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Math Science

Going Beyond Fermat's Last Theorem 357

Posted by Hemos from the advancing-the-field-of-knowledge dept.
amjith writes "An Indian mathematician, Chandrashekhar Khare, is poised to make a significant breakthrough in the field of number theory with his solution of part of a major outstanding problem in algebraic number theory. He is currently an associate professor in Mathematics Department of University of Utah. "
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Going Beyond Fermat's Last Theorem More

Going Beyond Fermat's Last Theorem

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  • Papers by Khare (Score:4, Informative)

    by yodha ( 636988 ) on Monday April 25, 2005 @11:58AM (#12337981)
    www.math.utah.edu/~shekhar/papers.html [utah.edu]

  • And being Indian ... (Score:2, Insightful)

    by ggvaidya ( 747058 )
    is in any way relevant why?
    • Well, they did practically invent Algebra, so I guess it's of interest from a historical perspective.

    • Re:And being Indian ... (Score:5, Funny)

      by Anonymous Coward on Monday April 25, 2005 @12:05PM (#12338072)
      And being an associate professor and at the University of Utah. Why oh why do they flood us with these details? :(
      • Okay, point duly noted :).

        It does just seemed to me as if the point'd been made gratuitously, though. Associate Prof (his current job status in the field: it would've be much more interesting if the breakthrough had come from a full Prof, or a grad student) and University of Utah (if you were interested in following up on it) seems to be more relevant than the country he was born in.

        When was the last time Albert Einstein was refered to as "that German professor", or Isaac Newton as "that English scientist
        • When was the last time Albert Einstein was refered to as "that German professor", or Isaac Newton as "that English scientist"?

          Right after George W Bush was referred to as "That WASP President".

        • Re:And being Indian ... (Score:5, Insightful)

          by Xoro ( 201854 ) on Monday April 25, 2005 @12:33PM (#12338438)
          Yes, it's just you.

          The phrase you find so objectionable is *the first paragraph* of the the linked article in The Hindu, written by one " T. Jayaraman".

          "MUMBAI: An Indian mathematician, Chandrashekhar Khare, is poised to make a significant breakthrough in the field of number theory: with his solution of part of a major outstanding problem in algebraic number theory."

          http://www.hindu.com/2005/04/25/stories/20050425 06 530100.htm

          One suspects that The Hindu wrote it that way because The Hindu takes a special interest in Indians around the world and their achievements -- does this make them racists?

          Only to you.

        • Re:And being Indian ... (Score:3, Insightful)

          by say ( 191220 )

          When was the last time Albert Einstein was refered to as "that German professor", or Isaac Newton as "that English scientist"? It's just not relevant.

          Uh... every textbook I've ever read refer to them that way, until the author of the textbook assumes that you know them and their history already.

          I checked my introduction to philosophy textbook, which almost exclusively refers to philosophers by nationality in the first paragraph they're mentioned.

          I think it's just you, yes.

    • There's a lot of that going arround here [slashdot.org] lately, it seems...
    • Its relevant in that it helps show that not everything in the world is done by Americans or done in the USA - something a lot of slashdotters seem to forget.

    • Re:And being Indian ... (Score:5, Insightful)

      by viscount ( 452242 ) on Monday April 25, 2005 @12:08PM (#12338123)
      It's extra information about the guy that made the breakthrough. It explains why the article that describes the achievement is The Hindu - an Indian newspaper. Obviously you are trying to make a not-so-subtle 'it's racist' comment. Would you have been quite so quick to jump on your high horse if the mathematician was of a different nationality - say American or British?

    • Re:And being Indian ... (Score:5, Insightful)

      by fatmonkeyboy ( 257833 ) on Monday April 25, 2005 @12:09PM (#12338130) Homepage
      Maybe it's not, but then neither is the fact that he's an associate professor at the Mathematics Department of the University of Utah.

      It's pretty common to mention where people are from when giving a news story. It's part of the human interest.

      I mean, look at the "Science" page RIGHT NOW:

      "First hypothesized to be possible 30 years ago by Russian physicist Victor Veselago, meta-material..."

      See? Russian physicist.

      Are you trying to imply there's some sort of racial overtone to the article? I don't get it.

      • Re:And being Indian ... (Score:2, Funny)

        by Anonymous Coward
        They're trying to prove that there is at least 1 non-white guy in Utah.
    • Srinivasa Ramanujan?

