Fields Medals awarded 132
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."
Useless ? (Score:2, Insightful)
So maybe 100 years ago, factoring into primes had no practical use ? Certainly nothing like it has today...
Re:Useless ? (Score:2)
Re:Well (Score:1)
Sudan received his PhD from Berkeley, but does his research at MIT.
Berkeley is top notch. For getting an education at least.
Re:Well (Score:2, Informative)
The central theme of his work seems to concern finding approximate solutions to hard problems.
A 1998 ACM journal paper by with Sudan as coauthor 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 proofverification, they showed that a broad class of NPhard problems called MAXSNP problems are really hard! Meaning that solving these problems approximately is as hard as solving them fully.
His paper on ReedSolomon 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 errorcorrecting capability of the code. For example maximum 2 errors can be corrected, then how do you efficiently recover from 5 errors?
New maths never had practical applications (Score:3, Insightful)
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.
Re:New maths never had practical applications (Score:1)
Of those "pure mathematical" developments of twenty years (or forty years) ago, what has been used outside mathematics?
Re:New maths never had practical applications (Score:2, Insightful)
Off the top of my head, I'd say lattice and group theory for designing error correcting codes. The SolomonReed ECC used in CDs and DVDs was designed from the structure of a special lattice.
A lot of "useless" theories (much more "concrete" than topology, though: Collatz bases, Cylindrical Algebraic Decomposition and whatnot) ended up in Computer Algebra Systems in very "useful" tasks as factoring polynomials and solving equations.
And, who knows, maybe the topological approach to Quantum Gravity does pan out in the end.
Re:New maths never had practical applications (Score:1)
Of those "pure mathematical" developments of twenty years (or forty years) ago, what has been used outside mathematics?
Don't know whether this counts as "oustside" mathmatics. But lots of this stuff finds uses in string theory.
Its also worth noteing that much of the math from ~100 years ago (group theory, differential geometry) is in wide use in physics now. Even in the more practical fields like condensed matt.
Re:New maths never had practical applications (Score:2)
Who would have thought that all the work done in prime numbers would pay off in a practical application?
True, a lot of the work done on prime numbers during World War II was directed at codes (both breaking them and coming up with new ones), but they were able to look back at a large library of previously researched work (with no application) and turn that into a concrete example of using previously inapplicable math.
Re:New maths never had practical applications (Score:3, Funny)
and now, we have Enron and Worldcom...
Re:New maths never had practical applications (Score:1)
Not always (Score:2)
Re:New maths never had practical applications (Score:1)
Madhu Sudan's homepage (Score:5, Informative)
Plus, Madhu is cool (Score:1)
We can always count on help from him on the toughest NY Times crossword puzzles, and sometimes he even picks up the tab at our student social nights. Plus, he was too modest to even mention winning this award, so the whole theory group was just as surprised as everyone else when it was announced.
And oh yeah, he's gotten a haircut since the picture on his web page
Re:Forget the maths, same article speaks of CS pri (Score:2)
His work [mit.edu] is a bit wider than just the CRC which by itself is "just" cyclic redundancy check. He talks about errorCORRECTING.
CRCs detect errors, don't correct them (Score:2, Informative)
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.
impractical? (Score:2, Funny)
Kevin
Re:impractical? (Score:1)
To be fair, Lafforgue and Voevodsky are hardly "average" mathematicians. The point of the Fields Medals is to recognize that they are extraordinary mathematicians.
Extraordinary journalists HAVE had major impacts on civilization.
l
Re:impractical? (Score:1)
a doughnut into a coffee cup (Score:4, Funny)
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.
Re:a doughnut into a coffee cup (Score:1)
[0] That maths with an s. Math is a Roman Catholic servith.
Re:a doughnut into a coffee cup (Score:1)
Re:a doughnut into a coffee cup (Score:1)
jam doughnut does not, and that's the problem you seem to be having.
My doughnut didn't go soggy because it's not half baked but YMMV.
Aren't doughnuts and coffee cups topologically the same or does a coffee cup have a plane poking out the side?
