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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."
When negative numbers were introduced they were known as a mathematical curiosity not useful for anything.
Similarly complex numbers were discovered simply to make basic algebra "closed", now they have hundreds of applications, similarly group theory originally had no practical applications yet is now used in many fields including analysis of molecular interactions which is essential to pharmecutical companies.
Give it 20 years and I'm sure an application will arise.
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 :)
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.
thank God the internet isn't a human right.
fields 2002
-Kevin
"Two Americans and a Frenchman have won prizes that are the mathematical and computer science near-equivalents of the Nobel Prize. "
;-)
Does this mean that...
Fields Medals ~ Nobel Prize
and
Fields Medals != Nobel Prize
?
A little planning goes a long way...
Yeah, that's what G. H. Hardy said about number theory back in 1940 (in A Mathematician's Apology). :)
-jfedor
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.
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.
So sodding what if it doesn't have direct application today ? Would the SFC complain about yet another Dean Kootz book or another pointless film with Tom Cruise in it ? No they wouldn't, but because these guys are doing research and pushing the boundaries of human knowledge it is therefore pointless because of its lack of application.
Maths has had a history of "not being practical" and then 50,100 or even more years later turning out to be 100% practical. Did Pythagorus et al do all that work because it was "practical", is set theory practical... oh hang on that is the basis of cryptography, which is an area that 200 years ago would have been totally "pure" and unsullied by being practical.
I say let these men live in their Ivory Towers, let them postulate and theorise. Because first come the ideas, then come the realities. A Turing maching isn't "practical" it require infinite tape, but damn have those ideas kicked in. Game Theory was created by a John Nash because of its maths, it then changed economics BUT that wasn't why he started thinking about it.
If one more arse with an English degree derides Maths just ask them... when was the last time an author helped changed the world, and what about the millions of others who just write pulp bestseller after pulp bestseller... what is the practical application of those, except to be recycled as loo roll.
An Eye for an Eye will make the whole world blind - Gandhi
Pure research doesn't only pay off 'eventually'.. it pays off right now.
/reality / human experience / art / imagination / etc.
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
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.
What makes the Fields medal special, in case you don't know is that:
a) There is no Nobel Prize for mathematics.
b) The Fields Medal is only awarded once every four years, vs. every year for the Nobel.
It's truly an achievement.
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.