    • Re:And being Indian ... (Score:3, Insightful)

      by jea6 ( 117959 )
      It was relevant in the context of the original article, published for an Indian audience on hindu.com.

    • Re:And being Indian ... (Score:5, Funny)

      by zzz1357 ( 863019 ) on Monday April 25, 2005 @12:21PM (#12338303)
      Because Indians are naturally better at higher math than other ethnic groups. Which is why, incidentally, that the early settlers in America tried to wipe them out.
    • I guess I'm the only one who bothered to RTFA.

      The article was from "The Hindu" http://www.hindu.com, which bills itself as "India's online newspaper".

      Which is probably why they care that the guy is INDIAN.
    • The article is in an Indian newspaper, I'm sure a Utah paper would stress the fact that he's at a local university ...

  • Somebody give that man tenure, quick! (Score:3, Insightful)

    by Dr. Spork ( 142693 ) on Monday April 25, 2005 @11:59AM (#12337996)
    I have a feeling a lot of excellent math departments will be looking to hire this guy from Utah.

  • But... (Score:5, Funny)

    by Tackhead ( 54550 ) on Monday April 25, 2005 @12:00PM (#12338008)
    > An Indian mathematician, Chandrashekhar Khare, is poised to make a significant breakthrough in the field of number theory with his solution of part of a major outstanding problem in algebraic number theory.

    503 - Service Unavailable. There is insufficient bandwidth in the server room to supply you with a copy of this paper.

  • Isnt everybody? (Score:5, Funny)

    by ShaniaTwain ( 197446 ) on Monday April 25, 2005 @12:00PM (#12338013) Homepage
    I know I'm poised to make a huge breakthrough, unfortunately I can never seem to make it over that last hurdle, which is, you know.. to make the actual breakthrough.
    • I'm the same. The problem with number theory for me is that they just dont add up.
    • Yeah, it's kind of like patent _pending_. Let me know when you actually _have_ the patent.
    • Without RTFA, I'd guess that it means that he has made some sort of advance, *assuming he's correct* (i.e. the results haven't been verified yet).
      • And after RTFA, I find out that I was wrong:
        In earlier work done with the French mathematician, J.P. Wintenberger, in December 2004, Dr. Khare outlined a two-part general strategy to prove the Serre conjecture fully. The present result is a first key step.

  • Fast Tenure for him (Score:2, Insightful)

    by afstanton ( 822402 )
    If htis pans out as well as it looks like it will, this guy will be a full professor in no time flat.
    • I'm kind of worried about him - the way he sits on that porch reminds me very much of Russell Crowe in A Beautiful Mind.

      (http://www.hindu.com/2005/04/25/stories/2005042 50 6530100.htm)

  • What is it about? (Score:5, Interesting)

    by ghoti ( 60903 ) on Monday April 25, 2005 @12:02PM (#12338031) Homepage
    Could somebody explain what this is about, and what this would mean? There isn't any concrete information on that in TFA ...

    Besides, this is kinda vaporware. Why is this even news? Why not talk about it once it's done?

  • Poised? (Score:5, Funny)

    by ScentCone ( 795499 ) on Monday April 25, 2005 @12:03PM (#12338057)
    So he's involved with outlining a two-part solution... and he's completed one part of it. That's sort of an actual accomplishment, isn't it?

    I mean, I'm poised to win the lottery. He's actually doing things.

    • Re:Poised? (Score:5, Funny)

      by lucabrasi999 ( 585141 ) on Monday April 25, 2005 @12:08PM (#12338117) Journal
      So he's involved with outlining a two-part solution... and he's completed one part of it.

      So, he's involved with outlining the first part of a potential two-part solution to something that is only a theory?

      • Only (Score:2)

        by dstone ( 191334 )
        Creating anything, material or philosophical, can be equally impermanent and unlikely to last. Build a bridge, it falls apart. Build a theory, it falls apart. Your "only a theory" implication of inferiority doesn't stand up.

        • Ah, I wasn't implying that the theory was inferior. I was implying that this story is only relevant when the professor actually completes his task. At this point, he isn't even half-way finished.

          • {throws hands up in the air}
            Right... and while we're at it, no updates on things like space shuttles or Mars missions. It's not relevant until they complete their task after all.

            {catches falling hands, stuffs them in his pockets}
            That said, I kind of know where you're coming from. The world of media is such a fastpaced world that they dare not sit on a story for fear of being "scooped" by opposition. From their perspective, if this guy flops, they quietly drop the story and no one will remember them. On

        • A rigorous proof of a theorem will never fall apart unless the basic axioms of logic fall apart. A proof is basically saying "assuming these things, this must be true."

