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Alex Kontorovich

@AlexKontorovich

#Math professor at @RutgersU. Editor-in-Chief of Experimental Mathematics @tandfSTEM. Dean of Academic Content at @MoMath1. Advisory Board at @QuantaMagazine

math.rutgers.edu/~alexk
Vrijeme pridruživanja: studeni 2018.

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    Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
    • Prijavi Tweet

    Collecting here a meta-thread of threads.

    13:09 - 23. ruj 2019.
    • 4 proslijeđena tweeta
    • 29 oznaka „sviđa mi se”
    • Mike Lawler CryptoNarc T Baruah Prakay Cc adn 👣 Patrick Heslin Chetan Ahuja Longest Serving Programmer Sebastian Cioaba
    1 reply 4 proslijeđena tweeta 29 korisnika označava da im se sviđa
      1. Novi razgovor
      2. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on Pi Dayhttps://twitter.com/AlexKontorovich/status/1105291206337138688?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Some people have asked about #PiDay, so here are some thoughts (warning: long-ish thread). The number π ≈ 3.14, that is, the ratio of circumference to diameter of any circle, has continually captivated mankind since at least the ancient Babylonians four millennia ago.
        Prikaži ovu nit
        1 reply 0 proslijeđenih tweetova 0 korisnika označava da im se sviđa
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      3. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on the 3x+1 (Collatz) Conjecturehttps://twitter.com/AlexKontorovich/status/1172715174786228224?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Unpopular opinion: The 3x+1 Conjecture might be False! Here's why I think this may be the case. (thread) My first paper, with Y. Sinai in 2002, https://arxiv.org/abs/math/0601622 … proves that 3x+1 paths are a geometric Brownian motion (in a precise asymptotic sense), with drift log 3/4 < 0
        Prikaži ovu nit
        1 reply 0 proslijeđenih tweetova 2 korisnika označavaju da im se sviđa
        Prikaži ovu nit
      4. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on the origin of Fourier serieshttps://twitter.com/AlexKontorovich/status/1171519369089667072?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        As often happens in mathematics, Fourier was trying to do something completely unrelated when he stumbled on Fourier series. What was it? (thread) He was studying the propagation of heat in a uniform medium. To keep things as simple as possible, say you have a 1-d pipe, (cont'd)
        Prikaži ovu nit
        1 reply 0 proslijeđenih tweetova 2 korisnika označavaju da im se sviđa
        Prikaži ovu nit
      5. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on origins of trigonometry (the Sun and Half-Moon)https://twitter.com/AlexKontorovich/status/1163931635462627328?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Ah both the sun and the (almost) half-moon in the sky! The birthplace of trigonometry! To be a half-moon, the sun-moon-earth triangle has a right angle at the moon. That means we can calculate the relative distances of sun & moon to earth! Point one hand to the sun and (cont’d) pic.twitter.com/qzOpPZkpOJ
        Prikaži ovu nit
        1 reply 1 proslijeđeni tweet 3 korisnika označavaju da im se sviđa
        Prikaži ovu nit
      6. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on the integral int X^s ds/s which arises in the study of the Prime Number Theoremhttps://twitter.com/AlexKontorovich/status/1154047557099773953?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Let's talk about this really fun (not obvious! unless you recently took/taught complex analysis) integral: int X^s ds/s, where X>0 and int is over the vertical line Re(s)=c>0. This could be a fun thing for someone (*ahem*) to animate. The fancy way of thinking about it is... https://twitter.com/3blue1brown/status/1153901399576420352 … pic.twitter.com/BN5PoQAsoi
        Prikaži ovu nit
        1 reply 0 proslijeđenih tweetova 0 korisnika označava da im se sviđa
        Prikaži ovu nit
      7. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on the Prime Number Theoremhttps://twitter.com/AlexKontorovich/status/1153414602966933513?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        What do primes have to do with "e"? (thread) Recall Euler product formula: (1+1/2^s+1/3^s+1/4^s+1/5^s+...)(1-1/2^s)(1-1/3^s)(1-1/5^s)(1-1/7^s)... = 1, (For rigor, need Re(s)>1, but ignore that.) Try it for yourself! Multiply out just the terms above; what's left?... https://twitter.com/3blue1brown/status/1153382098348068865 …
        Prikaži ovu nit
        1 reply 0 proslijeđenih tweetova 0 korisnika označava da im se sviđa
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      8. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on the "mathematics of the seasons"https://twitter.com/AlexKontorovich/status/1138452352481079296?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        With summer coming soon, I was asked to explain the mathematics of the seasons. "The Mathematics of the Seasons, an Ode to Trigonometry" Many creatures on Earth experience seasons, here transitioning from spring towards summer. Why does this actually happen? And how do we know?
        Prikaži ovu nit
        1 reply 0 proslijeđenih tweetova 0 korisnika označava da im se sviđa
        Prikaži ovu nit
      9. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Remembering Jean Bourgain (1954-2018)https://twitter.com/AlexKontorovich/status/1135404522505986051?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Huge thanks again to @the_IAS, @RHDijkgraaf, and organizers Peter Sarnak and Helmut Hofer, for such a touching memorial/celebration of Jean Bourgain. Just incredible to see so many of the world's greatest mathematicians (Fields/Wolf/Abel/Shaw etc laureates) revering him. (Thread)