Re:a doughnut into a coffee cup (Score:1)
Re:a doughnut into a coffee cup (Score:1)
Re:a doughnut into a coffee cup (Score:1)
Re:a doughnut into a coffee cup (Score:2)

@ handle
base O
I'm don't know how the topology works though but I can't see how the sphere can be merged into the doughnut
Re:a doughnut into a coffee cup (Score:1)
In the area of topology they are disucssing (where a donut and a coffee cup are the same), you look at how points are related to eachother "connectivity" wise, not "distance" wise.
Topologically they are isomorphic, metrically they are VERY different.
The use of this type of visualization experiment is to see how problems are related and how they differ.
Felix Kline did some of the pioneering work in this area. The study of knot theory has been useful in managing 3D structure and composition of DNA/RNA...
Lots of "practical" applications, it just requires imagination.
Re:a doughnut into a coffee cup (Score:1)
I wan't sure if the plane counted as seperating the sphere and the doughnut or not, because it's only solid in 2d not 3d.
if not then the sphere(solid) is just a part of the doughnut.
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here's a link with ACTUAL INFORMATION (Score:5, Informative)
fields 2002 [maa.org]
Kevin
Re:here's a link with ACTUAL INFORMATION (Score:1)
I can see why the SF and BBC articles didn't include any extra information. You would need a fields medal just to understand it.
This guy is really gifted (Score:1)
Re:This guy is really gifted (Score:1, Informative)
Re:This guy is really gifted (Score:1)
Re:This guy is really gifted (Score:1)
... near equivalents? (Score:3, Funny)
Does this mean that...
Fields Medals ~ Nobel Prize
and
Fields Medals != Nobel Prize
?
Re:... near equivalents? (Score:2, Funny)
Re:... near equivalents? (Score:1)
Re:... near equivalents? (Score:1)
may have been getting a little action on the side from a mathematician  so mathematicians had to come up with their own award, because Nobel wasn't about to give his prize to anyone from that group.
Re:... near equivalents? (Score:1)
Re:... near equivalents? (Score:2, Interesting)
This is why many of the mathematicians have won their prizes in economics or other areas.. eg: Nash ( Game Theory ), Merton, Scholes ( BlackScholes equation for options pricing ). Both are fairly simple mathematically but have proven far more useful than say determining that a doughnut and coffee cup are topological equivalents.
Re:... near equivalents? (Score:1)
No practical use (Score:3, Informative)
Re:No practical use (Score:1)
This is why people like the NSA just love pure maths specialists.
Not even just 'eventually' (Score:4, Insightful)
First off, these fields aren't as dead as the SF article suggests: topology is a very big game right now with highlevel 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 spinoff 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.
Re:Not even just 'eventually' (Score:2)
Re:Not even just 'eventually' (Score:2)
Most people, I think, would say the opposite  a vibrant teaching environment creates a vibrant research environment. Stories of the Institute for Advanced Studies (a great physicists only place, where there were no students) indicates that with nobody around asking the "obvious" questions actually creates a sterile environment.
Re:Not even just 'eventually' (Score:1)
First off, these fields aren't as dead as the SF article suggests: topology is a very big game right now with highlevel 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.
Actually a subfield (Oh the puns I could make too much algebra lately) of topology, Knot Theory, seems to be making inroads into Biology which is kind of ironic when you consider that Knot Theory was invented for chemists; it was believed that molecules were formed by atoms "knotting" themselves toghether. Anyway It turns out that DNA is very tightly knotted inside the nucleus of the cell and viruses seem to operate by knotting and unknotting DNA. Do I need to explain the implications here? Can you see the headline: "Mathematicians cure the common cold?" :)
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.
Actually truth is kinda relative here. One could reasonably make the argument that the Earth is the center of the universe. In an infinite universe every point is the center. And I believe that an model similar to Brah's will work i.e. the Sun rotates around the Earth and all other planets rotate around the Sun. However, the Sun centered model is MUCH simpler.
Gotta run Topology Qualifier in 3 hours!!
