Slashdot Mirror
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."
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 :)
fields 2002
-Kevin
You have to be under 40 to get this particular award.
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.
Lafforgue's work is about the Langlands program, but it's extremely difficult to find info about it on the Web. Can anyone provide pointers?
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.
And that do no good if you can't retransmit the information, eitheir because impractical (e.g. space probe really far away) or because you're reading from some damaged media (e.g. scratched CD). That's where error correcting code are used.
You usually design you code to withstand some kind of error rate (e.g. 1% of the bits are reversed) and the right code can ensure by encoding data with some redundancy that your data comes intact.
Old one used where things inspired by the work of guis like Hamming, Berlekamp, Massey, Reed and Solomon (used in satelite transmissions and CD reading). Sundan's work should be an improvement over that and will be used everywhere.
Madhu Sudan leaves an impressive trail of prestigious prizes in CS theory: ACM doctoral dissertation award in 1993, Godel Prize for Computer Science in 2001 and now the Nevanlinna Prize.
The central theme of his work seems to concern finding approximate solutions to hard problems.
A 1998 ACM journal paper by with Sudan as co-author showed that this can be done with high probability of success by inspecting only logarithmic number of random bits of the solution.
The way they did this was by characterizing NP in a new way that integrates interacting computing agents with randomized computation.
Then from this result on randomized proof-verification, they showed that a broad class of NP-hard problems called MAX-SNP problems are really hard! Meaning that solving these problems approximately is as hard as solving them fully.
His paper on Reed-Solomon codes for error correction discovered an efficient algorithm for approximately recovering from too many errors in the received codeword. "Efficient" meaning that its running time is polynomially bounded and "too many" meaning the errors are more than the error-correcting capability of the code. For example maximum 2 errors can be corrected, then how do you efficiently recover from 5 errors?
'True to form, Lafforgue and Voevodsky's mathematical research has no known practical applications' A little over 100 years ago the study of artificial language, number theory, algorithms, etc. were little more than intillectual curiosities. Only in the past 50 years have we seen all these "theoretical" areas of study be thrust into the forefront of science and engineering. It seems a bit pretnentious and short-sighted to ignore discoveries or minimize their importance simply because we haven't learned enough as a society to figure out what those discoveries truly imply. Just mho