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Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

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Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#41

Post by wenc »

martinbalsam wrote: post #12

Oh, Robert Langlands! I worked on a short film about him, for the Abel Prize ceremony, last March. http://www.abelprize.no/artikkel/vis.html?tid=73176

Nice short film. Langlands was a theory builder as opposed to someone like Erdos who was more interested in solving problems. Theory builders are often admired, but because the endeavor is so broad, very few of them emerge and even fewer are actually successful.

I like the part where he said he began to write before he understood everything, and in order to write he had to discover many things, and even had to discover them after he started to write.

It underscores the crucial role of writing in discovery. Most writers will tell you they are exploring the space during the writing process. Writing isn't a process of committing what you already know to paper; it's a process of learning what you don't know and or haven't considered. It often leads you down paths you would never expect. (this happens to me with my HN comments too -- I often myself writing a very different comment from the one I set out to write)

This is why I think a Ph.D. dissertation should be a continuously evolving collection of notes, and not something you "write-up" in the end after all the work is ostensibly done.

Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#42

Post by gjm11 »

ColinWright wrote: post #23
imron wrote: post #19

But did he win the Putman?

It seems to me that doing well in competitions is a separate question from going on to do amazing research. There are plenty of people who did phenomenally well in competitions and then went on to be successful being mathematicians in other fields, working at Big Co, or starting up their own company, but most of the really, really top mathematicians that I know didn't go in for competitions. There are exceptions, but…

I'm pretty sure the comment you're replying to wasn't so much a serious question as a reference to this little incident on HN: https://news.ycombinator.com/item?id=35079

Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#44

Post by ColinWright »

gjm11 wrote: post #42
ColinWright wrote: post #23

Earlier quoted context omitted.

It seems to me that doing well in competitions is a separate question from going on to do amazing research. There are plenty of people who did phenomenally well in competitions and then went on to be successful being mathematicians in other fields, working at Big Co, or starting up their own company, but most of the really, really top mathematicians that I know didn't go in for competitions. There are exceptions, but…

I'm pretty sure the comment you're replying to wasn't so much a serious question as a reference to this little incident on HN: https://news.ycombinator.com/item?id=35079

Indeed, but I like to play with a straight bat, and I think the point was worth making regardless.

Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#46

Post by nilkn »

If you haven't heard of Langlands but have heard of Andrew Wiles and his proof of Fermat's Last Theorem, you may be interested to learn that the two are somewhat closely related. Wiles actually proved a part of the modularity theorem, which had been shown by Frey, Serre, and Ribet to imply FLT in the 80s.

The modularity theorem is very much a Langlands-style theorem and could be seen as a more concrete version of many of the ideas and conjectures that form the Langlands program. The conjecture now known as the modularity theorem was formulated as early as the 50s and 60s by Taniyama and Shimura, thus predating the Langlands program, and it was taken seriously once Weil gave conceptual evidence for it (but did not come close to a proof).

In fact, the modularity theorem is just a very oddly phrased reciprocity law. General reciprocity laws often look astonishingly nothing like the simple law of quadratic reciprocity, or they require some clever squinting to see the relationship. Modularity gives you for any rational elliptic curve E a modular form which is a simultaneous eigenvector for the Hecke operators (one for each prime number p) and whose eigenvalues give the solution counts of the elliptic curve equation modulo p for various primes p. These eigenvalues are also the coefficients in the Fourier expansion of the modular form.

Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#47

Post by maliker »

More like greatest mathematician whose work I’ve never understood. Sadly. At least I can reduce Grothendieck to algebraic topology or Wiles to number theory plus that one old problem. Terry Tao to analysis. But Langlands? Interconnectivity of all sub-fields? I’ve got nothing.

Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#48

Post by ColinWright »

thanatropism wrote: post #24
impendia wrote: post #21

Earlier quoted context omitted.

A half-remembered, and possibly apocryphal, story which another mathematician once told me: Langlands was once invited to lecture in France, and he chose to give his talk in French. Evidently his accent was not all that good, and the audience found it a bit painful. Jean-Pierre Serre, one of the leading mathematicians of the 20th century, and a Frenchman, was attending the lecture that day. He interrupted to ask a qu…

Frenchmen are legendarily intolerant of badly-spoken French. This was a recurring theme in my couple of years as a student at Alliance Française - when in France (most people hoped to go to college or grad school there) if you're not solid don't even try. In Brazil people will be glad you're trying and try to speak slowly in return.

This is completely at odds with my experience of speaking French in France, both in major cities and small villages. My spoken French is appalling, and yet I've encountered nothing but good will from the French, happy to encourage me, and to work together to figure out what I'm trying to say.

Obviously YMMV, but your assertions are contrary to my experience.

Edit: Down-voted. Thanks for the reality check.

2nd edit: Up-voted, perhaps to compensate. Thank you to whoever did that.

Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#49

Post by soperj »

impendia wrote: post #21
aquadrop wrote: post #20

Earlier quoted context omitted.

According to Wikipedia: " Langlands likes to learn foreign languages, both for better understanding of foreign publications on his topic and just as a hobby. He speaks French, Turkish, German and Russian". I'd say it's not _that_ weird, if he likes foreign languages, to combine both his passions and write one paper in Russian :) Also considering there are actually a lot of mathematicians who can read and write Russia…

A half-remembered, and possibly apocryphal, story which another mathematician once told me: Langlands was once invited to lecture in France, and he chose to give his talk in French. Evidently his accent was not all that good, and the audience found it a bit painful. Jean-Pierre Serre, one of the leading mathematicians of the 20th century, and a Frenchman, was attending the lecture that day. He interrupted to ask a qu…

I'm fluent in French. Quebecois French. In France they're just rude about it, even when they speak terrible english. I would absolutely do the same thing.

Re: Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?

#50

Post by cmyr »

ColinWright wrote: post #48
thanatropism wrote: post #24

Earlier quoted context omitted.

Frenchmen are legendarily intolerant of badly-spoken French. This was a recurring theme in my couple of years as a student at Alliance Française - when in France (most people hoped to go to college or grad school there) if you're not solid don't even try. In Brazil people will be glad you're trying and try to speak slowly in return.

This is completely at odds with my experience of speaking French in France, both in major cities and small villages. My spoken French is appalling, and yet I've encountered nothing but good will from the French, happy to encourage me, and to work together to figure out what I'm trying to say. Obviously YMMV, but your assertions are contrary to my experience. Edit: Down-voted. Thanks for the reality check. 2nd edit: U…

There's sort of an uncanny valley sort of situation, in my experience (as an anglophone canadian with the french of a 3-4 year old): If you're clearly a foreign visitor, and you're speaking bad french, it's often appreciated and maybe found slightly charming. But once you get to the point where your french is reasonably good, but you have an obvious accent, then (some) people (might, sometimes) be more inclined to be a bit snooty about it.
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