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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."
So maybe 100 years ago, factoring into primes had no practical use ? Certainly nothing like it has today...
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 :)
-Kevin
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...
His work is a bit wider than just the CRC which by itself is "just" cyclic redundancy check. He talks about error-CORRECTING.
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?
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.
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?
I think it was Hitler who changed the world, and the book is only important because of his actions. Better examples of authors who changes the world would be Nietzsche, Muhammad, Huxley and Orwell.
We need a cool funky page like the Nobel's Page for the Fields award. Currently we only have these text based ones because the people maintaining them are too busy working on math to create a cooler looking one. :-)
It would be really cool to have a nice looking math page online. Something that will get people's attention.
Does anyone know of a better looking and still accurate Field's page?
~ kjrose
There are only three kinds of people in this world; those that can count, and those that can't.
'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
I'm really surprised that only two Fields Medals were awarded this time around- at least three have been awarded every four years since 1974. Is Preda Mihailescu's proof of Catalan's Conjecture considered too recent for consideration? I'd think that sort of thing, combined with his work on noted hot topic primality would make him an attractive candidate.
Of course, I'm sure they are many others who were also very deserving as well. No, I am not Dr. Mihailescu, and have never met him in fact; it's just when I saw that the Fields Medals were awarded, my first thought was, "I wonder if they gave one to that guy who proved Catalan's Conjecture?" As recent as the proof was (considering the slow, careful peer review that accompanies important purported mathematical proofs), I wasn't shocked to not see his named- I was far more surprised that the committee chose to not award the remaining two prizes to anyone.
"FDA staff reviewers expressed concern about the number of patients who were left out of the study because they died."
Fields medal winners do have practical applications, like that guy in Good Will Hunting...
Davidson had 400 words to write about three medalists, each in a different field of mathematics. Along with the explanation of what the medals are and why we should care (the reason for the throwaway 'it doesn't have any immediate applications' section), where the medalists are from, where and when the prizes were awarded, he has to explain what the three sets of research are about (defining terms as basic as "topology" along the way) *and* get an outside comment. That's incredibly difficult, and given the constraints, he did a credible job. Most of the other papers won't touch this subject because it's simply too hard to explain to the lay reader. At least Davidson tried. Give the guy a break.
Not all new math follows the trend from theory to practice. Quite a lot goes the other way. Consider Claude Shannon's mathematical theory of communication. He created it to help reduce static on phone lines, but it turns out to have deep theoretical implications in many fields.
Topology is a psychiatric disorder characterized by the inability to distinguish between a donut and a coffee cup. Some theorists speculate that it may be caused by overexposure to university cafeterias, in which such distinctions are academic at best.