Re:No practical use (Score:2)
No practical applications? (Score:5, Informative)
jfedor
Re:No practical applications? (Score:2, Interesting)
Re:No practical applications? (Score:1)
Arrrgh (Score:5, Informative)
"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 (Score:1)
You must be one of the rare "normal" math types :).
I have to wonder what the point of even discussing the Fields medal is if you're going to talk about topology in such silly terms. "Wait, I'll flip to NASCAR in a second. Jeezus ma! This brainy feller solved the doughnut problem!"
Kevin
Re:Arrrgh (Score:5, Funny)
Re:Arrrgh (Score:2)
Re:Arrrgh (Score:1)
Cheers,
Scott
Re:Arrrgh (Score:2)
At least that is what I learned in topology. But I confess I just did not specialize in topology, when I learned about ktheory, bott periodicity and homotopy theory and the proof that the 7sphere is parallelizable I thought I felt I should stop, otherwise my brain would explode
Explicitly writing down homeomorphism was never done, apart from some trivial beginner examples (and I'm very thankful for that).
A better explanation would IMO have been to tell something about knots.
Re:Arrrgh (Score:2)
Which is easy, of course, as both are instances of a torus.
What really impresses me was turning a Klein bottle into a coffee cup... resulting in the Klein Stein [kleinbottle.com]
(Why yes, that's a shameless plug for Cliff Stoll's Klein Bottles [kleinbottle.com]. And despite the fact that it's toplogically identical to every other Klein bottle, and therefore definitely not a torus, I gotta say the Klein Stein is an amazing bit of glasswork. It holds a lot of liquid for something with no volume.)
Yeah, there are better ways to put it. (Score:2)
Re: Arrrgh (Score:1)
I don't see why the donutcoffee cup description of topology upsets people so much. It's just an old joke. The Berkeley math dept. sells (or used to sell) mugs that had a yellow sign reading, "Caution! Not a donut." Perhaps the sensitive mathematicians would be appeased if we used other functionally equivalent analogies, like, "Topology tells you that you can take off your shirt without removing your jacket," or, "you don't really need to put on your socks before your shoes."
Re:Arrrgh (Score:1)
Re:Arrrgh (Score:2)
Re:Arrrgh (Score:1)
It's the study of spaces where you don't have knowledge of the distance between points.
Sorry if he tacked on "It's difficult". It really and truly is, but I think even a child could understand the basic notions with that onesentence description.
Re:Arrrgh (Score:1)
It's like a pocket protector, except different and four dimensional and there aren't any women either. Now the engineers should get it.
Seriously, topology is basically the study of ndimensional shapes/surfaces (generically called manifolds). Have you ever seen the cool Mathematica pictures of those three dimensional knots? Topology has applications in parallel processing, cosmology, semiconductor physics, and other areas. I'm no math guy, but that's my simplistic understanding.
Kevin
Re:Arrrgh (Score:1)
Re:Arrrgh (Score:2, Interesting)
One thing that's interesting (to me) is how difficult it is to solve something like the Poincaré conjecture which seems so simple at first. It's only been solved for generalized versions where n > 3, and getting down to 4 took a long long time!
Even though I only understand a bit (my math background is applied mathematics), topology is pretty fascinating in an abstract sense. Incredibly brilliant people.
Kevin
Re:Arrrgh (Score:1, Informative)
Hey finanly another person like me ( applied mathematician ). I genenerally understand basically nothing that these people talk about: Group theory, Topology, Rings & Knots, Galiol whatevers, etc... thoguh being a canadian I am quite familiar with donuts
Re:Arrrgh (Score:1)
Langlands Program (Score:2, Informative)
Re:Langlands Program (Score:4, Informative)
Here [springer.de] 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 [ams.org] is the Mathematical Reviews citation for the Lafforgue paper. You can browse the articles cited by him.
Also, if anyone is interested, here [lanl.gov] is a paper by Voevodsky about some of his work in motivic cohomology.
