MetaFilter posts tagged with numbers and maths
http://www.metafilter.com/tags/numbers+maths
Posts tagged with 'numbers' and 'maths' 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 -0800kliulessbinding 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 -0800kliulessProof 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 -0800kliulessBig (and small) Numbers
http://www.metafilter.com/115929/Big%2Dand%2Dsmall%2DNumbers
<a href="http://fatfonts.org/">FatFonts</a> creates <a href="http://www.newscientist.com/article/mg21428635.500-font-for-digits-lets-numbers-punch-their-weight.html">numerical</a> <a href="http://calculatedimages.blogspot.ca/2012/05/fatfonts.html">fonts</a> where the amount of ink/pixels for each number is in direct proportion to its <a href="http://infosthetics.com/archives/2012/05/fatfonts_new_font_links_value_of_a_number_to_amount_of_pixels.html">value</a>. tag:metafilter.com,2012:site.115929Mon, 14 May 2012 11:09:42 -0800fearfulsymmetryFinite formula found for partition numbers
http://www.metafilter.com/99788/Finite%2Dformula%2Dfound%2Dfor%2Dpartition%2Dnumbers
<a href="http://esciencecommons.blogspot.com/2011/01/new-theories-reveal-nature-of-numbers.html">New math theories reveal the nature of numbers</a> [<a href="http://www.aimath.org/news/partition/folsom-kent-ono.pdf">1</a>,<a href="http://www.aimath.org/news/partition/brunier-ono.pdf">2</a>] - "We prove that <a href="http://blogs.plos.org/badphysics/2011/01/20/ono/">partition numbers</a> are 'fractal' for every prime. <a href="http://www.science20.com/news_articles/partition_numbers_behave_fractals_says_mathematician-75556">These numbers</a>, in a way we make precise, are <a href="http://hiddencause.wordpress.com/2011/01/20/pn-is-a-fractal-when-n-is-prime/">self-similar</a> in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (<a href="http://science.slashdot.org/story/11/01/21/2047229/Eulers-Partition-Function-Theory-Finished">/.</a>|<a href="http://economistsview.typepad.com/economistsview/2011/01/links-for-2011-01-20.html">via</a>) BONUS
<li><a href="http://arstechnica.com/science/news/2011/01/fractals-plus-quantum-mechanics-equals-chaos.ars">Fractals plus quantum mechanics equals chaos</a> - "investigating the properties of light when it is confined to a fractal object"
<li><a href="http://science.slashdot.org/story/11/01/20/1546206/Polynomial-Time-Code-For-3-SAT-Released-PNP">Polynomial Time Code For 3-SAT Released</a> - "This is not a P=NP paper."</li></li> tag:metafilter.com,2011:site.99788Sat, 22 Jan 2011 10:40:18 -0800kliulessPrime Prize
http://www.metafilter.com/60240/Prime%2DPrize
In September 2006 the largest known prime number, <a href="http://primes.utm.edu/largest.html">a 9.8 million digit number</a>, was discovered. If you find one over ten million digits you can win <a href="http://www.eff.org/awards/coop.php">US$100,000</a> (<a href="http://www.mersenne.org/prize.htm">of which you get to keep $50,000</a>). No maths is required - just <a href="http://www.mersenne.org/freesoft.htm">download the software </a>and you're away. Warning: <a href="http://www.mersenne.org/works.htm">it takes about a month to run one primality check</a> so some patience is required. Look out though Cooper and Boone look like they might beat you to it. tag:metafilter.com,2007:site.60240Thu, 12 Apr 2007 17:57:14 -0800meechLet's Party Like It's MCMXCIX
http://www.metafilter.com/54037/Lets%2DParty%2DLike%2DIts%2DMCMXCIX
<a href="http://scienceblogs.com/goodmath/2006/08/roman_numerals_and_arithmetic.php">Roman Numerals and Arithmetic</a> tag:metafilter.com,2006:site.54037Sat, 19 Aug 2006 04:30:40 -0800jack_mo