        Prikaži ovu nit
        1 reply 0 proslijeđenih tweetova 0 korisnika označava da im se sviđa
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      10. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on why sums of three cubes are so poorly understood theoretically (hence recent resurgence in computational progress):https://twitter.com/AlexKontorovich/status/1110591489049010181?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Great @QuantaMagazine article on 33 being the sum of three cubes: https://www.quantamagazine.org/sum-of-three-cubes-problem-solved-for-stubborn-number-33-20190326/ … As a number theorist and fan of primes, I must admit I roll my eyes when a new Mersenne number is found and people get all excited. It's nice for math to get some press and all, (cont'd)
        Prikaži ovu nit
        1 reply 1 proslijeđeni tweet 1 korisnik označava da mu se sviđa
        Prikaži ovu nit
      11. Alex Kontorovich‏ @AlexKontorovich 23. ruj 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on new conjectures about Fibonacci numbers (based on joint work with Jeff Lagarias):https://twitter.com/AlexKontorovich/status/1098076629371441154?s=20 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        1/Spoke today about a fun new conjecture (joint with Lagarias) about Fibonacci numbers, explainable to grade-schoolers: There's a constant we call beta ≈ 0.373365, so that the total number of prime factors of F_{2n}, divided by log n, has lower limit beta https://arxiv.org/pdf/1808.03235.pdf … pic.twitter.com/NZnYoLEx9O
        Prikaži ovu nit
        1 reply 1 proslijeđeni tweet 6 korisnika označava da im se sviđa
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      12. Alex Kontorovich‏ @AlexKontorovich 31. lis 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Thread on decidability of Goldach and Riemann hypothesis (see sub threads for more discussion...)https://twitter.com/alexkontorovich/status/1099015870603558912?s=21 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Always great to hear @stevenstrogatz on @Radiolab, here talking about Godel incompleteness. Just one quibble: if Goldbach is undecidable, then it’s true! Same holds with any finitely-falsifiable statement, and could be an insane way to prove the Riemann hypothesis! (cont’d) https://twitter.com/Radiolab/status/1099007885923766278 …
        Prikaži ovu nit
        1 reply 1 proslijeđeni tweet 3 korisnika označavaju da im se sviđa
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      13. Alex Kontorovich‏ @AlexKontorovich 18. stu 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Not a thread but wanted to record this (came up recently)https://twitter.com/AlexKontorovich/status/1146510081720295426 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Odgovor korisniku/ci @_nilradical
        Langlands program in a tweet: I give you a recipe for coefficients, e.g.: a_{2n} = (-1)^n/n!, a_{odd}=0. Prove that the resulting power series F(x)=1-x^2/2+x^4/4!-x^6/6!+... has “non-obvious” symmetry F(x+2pi)=F(x). “Program”: Discover automorphy F(x)=cos(x). Now generalize
        1 reply 0 proslijeđenih tweetova 1 korisnik označava da mu se sviđa
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      14. Alex Kontorovich‏ @AlexKontorovich 20. stu 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Recording this. Actually I was trying to make a pedagogical point: most intros to Euler characteristic begin “compute V-E+F for a bunch of examples.” But why that, and not V^2+4E-2F^3? How would you discover it on your own? Just plot them all; plane’s normal vector is (1,-1,1).https://twitter.com/AlexKontorovich/status/1197197771310338049 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Take a bunch of your favorite polyhedra and plot them in R^3 at coordinates (#vertices,#edges,#faces). Notice anything? What's the equation of this plane? :) pic.twitter.com/WVBKD99BHQ
        Prikaži ovu nit
        1 reply 2 proslijeđena tweeta 8 korisnika označava da im se sviđa
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      15. Alex Kontorovich‏ @AlexKontorovich 20. stu 2019.
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Was reminded to record this as well. #MTBoS #iteachmathhttps://twitter.com/AlexKontorovich/status/1069288773236723717 …

        Alex Kontorovich je dodan/na,

        Alex Kontorovich @AlexKontorovich
        Teaching little kids Cartesian coordinates pic.twitter.com/O68YCaB3No
        1 reply 0 proslijeđenih tweetova 2 korisnika označavaju da im se sviđa
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      16. Alex Kontorovich‏ @AlexKontorovich 3. sij
        • Prijavi Tweet

        Alex Kontorovich je proslijedio/a tweet korisnika/ceAlex Kontorovich

        Forgot to record this. Adding to meta-thread (so I can find it again later...)https://twitter.com/AlexKontorovich/status/1199018641439830021?s=20 …

        Alex Kontorovich je dodan/na,

        1:06
        Alex Kontorovich @AlexKontorovich
        Why is the Riemann Hypothesis hard? Just one reason (of very many): it's not an analytic question. Here are the values of zeta on the 1/2-line (where at least 40% of the zeros are, all should be) and the 4/5-line, where none should be. The latter gets arbitrarily close to 0, i.o. pic.twitter.com/qSHhwwCY6X
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        0 replies 2 proslijeđena tweeta 3 korisnika označavaju da im se sviđa
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      17. Kraj razgovora

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