Number Theory News

  • Andrew Wiles is the recipient of this year’s Abel Prize. I have to confess that I found this surprising, since I assumed he’d already won this. His work in general and specifically the work that led to the proof of Fermat’s Last Theorem is on any reasonable list of the top few achievements in mathematics in recent decades.

    If you haven’t seen the documentary about the FLT proof, you really should, it was a BBC Horizon show in the UK, Nova here in the US, transcript here.

    I’d heard and Nature confirms that Wiles has for quite a while now been working quietly on the BSD Conjecture, maybe some day there will be another very dramatic moment in the subject, and another documentary.

  • Erica Klarreich at Quanta has the story of a surprising new result about prime numbers from Kannan Soundararajan and Rober Lemke Oliver. They have found that, given a prime number with a certain last digit, there are different probability for the last digit of the next one (among the various possibilities). This violates usual assumptions that such things are in some sense “random”, indicating just how subtle this “randomness” is.

    For more details, there’s an excellent blog post from Terry Tao. This might be a good time to point out that people sometimes complain about the quality of coverage of scientific advances aimed at non-experts. From what I’ve seen in recent years, the coverage of mathematics advances has been of extremely high quality, with this story a good example.

  • April 29 is the release date for The Man Who Knew Infinity, a film about the life of Ramanujan. It’s based on a great biography and a fascinating story. I hope this turns out better than the similar situation with the film about Turing.

Update: It turns out that an astronomer, Chung-Ming Ko, had already a while ago done some calculations showing non-randomness in the last digits of primes, see here. The new paper has been updated to refer to that.

Reports about the Ramanujan film are that they took great pains to get the mathematics right, with Ken Ono and Manjul Bhargava working extensively on the film.

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20 Responses to Number Theory News

  1. Jeff M says:

    It should be noted that the result on primes is suggestive and not a proof. Essentially they noticed something numerically, and came up with heuristic arguments, which depend on a conjecture of Hardy and Littlewood, to explain the numerical results. So, might be true, might not be. I’m perfectly willing to believe Terrence Tao, who thinks it makes sense – he’s a much better number theorist than I am 🙂

  2. Roger says:

    The Abel Prize only started in 2003, so it had a backlog of deserving recipients.

  3. Peter Woit says:

    Sure, he’s only the 17th recipient ever of the prize. My surprise was just that I would have guessed he’d have been much higher on the list ordered from the beginning of people awarded the prize.

  4. anon says:

    I think he’s the youngest person to receive the prize thus far. Maybe the committee has prioritized older people when they’ve started clearing the backlog. Many recipients were in their late 70s or 80s, so they wouldn’t have necessarily had that many years left (though I think all but Nash are still alive).

  5. Peter Woit says:

    I think that’s right. I hadn’t realized they were still so heavily concentrating on much older people and hadn’t yet gotten down to those in their sixties.

  6. geometriclanglander says:

    I do feel it’s a great shame that Israel Gelfand wasn’t awarded the Abel Prize before he died.

  7. Jeffrey M says:

    In addition to the age issue, the Abel hasn’t been for a single result, it’s been for people who’ve made multiple high level contributions to math in diverse areas. It’s not like the Nobel. Wiles was too old for a Fields, but he was given a special citation at the ICM the year he would have won the Fields.

  8. Daryl says:

    Hasn’t Wiles already proven a special case of BSD conjecture?

  9. I’d like to point to Evelyn Lamb’s article as another example of excellent coverage 🙂

    And I’m glad I’m not the only one who thought that Gelfand should have gotten the Abel.

  10. Mário da Silva says:

    Not only Gel’fand… They probably thought Arnol’d would have lived longer (he died too young for nowadays standards). He did not receive a Fields Medal for mysterious reasons. At least he was awarded the Wolf Prize.

    Anyway, there is now that “Breakthrough Prize in Mathematics”, but with such a dumb name I doubt it will catch the others in prestige.

  11. Michael Weiss says:

    It is wonderful when the Abel Prize goes to an extraordinary senior mathematician who in his or her younger years did not receive the Fields Medal. A joyous example was John Tate, whose generosity and deep insights were seldom accompanied by a drive to publish. Despite the legendary status of his PhD Thesis at Princeton, this work was not formally published for almost 20 years. Yet scores of landmark publications by others thanked Tate for sharing key insights and relied on methods that he pioneered and conveyed in meetings. Tate’s methods also contributed as an essential foundation to Wile’s proof of FLT. As an aside, generations of Harvard undergraduates found Tate to be inspiring and approachable, not only in formal courses but also in the dining halls of Adams House and later Dunster House — and even on the basketball court! The prestige of the Abel Prize was enhanced by John Tate’s recognition.

  12. JSM says:

    Much as Wiles deserved the prize, this appears to confirm that they are not going to give it to Langlands. If they were going to, this should have been the year.

  13. Bob says:

    JSM, that’s just a Langlands conjecture …

  14. Mario says:

    Peter – is there some reason that you did not cover the update of the 750GeV diphoton resonance? You were my source #1 for rumors on the Higgs in 2012. Can’t you use some of your connections? 🙂

  15. Peter Woit says:

    I just don’t have any information or thoughts about that that aren’t much better discussed elsewhere. I can only keep telling people to read Jester at Resonaances so often….

    I don’t think the recent update materially changes the situation. The evidence is marginal, and we should know for sure one way or another later this year (July if you’re an optimist). If there really is a state at 750 GeV it will revolutionize the field, which will be quite exciting.

    Maybe reliable rumors will appear here, but at the moment it seems others have better sources, and you should look to them for the latest on this.

  16. Pingback: Can randomness be “subtle”? | Uncommon Descent

  17. geometriclanglander says:

    The paper by Ko was published in Chaos, Solitons and Fractals… it’s unfortunate really, given that journal’s rather chequered reputation. One can’t really be too surprised if it wasn’t taken seriously.

  18. IM says:

    Off-topic, but probably you should mention in a future posting that the second part
    of Grothendieck’s obituary has come out in the AMS Notices.

  19. Peter Woit says:

    Thanks for pointing that out. I noticed that the last page of the Grothendieck obituary material in the AMS Notices included a large recruitment ad for the NSA. May be some spinning in his grave going on…

  20. Pingback: Links for March 2016 - foreXiv

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