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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?

#71

Post by c3534l »

wenc wrote: post #41
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 discov…

That's also why I detested the formal, algorithmic writing method you learn in English classes. They always wanted you to turn in an outline before you had even begun your paper. How are you supposed to organize a paper before you even have anything to organize?

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

#72

Post by c3534l »

zornthewise wrote: post #61
vanderZwan wrote: post #60

> Most mathematicians also agree that the Langlands Program could help find a proof for the Riemann Hypothesis, probably the most famous unsolved mathematical problem (about the distribution of prime numbers). These problems are just as abstract as Langlands’s own work, however, which means his research program as it was originally conceived has little relevance to everyday life. I dunno, figuring out the Riemann Hyp…

No, for any practical applications, we might as well work assume it is true, the same way we assume quantum physics or relativity are true when building stuff.

And if we actually prove it's not true?

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

#73

Post by kenbellows »

Koshkin wrote: post #31
celticninja wrote: post #28

Earlier quoted context omitted.

Yeah, this is my experience too. You should always attempt to use the language of where you are except in France. They would rather you spoke English than butchered their language. I usually keep it to please and thank you in french as a result. Although I did once use my high school french to ask where the swimming pool was once and had a bit of trouble deciphering the response I got (in french). So swimming pools a…

I think problem is, English accent is probably the worst . This is because pronunciation-wise there hardly are other two languages as different as English and French. (The French return the favor, obviously - their accent sounds just as terrible.)

Which is ironic, given that English developed as basically French + German (or some old versions of those languages).

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

#74

Post by thanatropism »

metalsteady wrote: post #62
thanatropism wrote: post #56

Earlier quoted context omitted.

I'm not entirely sure what he meant, but the flow maps of vector fields are semigroups. If irreversible, they're groups. And a field is like a group and a ring over the same set, right?

A group is a set with a single operation defined on it that abides by certain axioms. A field is a set with two operations defined on it. But the field operations must abide by more axioms than a group operation. While vector spaces and fields are very similar (two operations, similar number of axioms), vector spaces are defined over fields (for example, an element cv is defined where v is a vector and c is a scalar)…

Flow maps: take for example an autonomous ODE

    x'(t) = f(x(t))
f(.) describes a vector field, right? A flow map is a function w_t(u) = x(t) that solves the ODE with x(0) = u, for fixed t. If f(.) is invertible, then each flow map is a group in the very same way rotations of a Rubik cube are a group. If not, it's a semigroup, which is a group without an invertibility. The former describes systems that you can track back in time and calculate initial conditions only from looking at the present state.

My dissertation was actually about numerically integrating symplectic vector fields; I spent a lot of time hunching over Arnold's "Mathematical methods of classical mechanics".

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

#75

Post by celticninja »

Koshkin wrote: post #66
celticninja wrote: post #59

Earlier quoted context omitted.

Accent is such a non issue, in the UK the accent can be very different even 30 miles from one another, so let alone someone speaking it with a French, German or Spanish accent. It's still English and 99% of the time you can understand it. I assume the same is true of other languages too.

> Accent is such a non issue But for the French it apparently is (and understandably so).

I meant that you can still understand the speaker, and if so it is courteous to answer. Refusing to understand because you don't like the accent is hardly courteous.

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

#76

Post by maliker »

nicklaf wrote: post #67
maliker wrote: post #47

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.

I highly recommend reading Edward Frenkel's memoir, Love and Math , which is more or less an up close and personal popular account of the author's involvement with the Langlands Program: Perhaps the most remarkable part of the book though is the way it makes a serious attempt to tackle the problem of explaining one of the deepest sets of ideas in mathematics, those which go under the name of the “Langlands program”.…

Thanks! I'll take a look.

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

#77

Post by JadeNB »

wenc wrote: post #41
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 discov…

> Langlands was a theory builder as opposed to someone like Erdos who was more interested in solving problems.

No 'was' about it, by the way; he's still alive, and (last I heard from him) still working.

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

#78

Post by JadeNB »

Koshkin wrote: post #70
wenc wrote: post #41

Earlier quoted context omitted.

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 discov…

> as opposed From The Rising Sea: Grothendieck on simplicity and generality by C. McLarty: Grothendieck describes two styles in mathematics. If you think of a theorem to be proved as a nut to be opened, so as to reach “the nourishing flesh protected by the shell”, then the hammer and chisel principle is: “put the cutting edge of the chisel against the shell and strike hard. If needed, begin again at many different po…

Incidentally, I have heard Serre's work described as the exemplar of the hammer-and-chisel approach. (McLarty goes on to say that Bourbaki's work fits in the rising-sea approach, which is surprising to me.)
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