MetaFilter posts tagged with Math and numbertheory
http://www.metafilter.com/tags/Math+numbertheory
Posts tagged with 'Math' and 'numbertheory' at MetaFilter.Fri, 05 Aug 2016 17:35:03 -0800Fri, 05 Aug 2016 17:35:03 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Monumental Proof to Torment Mathematicians for Years to Come
http://www.metafilter.com/161450/Monumental%2DProof%2Dto%2DTorment%2DMathematicians%2Dfor%2DYears%2Dto%2DCome
Nearly four years after Shinichi Mochizuki (<a href="http://www.metafilter.com/153893/The-likelihood-that-theres-interesting-or-important-math-is-pretty-high">previously</a>, <a href="http://www.metafilter.com/127954/Proof-and-Community-Standards">previously</a>, <a href="http://www.metafilter.com/119847/Mathematics-world-abuzz-with-a-proof-of-the-ABC-Conjecture">previously</a>) unveiled an imposing set of papers (<a href="http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf">1</a>, <a href="http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20II.pdf">2</a>, <a href="http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf">3</a>, <a href="http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf">4</a>) that could revolutionize the theory of numbers, other mathematicians have yet to understand his work or agree on its validity — <a href="http://www.nature.com/news/monumental-proof-to-torment-mathematicians-for-years-to-come-1.20342">although they have made modest progress</a>.</a> Some <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8663">four dozen mathematicians converged last week</a> for a rare opportunity to hear Mochizuki present his own work at a conference on his home turf, Kyoto University's Research Institute for Mathematical Sciences (RIMS).
Mochizuki's theorem aims to prove the important <a href="https://en.wikipedia.org/wiki/Abc_conjecture">abc conjecture</a>, which dates back to 1985 and relates to prime numbers.
<a href="https://www.newscientist.com/article/2099534-mathematicians-finally-starting-to-understand-epic-abc-proof/">The glimmer of understanding</a> that has started to emerge is well worth the effort, says [University of Nottingham's Ivan] Fesenko. "I expect that at least 100 of the most important open problems in number theory will be solved using Mochizuki's theory and further development." tag:metafilter.com,2016:site.161450Fri, 05 Aug 2016 17:35:03 -0800stinkfootWhat else have we missed about the primes?
http://www.metafilter.com/157880/What%2Delse%2Dhave%2Dwe%2Dmissed%2Dabout%2Dthe%2Dprimes
<a href="https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/">Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them.</a> tag:metafilter.com,2016:site.157880Mon, 14 Mar 2016 04:13:49 -0800Proofs and RefutationsThe emperor was naked, and so is this.
http://www.metafilter.com/155378/The%2Demperor%2Dwas%2Dnaked%2Dand%2Dso%2Dis%2Dthis
<em>"Respected research math is dominated by men of a certain attitude. Even allowing for individual variation, there is still a tendency towards an oppressive atmosphere, which is carefully maintained and even championed by those who find it conducive to success."</em> Recent Princeton graduate Piper Harron's PhD thesis isn't written for these men. It is very cool number theory, and <a href="http://www.theliberatedmathematician.com/wp-content/uploads/2015/11/PiperThesisPostPrint.pdf">it is art.</a> tag:metafilter.com,2015:site.155378Tue, 08 Dec 2015 21:24:32 -0800bergamot and vetiverThe likelihood that there's interesting or important math is pretty high
http://www.metafilter.com/153893/The%2Dlikelihood%2Dthat%2Dtheres%2Dinteresting%2Dor%2Dimportant%2Dmath%2Dis%2Dpretty%2Dhigh
<a href="http://www.nature.com/news/the-biggest-mystery-in-mathematics-shinichi-mochizuki-and-the-impenetrable-proof-1.18509">Shinichi Mochizuki and the impenetrable proof</a> - "Fesenko has studied Mochizuki's work in detail over the past year, visited him at RIMS again in the autumn of 2014 and says that he has now verified the proof. (The other three mathematicians who say they have corroborated it have also spent considerable time working alongside Mochizuki in Japan.) The overarching theme of inter-universal geometry, as Fesenko describes it, is that one must look at whole numbers in a different light — leaving addition aside and seeing the multiplication structure as something malleable and deformable. Standard multiplication would then be just one particular case of a family of structures, just as a circle is a special case of an ellipse." (<a href="https://www.newscientist.com/article/dn26753-mathematicians-anger-over-his-unread-500-page-proof/">previously</a>: <a href="http://www.metafilter.com/119847/Mathematics-world-abuzz-with-a-proof-of-the-ABC-Conjecture">1</a>,<a href="http://www.metafilter.com/127954/Proof-and-Community-Standards">2</a>; <a href="https://twitter.com/Noahpinion/status/652145064043347968">via</a>) <blockquote>"Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space," [<a href="http://www.metafilter.com/user/21049">mefi's own</a>] number theorist Jordan Ellenberg, of the University of Wisconsin–Madison, wrote <a href="https://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/">on his blog</a> a few days after the paper appeared.</blockquote>
also btw...
