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Robert Langlands, who linked number theory, analysis, and geometry (2015)
- fouc 9y agoIt's about Robert Langlands of https://en.wikipedia.org/wiki/Langlands_program https://en.wikipedia.org/wiki/Langlands_program >linking math’s main branches — number theory (once called arithmetic), harmonic analysis, which includes calculus, and geometry. >To mathematicians, this is mind-blowing stuff. The branches deal with completely different things: number theory is about, yes, numbers, harmonic analysis studies motion and geometry deals with shapes. They may as well be different planets.
- naasking 9y agoDifferent planets on which you find all of Shakespeare's works, depsite no apparent common origin.
- 7dare 9y agoI think that may be an exxageration. I study maths at a much lower level and the teacher regarily points out links between these domains. I believe number theory is already strongly linked with analysis.
- whatshisface 9y agoThose links only became apparent after centuries of development in total isolation. Now that we know they are there, we involve them in teaching because they change how we see things.
- ginnungagap 9y agoFor the Langlands program he was awarded the Abel prize just a few weeks ago, following the link "Read more about Robert P. Langlands" at the end of the official page [1] for the Abel prize you can read a short and informal explanation of his work written by Alex Bellos [1] http://www.abelprize.no/nyheter/vis.html?tid=73025 http://www.abelprize.no/nyheter/vis.html?tid=73025
- dang 9y agoDiscussed a bit at https://news.ycombinator.com/item?id=16632364 https://news.ycombinator.com/item?id=16632364.
- cobbzilla 9y agoTangentially related, Jakow Trachtenberg invented a new and much faster system for mental arithmetic [1] while imprisoned in a Nazi concentration camp. It's a far cry from Common Core math, not easy to learn but once you know it, wow, you can multiply arbitrary 3-digit numbers in your head nearly instantly. 4-digits and higher gets a little trickier but the mental difficulty increases slowly. [1] https://en.m.wikipedia.org/wiki/Trachtenberg_system https://en.m.wikipedia.org/wiki/Trachtenberg_system
- y7 9y agoHow is this related?
- aje403 9y agoTangentially related as well, I had 1 blueberry muffin for breakfast and 2 slices of bacon
- jimmy1 9y agoSide bacon or belly bacon?
- cobbzilla 9y agoThinking in a brand new way about Math, a way no one else has, to come up with novel new connections?
- nkoren 9y agoArithmetic is to mathematics as typing is to being a writer. If the subject of an article is a brilliant author, then a cool new keyboard that makes it easier to type really isn't related, not even tangentially.
- jchook 9y agoHowever, tangents themselves are part of geometry, which is tangentially related to Langlands' work.
- jesuslop 9y agoThe book of Frenkel (the guy of the photo), Love and Math, is one way to go from zeto to not being 100% clueless about the Langlands program, and enjoy the time at the same time. Very likable.
- Koshkin 9y agoA somewhat accessible account of the Langlands Program can be found in Edward Frenkel's book Love & Math.
- mathgenius 9y agoHere is Frenkel giving a talk on the geometric Langlands program [1]. I wouldn't say it is "accessible", but if you have seen some physics maybe give it a go. [1] "What Do Fermat's Last Theorem and Electro-magnetic Duality Have in Common?" http://online.itp.ucsb.edu/online/bblunch/frenkel/ http://online.itp.ucsb.edu/online/bblunch/frenkel/
- jessup 9y agoA lecture series by Langlands for a lay audience: https://video.ias.edu/The-Practice-of-Mathematics https://video.ias.edu/The-Practice-of-Mathematics The video is not great, but the content. From the summary: "In spite of forty years as a mathematician, I have difficulty describing these problems, even to myself, in a simple, cogent and concise manner that makes it clear what is wanted and why. As a possible, but only partial, remedy I thought I might undertake to explain them to a lay audience."
- hyperpallium 9y ago> If it works out, I would like to continue in following years on classical fluid mechanics and turbulence Since it's dated 1999, I guesss he didn't continue with fluid mechanics?
- Brozilean 9y agoHahaha I love how the title of this post implies the idea that the idea of a Canadian being a good mathematician is a shocker. In my head I read it the same as "John, an octopus, is the world's greatest mathematician".
- jessriedel 9y agoThe Star is a Canadian publication. The clear interpretation is of national pride.
- ajeet_dhaliwal 9y agoStill somewhat over the top. They mention he’s a Canadian three times in the first half of the article. In case you missed it, he’s a Canadian. Although looking him up it seems he’s also an American.
- vanjoe 9y agoIt's kinda like Alexander Graham Bell, claimed by the Scots (in England they call him British) the Canadians and the Americans.
