Follow Slashdot blog updates by subscribing to our blog RSS feed

 



Forgot your password?
typodupeerror
Check out the new SourceForge HTML5 internet speed test! No Flash necessary and runs on all devices. ×
Announcements

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."
This discussion has been archived. No new comments can be posted.

Fields Medals awarded

Comments Filter:
  • Useless ? (Score:2, Insightful)

    by Lorens ( 597774 )

    So maybe 100 years ago, factoring into primes had no practical use ? Certainly nothing like it has today...
  • by Anonymous Coward on Wednesday August 21, 2002 @04:46AM (#4110194)
    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.
    • New maths never had practical applications

      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.

      I think these are the exceptions rather than the rule, although I'm not sure about this. Newton, Gauss, Euler, Legendre and many others worked on problems from physics and astronomy.

      Of those "pure mathematical" developments of twenty years (or forty years) ago, what has been used outside mathematics?

      • Of those "pure mathematical" developments of twenty years (or forty years) ago, what has been used outside mathematics?

        Off the top of my head, I'd say lattice and group theory for designing error correcting codes. The Solomon-Reed 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.

      • 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.

      • One word: Cryptology.

        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.
    • speaking of negatives, they were of no real importance until our society became on of currency. the barter system (still available for research in a few remote places) never gave us the idea of a 'minus.'

      and now, we have Enron and Worldcom...
    • 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.
    • This is not true. When calculus was a "new math" (long after negative numbers were new) being developed by Newton and Leibnez, the applications of calculus to physics were immediately recognized; really, physics was the motivating force. I believe Newton initially thought of y, the dependent variable, as varying with time, as opposed to a pure x variable. Thus he called the quantities fluents. It took a while for Newton to interpret his results in a "pure math" form instead of tying them to physics and the idea of time. This is an example when the application actually motivated the mathematics.
  • by jukal ( 523582 ) on Wednesday August 21, 2002 @04:47AM (#4110198) Journal
    the "error-correcting-guy" has his homepage here [mit.edu], his papers are here [mit.edu]. Really interesting stuff. But what can you expect from a guy whose hairstyle has similarities to Einstein's :)
    • He's also a damn cool guy.

      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 :).
  • by khuber ( 5664 )
    Yeah, not like the revolutionary impact the average newspaper journalist has on civilization. (note sarcasm)

    -Kevin


    • 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
    • Hey you just read that journalists work have you ever even heard of the other two before?
  • by oliverthered ( 187439 ) <oliverthered AT hotmail DOT com> on Wednesday August 21, 2002 @04:52AM (#4110215) Journal
    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.
    • Yeah, but now the dough is all soggy and the jam has leaked down your shirt. As ever, theres more subtlety to advanced maths[0] than laymen appreciate.

      [0] That maths with an s. Math is a Roman Catholic servith.
      • "How do I calculate the fundamental group of a smushed doughnut?"
      • doughnut as the name might suggest has a hole in the middle.

        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?

        • If the coffee cup has a handle with a hole in it, then they're indentical. They both have a fundamental group isomorphic to Z, which basically means you can start at a point, run around the hole an integer number of times, and get back to where you started, and that line you draw can not be continiously deformed to a point, because of the hole in the middle.
          • They are not identical, and thinking that they are will get you into trouble sooner or later. They are homeomorphic, but this does not mean identical. Think about the expressions 2+2 and 4. They are equal, but are not identical. In topology you have the notions of homeomorphism, homotopy, diffeomorphism, etc. These are all ways of classifying topological spaces into equivalence classes. So saying two spaces are equivalent, or homeomorphic, or "equivalent up to homeomorphism", are all ok, saying two spaces are identical, the same, etc. is much stronger.
  • by khuber ( 5664 ) on Wednesday August 21, 2002 @04:54AM (#4110216)
    That SFC article is crap.

    fields 2002 [maa.org]

    -Kevin

  • As he is only 35 which is really really young for a such distinction
  • by Ratface ( 21117 ) on Wednesday August 21, 2002 @04:55AM (#4110219) Homepage Journal
    "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

    ? ;-)

    • There exists a homoorphism but not an isomorphism between the two. Maybe I shouldn't attempt math humor at 3am.
    • What this means is that Alfred Nobels wife
      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.
      • That's probably not true, but I've heard it so many times, that maybe it is true.
      • by Anonymous Coward
        Nope not true. Alfred Nobel was never married. Just an urban myth to try and explain why a nobel prize was never awarded in math. Basically the Nobel prize is awarded not to the best researcher in a field per see but to the person in each field whose work has the greatest impact on society, etc. Nobel never thought math was like that.

        This is why many of the mathematicians have won their prizes in economics or other areas.. eg: Nash ( Game Theory ), Merton, Scholes ( Black-Scholes 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.
  • No practical use (Score:3, Informative)

    by PhilHibbs ( 4537 ) <snarks@gmail.com> on Wednesday August 21, 2002 @04:59AM (#4110227) Homepage Journal
    'True to form, Lafforgue and Voevodsky's mathematical research has no known practical applications',
    That's what George Boole said about his own invention, Boolean Algebra. Pure mathematical research will usually pay off eventually.
    • Um, say for example prime numbers. Not much to anyone until the invention of public-key cryptography. Now it is extremely relevant.

      This is why people like the NSA just love pure maths specialists.

