Fields Medals awarded

prostoalex writes "Every four years the Fields Medals are awarded to top mathematicians for outstanding research. This year's winners, as this San Francisco Chronicle article reports are Vladimir Voevodsky from Institute for Advanced Study and Laurent Lafforgue from Institut des Hautes Etudes Scientifiques. 'True to form, Lafforgue and Voevodsky's mathematical research has no known practical applications', notes SF Chronicle."

Comments

Madhu Sudan's homepage

[jukal]

the "error-correcting-guy" has his homepage here, his papers are here. Really interesting stuff. But what can you expect from a guy whose hairstyle has similarities to Einstein's :)

a doughnut into a coffee cup

[oliverthered]

Hey that's easy any idiot can do that.
1: take the doughnut in you right hand
2: take the coffee cup in you left hand
3: move you right hand towards the coffee cup, ensure that you 'turn the doughnut into the coffee cup ' on you approach.

Maths is easy.

here's a link with ACTUAL INFORMATION

[khuber]

That SFC article is crap.

fields 2002

-Kevin

No practical applications?

[jfedor]

Yeah, that's what G. H. Hardy said about number theory back in 1940 (in A Mathematician's Apology). :)

-jfedor

Arrrgh

[platypus]

As a (former) mathematician, I sometimes wish people wouldn't try to explain mathematical things in laymans terms:

"His study is related to topology, the mathematical science of shapes. Among other things, topologists study how one shape can be changed into another shape -- say, a doughnut into a coffee cup -- without removing the one feature they have in common -- the hole in the doughnut and the hole in the cup's handle"

First, this sounds soo cheesy, and second, this is _not_ what topology is about (the "how" doesn't normally matter, the question is "if").
I can see people imagining mathematicians sitting in the offices with a big pile of knead and trying to form proper coffee cup handles out of doughnuts.

Re:Arrrgh

[mill]

Turning a doughnut into a coffee cup and vice versa would have serious practical applications for our people in law enforcement though. /mill

No Practical Applications?

[Anonymous Coward]

Dammit, I'm sick of the Langlands Program getting dumped on in the media. A man proves global correspondence for function fields and all the media can say are there are 'no practical applications'!

Yeah sure, maybe today, it's the topology and set theory guys who get all the chicks and who get invited to the Oscars and stuff, but just you wait, two-three years, it's going to be ALL ABOUT the Langlands Program!

On the other hand, take cohomology theory for algebraic varieties: that shit's just weird.

Not even just 'eventually'

[DoctorNathaniel]

Pure research doesn't only pay off 'eventually'.. it pays off right now.

First off, these fields aren't as dead as the SF article suggests: topology is a very big game right now with high-level particle theory. I don't pretend to understand it, but building 'topological field theories' is something people spend a good chunk of time trying to do. Although this research probably isn't directly applicable, it's neccessary to push a field generally before you get to something specifically good.

(Of course, many would believe that theoretical particle physics has no application, either, and they wouldn't be entirely wrong.)

Another point to make, though, and I can't stress this enough, is that pure research is valuable even if it leads to NO application, for several reasons:
- It creates spin-off technologies. (In the case of mathematics, the 'technology' might be pretty abstract but still useful.)

- It creates a vibrant research community, which is good for a vibrant teaching environment. (Debatable, but at least some people think so.)

- It expands our knowledge of the universe /reality / human experience / art / imagination / etc.

My favorite example: Even though Copernicus didn't really do anything for us but give us a few interplanetary probes, a useless moonshot of two, and slightly improved timetables, most people would be happy to know that the earth goes around the sun, not vice versa, not because it's USEFUL, but because it's TRUE.

---Nathaniel,
Shooting his mouth off about his favorite topic.

Re:Langlands Program

[sympleko]

Here is an expository article from the Journal of the AMS about the Langlands program. Results of Lafforgue are used to prove some very nice theorems.

Here is a link to an article by Lafforgue in Inventiones Mathematicae, one of the world's most prestigious mathematics Journals. Malheursement, cet article est en français.

Here is the Mathematical Reviews citation for the Lafforgue paper. You can browse the articles cited by him.

Also, if anyone is interested, here is a paper by Voevodsky about some of his work in motivic cohomology.