- Erica Klarreich at Quanta magazine has a wonderful profile of Peter Scholze. Scholze has been busy revolutionizing various parts of arithmetic geometry in recent years, and the article does a good job of giving some of the flavor of this. I noticed this morning that Scholze has a new preprint out, about a q-deformation of de Rham cohomology, so that may be the latest, hottest news in the subject.
The new paper was written for the occasion of his acceptance of the 2015 Fermat Prize. Another Quanta piece makes the obvious point that we already know who one winner of the 2018 Fields Medal will be. While Scholze has been awarded a fair number of prizes already, it’s interesting that he’s not universally in favor of the prize phenomenon: see here for some discussion of his decision last year to turn down one of the 2016 Breakthrough Prizes.

- In addition to being a great mathematician, Scholze also seems to be a fine human being. The AMS Notices this week has an interview with another such mathematician, Robert Bryant, who is now the AMS President, recently head of MSRI. Unlike Scholze, I’ve had the pleasure of getting to know Bryant a little bit, since he was a visitor one semester here at Columbia. The Notices article explains his interesting background, which is somewhat unusual for an academic mathematician. The math community is lucky to have leading figures like him combining mathematical talent and excellent personal qualities.
I first heard about him back when I was a post-doc at Stony Brook, trying to learn more about mathematics and the math community. At some point I asked Claude LeBrun (a young geometer then, now an older one, with a conference in his honor next week in Montreal) who he thought the best young geometers were. He told me about Robert Bryant, and when I asked “why him?”, his answer was “He’s read and understood all of Cartan”. I wasn’t sure whether to take that seriously, but from the AMS interview, he was quite right about that.

- For one last piece of mathematics news, fans of geometric Langlands may want to take a look at the new preprint by David Ben-Zvi and David Nadler on a Betti form of geometric Langlands.
- Turning to physics, last week UCLA announced a $11 million donation to fund a Mani L. Bhaumik Institute for Theoretical Physics at UCLA. As NSF funding for theoretical physics stays flat or declines, at least in the US it is private funding like this that is becoming much more important.
- At CERN the LHC has reached design luminosity, and is breaking records with a fast pace of new collisions. This may have something to do with the report that the LHC is also about to tear open a portal to another dimension. Not clear why people are worrying about the 750 GeV state with this going on.

Soon heading North for a week-long vacation, blogging likely slim to non-existent.

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Update**: For geometric Langlands fans, this and this on the arXiv from Dennis Gaitsgory tonight.

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I sometimes wonder if there is an upper limit for mathematical prodigy. Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100. Are people like Scholz, Bryant or Tao close to 80? Maybe even close to 100? Better?

Heiko242,

I don’t think mathematicians can be usefully ranked like that. If one looks at the best work of mathematicians like Scholze, Bryant and Tao, I think one sees both different, incommensurable, technical talents, as well as different backgrounds that come into play. Bryant’s story about his engagement with the works of Cartan is a good example. If he hadn’t pursued that, but had gone in some other direction, would he have accomplished as much? Scholze’s story about starting with the Wiles proof and working backwards is another example of a very special way of entering mathematics that worked out for him. It’s possible that if Scholze had devoted himself to reading Cartan, and Bryant to trying to understand the Wiles proof, neither would have had anything like the same success.

Great new mathematics comes out of a complicated mixture of having learned the right things, having the right talents, being in the right place to talk to people who can help, having the time and dedication to focus on something, and choosing the right thing to focus on. As mathematics progresses, in some sense easier things get done and what is left is harder. On the other hand, the way the community is organized and the way mathematicians are trained also evolves, making it possible for them to effectively specialize and attack problems beyond what their predecessors were able to deal with.

To the extent that some isolated notion of raw talent is part of the story, I don’t know of any reason to believe that the best mathematicians of today are particularly different than those of other eras.

I’m just writing to strongly endorse Peter’s response to Heiko. Like all human endeavors, math has context, and any simplistic ranking of mathematicians is essentially meaningless.

http://www.dw.com/en/dont-call-me-a-prodigy-the-rising-stars-of-european-mathematics/a-19421389