffin. <small>(<em>The Puzzling World of Polyhedral Dissections</em>, also by Coffin, is available <a href="http://www.johnrausch.com/PuzzlingWorld/default.htm">here</a>.)</small> tag:metafilter.com,2008:site.75321Wed, 01 Oct 2008 19:21:50 -0800cog_nateGeek Logik - math for every day
http://www.metafilter.com/56110/Geek%2DLogik%2Dmath%2Dfor%2Devery%2Dday
Geek Logik is <a href="http://www.powells.com/tqa/sundem.html">Garth Sundem</a>'s <a href="http://www.amazon.com/exec/obidos/ASIN/0761140212/metafilter-20/ref=nosim/">book </a>& <a href="http://geeklogik.blogspot.com">blog</a> about equations for every day living, including <a href="http://geeklogik.blogspot.com/2006/10/how-many-cups-of-coffee-do-you-need-to.html ">how many cups of coffee you require to be functional</a>, <a href="http://geeklogik.blogspot.com/2006/10/who-should-you-vote-for.html">who to vote for</a>, and others. tag:metafilter.com,2006:site.56110Tue, 07 Nov 2006 09:47:20 -0800xmutexWho has the fish?
http://www.metafilter.com/44031/Who%2Dhas%2Dthe%2Dfish
<a href="http://www.coudal.com/thefish.php">Who has the fish?</a> Einstein logic puzzle. If I can do it, you guys can. tag:metafilter.com,2005:site.44031Thu, 04 Aug 2005 15:22:41 -0800swiftNature of Mathematical Truth
http://www.metafilter.com/43828/Nature%2Dof%2DMathematical%2DTruth
<a href="http://www.edge.org/3rd_culture/vhd05/vhd05_index.html">Gödel and the Nature of Mathematical Truth</a> : A Talk with Verena Huber-Dyson tag:metafilter.com,2005:site.43828Fri, 29 Jul 2005 10:24:24 -0800GyanYou can't prove this title wasn't an attempt to illustrate Godel
http://www.metafilter.com/43130/You%2Dcant%2Dprove%2Dthis%2Dtitle%2Dwasnt%2Dan%2Dattempt%2Dto%2Dillustrate%2DGodel
Godel's theorems have been used to extrapolate a great <a href="http://www.sm.luth.se/~torkel/eget/godel.html">many</a> "truths" about the world. <a href="http://www.sm.luth.se/%7Etorkel/">Torkel Franzen</a> sets the record <a href="http://www.ucalgary.ca/~rzach/logblog/2005/06/franzn-on-use-and-abuse-of-gdels.html">straight</a> in his new book <a href="http://www.amazon.com/exec/obidos/ASIN/1568812388/metafilter-20/ref=nosim/">Godel's Theorem: An Incomplete Guide to Its Use and Abuse</a>. Read the <a href="http://www.sm.luth.se/~torkel/eget/tic.html">introduction</a> (PDF). If you want, check out his <a href="http://www.sm.luth.se/~torkel/eget/godel/theorems.html">explanation</a> of the theorems. tag:metafilter.com,2005:site.43130Wed, 29 Jun 2005 02:59:04 -0800GyanThe Complexity of a Controversial Concept
http://www.metafilter.com/42922/The%2DComplexity%2Dof%2Da%2DControversial%2DConcept
<a href="http://bactra.org/bulletin/logic-of-diversity.html">The Logic of Diversity</a> "A new book, <i>The Wisdom of Crowds</i> [<a href="http://www.metafilter.com/mefi/33307">..:</a>] by <a href="http://greg.org/archive/new_yorker_magazine_database.php">The New Yorker</a> columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to <a href="http://www.cscs.umich.edu/~spage/">Page's results</a>. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [<a href="http://www.randomhouse.com/features/wisdomofcrowds/contest.html">...</a>] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the <a href="http://en.wikipedia.org/wiki/Central_limit_theorem">central limit theorem</a> of statistics — it's far from being the only way in which <a href="http://www.cscs.umich.edu/diversity/">diversity</a> can be beneficial in problem solving." <a href="http://bactra.org/weblog/362.html">(Three-Toed Sloth)</a> tag:metafilter.com,2005:site.42922Mon, 20 Jun 2005 18:03:37 -0800kliulessPuzzleFilter.
http://www.metafilter.com/34927/PuzzleFilter
<a href="http://www.geocities.com/bob_kraus_2000/">"WARNING!!! The puzzles on this site are very difficult,</a> and most require the use of a good spreadsheet program in order to solve them. It will take many hours, perhaps days, to solve each puzzle..." tag:metafilter.com,2004:site.34927Wed, 11 Aug 2004 21:08:52 -0800limitedpieWhat Color is My Hat?
http://www.metafilter.com/7906/What%2DColor%2Dis%2DMy%2DHat
<a href="http://www.worlds-fastest-website.com/why-mathematicians-care-about-hat-color.htm">What Color is My Hat?</a> I [heart] these mathematical conundrums -- simple, easy-to-state, seemingly obvious logic problems that have solutions that completely defy common sense. Here's another you can spring on a friend: "You want to fry up three pieces of french toast. You have a frying pan that is just large enough to accomodate two pieces of bread at a time. If it takes you 30 seconds to fry one side of bread, and each piece of must be fried on both sides, how long will it take you to cook up three pieces (assuming that the act of flipping a piece or adding/ removing it to or from the pan takes no time). Think about it. Answer inside. tag:metafilter.com,2001:site.7906Fri, 25 May 2001 10:22:29 -0800Shadowkeeper