-<a href="http://www.nature.com/news/maths-whizz-solves-a-master-s-riddle-1.18441">UCLA mathematician Terence Tao has produced a solution to the Erdős discrepancy problem</a> [<a href="http://arxiv.org/abs/1509.05363">1</a>,<a href="https://terrytao.wordpress.com/2015/09/11/the-erdos-discrepancy-problem-via-the-elliott-conjecture/">2</a>,<a href="https://plus.google.com/+DavidRoberts/posts/edR1nqyTGxX">3</a>]
-<a href="https://www.youtube.com/watch?v=XFDM1ip5HdU">What does it feel like to invent math</a>?<a href="http://www.metafilter.com/135502/An-infinite-number-of-mathematicians-walk-into-a-bar#5366342">*</a> tag:metafilter.com,2015:site.153893Fri, 16 Oct 2015 09:34:05 -0800kliuless"Where is the door?"
http://www.metafilter.com/146501/Where%2Dis%2Dthe%2Ddoor
<a href="http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty">Profile: Breaking down the problem of bound gaps [New Yorker]:</a> After graduating with a Ph.D. in algebraic geometry from Purdue in 1991, Yiting Zhang kept the books for a friend's Subway franchise and found other odd jobs before taking up a part-time calculus teaching position at the University of New Hampshire in 1999.
<blockquote>"For years, I didn't really keep up my dream in mathematics," he said.<br><br>
"You must have been unhappy."<br><br>
He shrugged. "My life is not always easy," he said.</blockquote>
He published one paper in 2001. Then, in 2013, he submitted "<a href="http://ir.nmu.org.ua/bitstream/handle/123456789/23842/c18a29be5bb5b86f1bbeaa8616a7fe42.pdf?sequence=1">Bounded Gaps Between Primes</a>" to <i>Annals of Mathematics</i>, one of the most prestigious journals in the field, which contained a proof for a finite bound within which there exist an infinite number of pairs of primes. It was a stunning mathematical breakthrough. An excerpt on the many interesting types of primes:
<blockquote>Prime numbers have so many novel qualities, and are so enigmatic, that mathematicians have grown fetishistic about them. Twin primes are two apart. Cousin primes are four apart, sexy primes are six apart, and neighbor primes are adjacent at some greater remove. From "Prime Curios!," by Chris Caldwell and G. L. Honaker, Jr., I know that an absolute prime is prime regardless of how its digits are arranged: 199; 919; 991. A beastly prime has 666 in the center. The number 700666007 is a beastly palindromic prime, since it reads the same forward and backward. A circular prime is prime through all its cycles or formulations: 1193, 1931, 9311, 3119. There are Cuban primes, Cullen primes, and curved-digit primes, which have only curved numerals—0, 6, 8, and 9. A prime from which you can remove numbers and still have a prime is a deletable prime, such as 1987. An emirp is prime even when you reverse it: 389, 983. Gigantic primes have more than ten thousand digits, and holey primes have only digits with holes (0, 4, 6, 8, and 9). There are Mersenne primes; minimal primes; naughty primes, which are made mostly from zeros (naughts); ordinary primes; Pierpont primes; plateau primes, which have the same interior numbers and smaller numbers on the ends, such as 1777771; snowball primes, which are prime even if you haven't finished writing all the digits, like 73939133; Titanic primes; Wagstaff primes; Wall-Sun-Sun primes; Wolstenholme primes; Woodall primes; and Yarborough primes, which have neither a 0 nor a 1.</blockquote>
<a href="http://www.metafilter.com/128049/Quite-a-day-for-analytic-number-theory">Previously on Metafilter.</a> tag:metafilter.com,2015:site.146501Tue, 27 Jan 2015 08:29:12 -0800ilicetbinding 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 -0800kliulessQuite a day for analytic number theory
http://www.metafilter.com/128049/Quite%2Da%2Dday%2Dfor%2Danalytic%2Dnumber%2Dtheory
This afternoon, Yitang Zhang of the University of New Hampshire gave a special seminar at Harvard, <a href="http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989">in which he announced that he had proved that there are infinitely many pairs of prime numbers separated by no more than 70,000,000</a>, a result differing only by a constant factor from the venerable <a href="http://mathworld.wolfram.com/TwinPrimeConjecture.html">twin prime conjecture</a>. Dan Goldston, who together with Yildirim and Pintz made the last major advance on prime gaps, said, ""I was doubtful I would ever live to see this result." Not enough excitement for one day? Harald Helfgott has just posted to the arXiv <a href="http://arxiv.org/abs/1305.2897">a proof of the ternary Goldbach conjecture:</a> every odd number is the sum of three primes. tag:metafilter.com,2013:site.128049Mon, 13 May 2013 20:26:12 -0800escabecheProof 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 -0800painqualeWhat is the smallest prime?
http://www.metafilter.com/120047/What%2Dis%2Dthe%2Dsmallest%2Dprime
<a href="http://arxiv.org/abs/1209.2007">What is the smallest prime?</a> "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime." tag:metafilter.com,2012:site.120047Tue, 18 Sep 2012 13:42:13 -0800escabecheFinite 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 -0800kliulessNever tell me the odds.