          The application (the "theory" part) may fall apart, but once proved, the theorem will essentially last forever. That's one of the draws of mathematics.

  • Actual info (Score:4, Informative)

    by vossman77 ( 300689 ) on Monday April 25, 2005 @12:04PM (#12338066) Homepage
    He has proved what is known to specialists in the field as the `level-1 case of the Serre conjecture.' In earlier work done with the French mathematician, J.P. Wintenberger, in December 2004, Dr. Khare outlined a two-part general strategy to prove the Serre conjecture fully. The present result is a first key step.

    Wikipedia page [wikipedia.org] for Serre conjecture

  • you might want to change the URL (Score:3, Informative)

    by neye_eve ( 212185 ) * on Monday April 25, 2005 @12:04PM (#12338067)
    the underline appears all the way through " to make a significant breakthrough in the field of number theory with his solution "

    even though the word "solution" leads to a different link than all of the preceding words.

  • Serre Conjecture (Score:4, Interesting)

    by 00squirrel ( 772984 ) on Monday April 25, 2005 @12:08PM (#12338112)
    More info about the Serre Conjecture can be found here [wolfram.com].

    Pretty exciting stuff! (Relatively speaking, of course :-)

    • Re:Serre Conjecture (Score:3, Insightful)

      by tbjw ( 760188 )
      Somebody mod the parent '-1 Misleading'. There are two problems commonly known as the "Serre conjecture", and the parent happens to point to the wrong one. This problem has very little to do with number theory.

      It's probably best to refer to the conjecture that is on the verge of being solved as "Serre's reciprocity conjecture".

      The other conjecture was solved in 1976, and ought to be called "The Quillen-Suslin Theorem", except that that also could refer to another related but different result.

  • I thought... (Score:3, Interesting)

    by Stalyn ( 662 ) on Monday April 25, 2005 @12:13PM (#12338200) Homepage Journal
    that Serre's Conjecture [wolfram.com] was already proven [wikipedia.org]?

    • Re:I thought... (Score:3, Informative)

      by the_2nd_coming ( 444906 )
      umm.. no.. 3 of the 4 conjectures have been proven.. positivity of R/p and R/Q is still in question.. and no.. showing that it is non negative is not a proof of positivity.. 0 is not positive.

  • Every day... (Score:3, Informative)

    by exp(pi*sqrt(163)) ( 613870 ) on Monday April 25, 2005 @12:14PM (#12338203) Journal
    ...hundreds of new mathemtical theorems are discovered by people around the world. Many of these become peer reviewed and published. So why is this particular one on the front page? It's basically unknown outside of mathematical circles and is posted on a web site where any crackpot can post. Shall we start having stories about JSH on sci.math?

  • The Inevitable "What Use" Question (Score:4, Informative)

    by DumbSwede ( 521261 ) <slashdotbin@hotmail.com> on Monday April 25, 2005 @12:15PM (#12338221) Homepage Journal
    Just to speculate on a possible "what use" question that might arise, I can't help but notice the line This is one of the central themes of modern research in number theory and is devoted to the study of the relation between the symmetries of number theory and geometry. . If I may be so bold, anything that ties the study of pure math to geometry probably has implications for quantum mechanics. These objects may lie embedded in higher dimensions, and probably settle into stable configurations from near infinite possibilities. But they still have to satisfy some allowable mathematical model. This is just the type of thing that may allow us to better predict what those allowable states could be.

  • Beyond Fermat (Score:3, Interesting)

    by amightywind ( 691887 ) on Monday April 25, 2005 @12:15PM (#12338226) Journal
    This is the real problem beyond Fermat [claymath.org]

  • If it's Fermat's last theorem.. (Score:3, Funny)

    by HungSoLow ( 809760 ) on Monday April 25, 2005 @12:19PM (#12338289)
    How can you go beyond it? Is it not the last?!

    *ducks*

  • Is there a webcam? (Score:4, Funny)

    by Anonymous Coward on Monday April 25, 2005 @12:20PM (#12338292)
    Because I love to watch hot math action.

    No! no! Introduce a Lemma!
    Ya that's it, Proof by Counter-Example, that's the way I like it.
  • Why on slashdot?
    I dont have a clue what the proof is about, and it doesn't mention if he is going to use a computer to help with the proof.
    • You don't consider numbers theory and higher math "nerdy" professions?

      What color is the sky in your world?