    • by DoctorNathaniel ( 459436 ) <nathaniel...tagg@@@gmail...com> on Wednesday August 21, 2002 @06:35AM (#4110439) Homepage
      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.
      • Actually the sun does go around the earth. In fact, the whole universe spins around the earth. ;)
      • It creates a vibrant research community, which is good for a vibrant teaching environment. (Debatable, but at least some people think so.)

        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.
      • 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.

        Actually a sub-field (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!!

    • slashdot has "no known practical applications" but that doesn't stop it being interesting
  • by jfedor ( 27894 ) <jfedor@jfedor.org> on Wednesday August 21, 2002 @05:06AM (#4110243) Homepage
    Yeah, that's what G. H. Hardy said about number theory back in 1940 (in A Mathematician's Apology). :)

    -jfedor
  • Arrrgh (Score:5, Informative)

    by platypus ( 18156 ) on Wednesday August 21, 2002 @05:07AM (#4110247) Homepage
    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.

    • 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.

      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)

      by mill ( 1634 ) on Wednesday August 21, 2002 @05:28AM (#4110294)
      Turning a doughnut into a coffee cup and vice versa would have serious practical applications for our people in law enforcement though. /mill
      • Yeah, think of the efficiency! But why bother turning one into the other - as they're drinking their coffee, they could just eat the coffee cup as they go along. We don't need no fancy-ass topologists, just a really good baker and some waterproof icing!
    • It's actually not such a bad introductory analogy, speaking as a topologist. In essence topology is the study of spaces, however when most folk think of spaces and math their reference point is high school geometry. However, topology and geometry are not the same thing -- the principle distinction between them lies in the fact that geometry is concerned with distances (and often angles) where topology is not. So we can try to convey this topological focus on the global structure of spaces by explaining that to a topologist a torus' fundamental nature is independent of its particular "mug-like" or "donut-like" form.

      Cheers,
      Scott
      • Yes, but as I wrote, (algebraic) topology is mostely concerned with the _if_ there is a homeomorphism, not how it is constructed.
        At least that is what I learned in topology. But I confess I just did not specialize in topology, when I learned about k-theory, bott periodicity and homotopy theory and the proof that the 7-sphere 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.

    • > 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.

      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.)

    • 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.
    • I don't see why the donut-coffee 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."

  • Langlands Program (Score:2, Informative)

    by euroderph ( 598144 )
    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?
    • Re:Langlands Program (Score:4, Informative)

      by sympleko ( 455517 ) on Wednesday August 21, 2002 @06:59AM (#4110511)
      Here [ams.org] is an expository article from the Journal [ams.org] of the AMS [ams.org] about the Langlands program. Results of Lafforgue are used to prove some very nice theorems.

      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.

  • by Anonymous Coward on Wednesday August 21, 2002 @05:10AM (#4110254)
    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.

  • by MosesJones ( 55544 ) on Wednesday August 21, 2002 @05:53AM (#4110340) Homepage
    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.
    • 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 :)

    • 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.

      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 early-mid 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.
    • Hell YES!!!!

      Research beyond the realm of what's currently possible is the only way to expand the realm of the possible, not to mention practical!

    • 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 ?

      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 far-out math is worse...
    • Just to point out: "having parctical application" and "changing the world" are not exactly the same thing. If something has a practical application, it is a thought based upon which a device can be built: both human knowledge and the ability to change their environment have been enhanced. Books, on the other hand, can have an appreciable impact on society, historical import even. If that were not so, we would be no more than, uh, borgs perhaps?
      OK, so maybe it's just me whom the "no practical application" doesn't bother ... I am aware of the (strong) possibility of future application, and the worth as a contribution to human knowledge - but it still doesn't compare to other realms of venture. That is to say, *any* venture can benefit humanity - art, literature, phuque knows, creative landscaping. Except for maybe the debate on how many angels can dance on the head of a pin. That's pure bull ;)
    • Quoth the poster:
      Game Theory was created by a John Nash
      Actually, Game Theory was created by John von Neumann [newschool.edu], long before the popular media's revisionist historians got their hands on it.
  • by themaddone ( 180841 ) on Wednesday August 21, 2002 @06:40AM (#4110452)
    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.
  • by Anonymous Coward
    So what practical application do the recipients of the Oscars, Emmys, or Grammys perform?
  • We need a cool funky page like the Nobel's Page [nobel.se] 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?
  • 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
  • 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 poet-engineer!

    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

    • I agree that the SF Chronicle's piece wasn't terribly good, and that many reporters have no clue what they're doing. (Keay Davidson's actually a decent journalist; this was just not his best work.) However, your piece is far from a shining example of what science journalism should be, it seems your college paper didn't teach you that writing about science for the public is damn hard.

      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)

    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 [wolfram.com] 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.
    • Is Preda Mihailescu under 40? The only picture I can find of him I can't really guess for sure. The medal only goes to people under the age of 40 at the time of the congress awarding it.

  • well well well, looks like another runner-up in the Fields "I wish that Matt Damon forgot about those lines" will have to be forgone, since there is only one true champion.
    drunk aussies rule

    we rule
  • Fields medal winners do have practical applications, like that guy in Good Will Hunting...
  • Any one searching for some of Voevodsky's work should look for his name in the UIUC K-theory 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."

Every young man should have a hobby: learning how to handle money is the best one. -- Jack Hurley

Working...