http://www.metafilter.com/98217/Never%2Dtell%2Dme%2Dthe%2Dodds
<a href="http://jmanton.wordpress.com/2010/06/04/measure-theoretic-probability-why-should-it-be-learnt-and-how-to-get-started/">Measure-theoretic probability: Why it should be learnt and how to get started.</a> The <a href="http://www.johndcook.com/distribution_chart.html">clickable chart of distribution relationships.</a> Just two of the interesting and informative probability resources I've learned about, along with countless other tidbits of information, from statistician <a href="http://www.johndcook.com/">John D. Cook</a>'s <a href="http://www.johndcook.com/blog/">blog</a> and his probability fact-of-the-day Twitter feed <a href="http://twitter.com/ProbFact">ProbFact</a>. John also has daily tip and fact Twitter feeds for <a href="http://twitter.com/SansMouse">Windows keyboard shortcuts</a>, <a href="http://twitter.com/RegexTip">regular expressions</a>, <a href="http://twitter.com/TeXtip">TeX and LaTeX</a>, <a href="http://twitter.com/AlgebraFact">algebra and number theory</a>, <a href="http://twitter.com/TopologyFact">topology and geometry</a>, <a href="http://twitter.com/AnalysisFact">real and complex analysis</a>, and beginning tomorrow, <a href="http://twitter.com/CompSciFact">computer science</a> and <a href="http://twitter.com/StatFact">statistics</a>. tag:metafilter.com,2010:site.98217Sun, 05 Dec 2010 11:15:08 -0800grouseIt's not every day that you hear the proof of the century
http://www.metafilter.com/95204/Its%2Dnot%2Devery%2Dday%2Dthat%2Dyou%2Dhear%2Dthe%2Dproof%2Dof%2Dthe%2Dcentury
<a href="http://video.google.com/videoplay?docid=8269328330690408516#">1996 BBC documentary of the proof of Fermat's last theorem is now a Google video.</a> <a href="http://www.simonsingh.com/Behind_the_Scenes.html">John [Lynch] began researching the project, but Wiles was being very elusive. Although John did not know it, the flaw in Wiles's proof had been found, which is why Wiles was in hiding. Eventually the existence of the flaw emerged, and the TV project was abandoned</a>
A year or so later, the flaw was fixed...
<a href="http://www.simonsingh.com/The_TV_Film.html">More at SimonSingh.com.</a> tag:metafilter.com,2010:site.95204Sat, 28 Aug 2010 12:04:23 -0800Obscure ReferenceMore than you ever wanted to know about nothing at all
http://www.metafilter.com/53532/More%2Dthan%2Dyou%2Dever%2Dwanted%2Dto%2Dknow%2Dabout%2Dnothing%2Dat%2Dall
<a href="http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM">The Zero Saga</a> contains a great deal of information about the concept of zero, and its relation to other numbers and concepts in mathematics. It was linked in <a href="http://scienceblogs.com/goodmath/2006/07/zero.php">Good Math, Bad Math</a>; which contains a variety of other informative articles on the <a href="http://scienceblogs.com/goodmath/2006/08/e_the_unnatural_natural_number_1.php">numbers</a> that capture our <a href="http://scienceblogs.com/goodmath/2006/08/i.php">imaginations</a>. <small>(<strong>Note:</strong> You may want to skip past part 4 of the Zero Saga, as it contains replies to the site, and as such should probably be at the bottom of the page. But, to compensate, the comments on Good Math are better than most blogs I've read.)</small> tag:metafilter.com,2006:site.53532Thu, 03 Aug 2006 06:39:23 -0800Eideteker...almost, but not quite, entirely unlike tea.
http://www.metafilter.com/50428/almost%2Dbut%2Dnot%2Dquite%2Dentirely%2Dunlike%2Dtea
"...the answer to Life, the Universe, and Everything is..." "Yes? Yes!?" <a href="http://www.seedmagazine.com/news/2006/03/prime_numbers_get_hitched.php">"...42."</a><br><small>via Dyson, Montgomery, Princeton, a cup of tea - as presented by <a href="http://www.seedmagazine.com/">Seed Magazine.</a></small> tag:metafilter.com,2006:site.50428Tue, 28 Mar 2006 01:32:01 -0800loquaciousWho can name the bigger number?
http://www.metafilter.com/50105/Who%2Dcan%2Dname%2Dthe%2Dbigger%2Dnumber
<a href="http://www.scottaaronson.com/writings/bignumbers.html">Who can name the bigger number?</a> I guarantee you will lose to the Busy Beavers. (No, infinity is not allowed, the bigger infinity is a <a href="http://en.wikipedia.org/wiki/Aleph_number">different game.</a>) The author also <a href="http://www.scottaaronson.com/blog/2006/02/lord-send-no-sign.html">debunks</a> in very simple terms the recent story that quantum computers perform calculations <a href="http://www.news.uiuc.edu/news/06/0222quantum.html">without being turned on</a>. My first post and disclaimer: I know the author from our mutual field of <a href="http://www.cs.caltech.edu/~westside/quantum-intro.html">quantum information</a>. tag:metafilter.com,2006:site.50105Thu, 16 Mar 2006 00:16:49 -0800gregv