Re:Langlands Program (Score:1)
This page [sunsite.ubc.ca] looks particularly relevant.
No Practical Applications? (Score:5, Funny)
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, twothree 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.
Maths and practicallity... (Score:3, Insightful)
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.
Re:Maths and practicallity... (Score:1)
I wonder what's the problem with certain fields of Maths labeled as "without direct application". I thought it meant something like "interesting and still worth studying before it gets something that you can see in everyday life", only shorter.
Of course people in the real world are free to have a different translation, they just don't know what they're missing :)
Re:Maths and practicallity... (Score:1)
While I agree totally with the rest of your post, I have to point out to you that Nash certainly did not create game theory nor was he the first to apply it to economics. Game theory has roots going back thousands of years in fact. If anyone can be creditted with "creating game theory" it is John von Neumann (and his partner Oskar Morganstern) who did the most to develop the theory as a whole as well as apply it to economics in the earlymid 1900s. John Nash simply made a contribution to the theory (albeit a very important one).
There's a nice timeline of the development of game theory here [drexel.edu] if you're interested.
Re:Maths and practicallity... (Score:1)
Research beyond the realm of what's currently possible is the only way to expand the realm of the possible, not to mention practical!
Re:Maths and practicallity... (Score:3, Funny)
But the practical application of a Dean Koontz book or a Tom Cruise movie is apparant to everyone: ENTERTAINMENT.
Math is not fun to most people. And really farout math is worse...
Re:Maths and practicallity... (Score:2)
Math is not fun to most people
Their loss...
Actually, most people have no idea if they think math is fun or not, because most people have never even seen any math, much less done any.
Re:Maths and practicallity... (Score:1)
OK, so maybe it's just me whom the "no practical application" doesn't bother
Re:Maths and practicallity... (Score:2)
Re:Maths and practicallity... (Score:1)
Changing the world (Score:2)
Better than a nobel... (Score:3, Informative)
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.
No practical applications (Score:1, Insightful)
Fields page... (Score:2)
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?
Three kinds of people (Score:2, Funny)
No such thing as "no practicle application" (Score:2, Informative)
This has already been said, but... (Score:1)
What a shitty article!
This is NOT an example of how to translate useful scientific information into journalism that is acceptable to the masses. Yet another telltale sign that professionalism has been overly segregated. No longer is it possible to be a journalism proficient in science and mathematics or a poetengineer!
I write news for the paper at my University (U of Calgary, Canada)and it the inability of journalists to write about science is consistently shocking. I like to cover a broad range of stories, but because of my academic background, I am often assigned to stories of a scientific nature. Occaisionally, these end up being really important stories that are covered by the international media.
For instance, I covered this [136.159.250.102] story, which was reported by every major new outfit in the country (though I'm not sure if it made it south of the border.
My point (I know it's here somewhere) is that no one has heard about it since the initial press release. Why? Because there was a major flaw that the primary researcher spoke explicitly about at the press conference. Why is this a problem? Because of every story I read in all of Canada, mine was the only one to mention the flaw. In fact, after the press conference a reporter from one of Canada's national television networks (C*C) approached me and said "You shouldn't ask so many confusing questions with big long words because it makes the rest of us look bad." Cripes!
Frankly, we all put way too much stock in the news media. This is a problem that won't be rectified until the owners of newspapers and TV networks wake up and realize that the onus is on them to provide even the most menial of educations to their reporters before sending them out into the fray.
Sorry about the rant,
ws
Re:This has already been said, but... (Score:2)
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.
Only 2? (Score:2, Interesting)
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.
Re:Only 2? (Score:1)
unlucky (Score:1)
drunk aussies rule
we rule
Good Will Hunting (Score:2, Funny)
Voevodsky refs. (Score:1)
Any one searching for some of Voevodsky's work should look for his name in the UIUC Ktheory preprint archive [uiuc.edu]. This paper [uiuc.edu] is a good introduction to his homotopy theory, and if you have access to a research library, you may find a book he recently wrote with Suslin and Friedlander, "Cycles, Transfers, and Motivic Homology."