- jaclaz 9y ago>It's kinda like Alexander Graham Bell, claimed by the Scots (in England they call him British) the Canadians and the Americans. ... and "universally" (i.e. by the British, the Canadians and the US people) attributed the invention of the telephone, which was invented by an Italian, instead ... https://www.theguardian.com/world/2002/jun/17/humanities.internationaleducationnews https://www.theguardian.com/world/2002/jun/17/humanities.int... Though the Canadians are still not convinced: https://en.wikipedia.org/wiki/Antonio_Meucci#2002_U.S._Congressional_resolution https://en.wikipedia.org/wiki/Antonio_Meucci#2002_U.S._Congr...
- Naritai 9y agoYes, it's a little over the top. But as a Canadian, I can say that Canadian publications (especially left-of-center ones like the Star) tend to be a little nationalistic whenever a local does well. It's a natural response to the brain drain of many talented Canadians to our neighbor to the south.
- charlescearl 9y agoIt is inspirational that he is still active at 80+. Frankel’s videos are great, though I am still building to a real grasp of Langlands work.
- mathgenius 9y agoSomewhat randomly, I've been working with a mathematician that has convinced me to study the Langlands program with him. I feel ill-equipped for the journey, having boycotted number theory ever since they tried to get me to learn the multiplication table. But on the other hand, there is plenty of geometry involved! Who would have thought that the dodecahedron is involved with solving the quintic? It really does seem like this area (the Langlands program) is at a vast nexus of many different branches of mathematics. It's intense.
- goldenkey 9y agoShapes just come about when you are talking about objects with certain types of symmetries. One of the main "attacks" on polynomials is to realize that their roots are related to eachother, in terms of total, product, difference, etc. The simplest of these methods is just Vieta's formulas: https://en.wikipedia.org/wiki/Vieta%27s_formulas https://en.wikipedia.org/wiki/Vieta%27s_formulas I highly recommend Edward Frenkel's book, Love and Math. It was a great read about the mathematics itself, and also his troubles as a Jewish academic in Soviet Russia. Love and Math: https://amzn.to/2qcqUb4 https://amzn.to/2qcqUb4
- mathgenius 9y agoRight, but the dodecahedron is a modular curve, and I'm guessing this is how Hermite came up with the solution to the quintic using modular functions in 1858. If there are any real number theorists here they might be able to clarify this some more. Modular functions, modular forms, automorphic forms, these are all key ingredients of the Langlands program.
- goldenkey 9y agoI believe you're talking about the free algebras on groups of modular forms of a certain 'weight.' That's not exactly the modular forms themselves. Here's some more information: https://johncarlosbaez.wordpress.com/2017/12/31/quantum-mechanics-and-the-dodecahedron/ https://johncarlosbaez.wordpress.com/2017/12/31/quantum-mech...
- MaysonL 9y agoHis seminal paper, Problems in the Theory of Automorphic Forms is here: https://publications.ias.edu/sites/default/files/problems-in-the-theory-of-automorphic-forms.pdf https://publications.ias.edu/sites/default/files/problems-in...
- oggyhead 9y agoWasn't Category theory supposed to unify everything? Has it failed in doing so?
- qmalzp 9y agoCategory theory is basically a language. If one wanted to formulate an explicit conjecture corresponding to the original Langlands program, it could possibly be phrased as some kind of equivalence of a category of automorphic representations and a category of motives. Precisely defining those two categories is the hard part. So even with this language, one still has to do the work of actually proving these things. It's like having a nice programming language; you still have to write the code to do the thing!
- oggyhead 9y agoI see.thanks for the info and light
- Aspos 9y ago> “What normal person cares whether the square root of two is a rational number?” egh, is it?
- vladTheInhaler 9y agoThe way the title is formatted made me think this would be an obituary. I'm really glad that's not the case.
- kirkules 9y agoWhat's the intended purpose of this article? Why was it written? It's always frustrating to read pieces about mathematicians written by people whose attitude is "[I have no chance of ever grasping what ultimately makes this article possible]" and "'[Cartesian geometry?] I can recall sitting in that class,' I said, lying.". I know writing such things is often supposed to make the article more palatable to a lay audience who probably feels the same way, but honestly all it accomplishes is reinforcing to that audience that mathematics is an esoteric topic for geniuses. This kind of article, which pretends to be bringing mathematics to the masses, is just another one of the reasons students feel so comfortable incessantly returning to saying "I'm not a math person" instead of being empowered whenever they have some success with math. This is so frustrating because of course I approve of the apparent motivation behind writing an article like this.