      • Re:erm (Score:3, Interesting)

        by exp(pi*sqrt(163)) ( 613870 )
        I'm a pure mathematician and I think this story is both uninteresting and irrelevant. It's not nerdy at all. It's a parochial feel-good story for Indians but unfortunately, because it's available over the world, that's to the Web, it's been mistaken for relevant story about something interesting.
    • Are you sure you aren't trolling? :)

      Difference in opinion about /.'s purpose, perhaps. It is "News for Nerds" after all, and nerd-dom is not limited to computers.

  • Incredible!!! (Score:4, Funny)

    by Aumaden ( 598628 ) <Devon DOT C DOT Miller AT gmail DOT com> on Monday April 25, 2005 @12:26PM (#12338365) Journal
    Wow, and to think, Utah's Net Porn [slashdot.org] law has only been in effect for 4.5 weeks.

    With this kind of progress, we should have FTL engines by the end of next year.

  • How is better then when Andrew Wiles proved Fermat's Last Theorem in 1994? I mean Khare's work is also based in part on the Taniyama-Shimura theorem.

    Besides neither one is what Fermat claimed to be his [never/loss documented] answer.

  • Hmmm... (Score:4, Insightful)

    by MrByte420 ( 554317 ) * on Monday April 25, 2005 @12:42PM (#12338553) Journal
    Waiting on a math major to give a long-winded set of analogies to make this somehow releevant to the masses....

  • Serre's Conjecture (Score:4, Insightful)

    by ThosLives ( 686517 ) on Monday April 25, 2005 @01:35PM (#12339120) Journal
    I went hunting to find out what the Conjecture is since it appears to be so important, and stumbled across this [wolfram.com] It appears that this was already proved in 1976 and is now known as the Quillen-Suslin Theorem.

    I wonder, is there a second Serre's Conjecture, or do people not do research any more to see if their work has already been done? Every link I can find for Serre's Conjecture or Quillen-Suslin Theorem indicates that it has already been proved (Quillen got the Fields medal in 1978).

  • Slashdot and mathematics breakthroughs... (Score:5, Informative)

    by hanssprudel ( 323035 ) on Monday April 25, 2005 @01:52PM (#12339282)
    This site does not have a very good record with mathematical breakthroughs that it runs on the front page. Just to give some examples:

    1) A year and a half ago Slashdot ran a story [slashdot.org] (along with most of the MSM) about a Swedish girl having solved the 16th Hilbert problem. That turned out to be a completely bogus claim - she had, in fact, proved nothing.

    2) Slashdot ran with there being infinitely many twin primes [slashdot.org]. The proof was flawed.

    3) No, the Riemann hypothesis [slashdot.org] (the most coveted result in all of Mathematics) has not been proved.

    Those are just the examples I can remember off hand. There have been several more, and I cannot think of a single one that has turned out to actually be true. So please take vague stories about being "poised to make a great story" from local press with a pretty hefty grain of salt...

  • A little exposition (Score:5, Informative)

    by Anonymous Coward on Monday April 25, 2005 @02:34PM (#12339703)
    Glancing over the responses so far, I've come across several links to "the" Serre conjecture. Of course, since this is Slashdot (Land of the Karma Whore) it also looks like not a one of those referred to the conjecture relevant to this discussion.

    The particular conjecture of Serre that matters here focuses on the two-dimensional representations over a finite field of the Galois group Gal(Qbar/Q). Now since that's not particularly illuminating, let me say a bit more...

    First, Qbar denotes the algebraic completion of the rational numbers -- that is, all the stuff you need to add to the rationals so that you can do stuff like factor polynomials with rational coefficients. So things like sqrt(2) are in Qbar, but transcental numbers like pi aren't.

    Gal(Qbar/Q) is the group of symmetries of Qbar over Q -- the ways you can map it to itself while still preserving multiplication and addition, and leaving the rational numbers inside Qbar alone. For instance, complex conjugation gives an element of the Galois group.

    Now one way to understand any group of symmetries is by looking at its "linear representations" -- basically, ways of assigning matrices to each of the symmetries so that matrix multiplication matches up with the composition of symmetries.

    The conjecture talked about here claims to describe (in some sense) all such (irreducible) representations of Gal(Qbar/Q), at least if you limit yourself to 2x2 matrices and coefficients in a finite field.

    This is similar to the Langlands Correspondence, which (among other things) deals with representations of Gal(Qbar/Q) by complex matrices (though not just 2x2).

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