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Going Beyond Fermat's Last Theorem
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. "
www.math.utah.edu/~shekhar/papers.html
503 - Service Unavailable. There is insufficient bandwidth in the server room to supply you with a copy of this paper.
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.
Starsucks
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?
EagerEyes.org: Visualization and Visual Communication
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.
Don't disappoint your bird dog. Go to the range.
Well, they did practically invent Algebra, so I guess it's of interest from a historical perspective.
Javascript + Nintendo DSi = DSiCade
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 for Serre conjecture
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.
And being an associate professor and at the University of Utah. Why oh why do they flood us with these details? :(
Pretty exciting stuff! (Relatively speaking, of course :-)
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?
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.
It was proved in 1995 by English mathematician Andrew Wiles.
Wikipedia page of the theorem
I don't follow the field close enough to know its relation to Serre's multiplicity conjectures.
From the wikipedia article: "The word algebra itself comes from the name of the treatise first written by a Persian mathematician Al-Khwarizmi 700 AD, who wrote a treatise titled: Kitab al-mukhtasar fi Hisab Al-Jabr wa-al-Moghabalah meaning The book of summary concerning calculating by transposition and reduction. The word al-jabr (from which algebra is derived) means "reunion", "connection" or "completion"."
Computers are useless. They can only give you answers.
-- Pablo Picasso
Um ... the only one related to crypto would be the theorem that a^p mod p == a if p is prime and a is co-prime to p.
That's not only not the famous Fermat Last Theorem but it's also trivially provable with basic number theory.
Tom
Someday, I'll have a real sig.
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.
Letter To Iran
Muslims borrowed heavily from India when they invaded India. The Islamic role in the sciences tended to be more about preserving the best of what they had conquered. As traders, they acted as a point where that knowledge could be disseminated to Europe.
This is my sig.
*ducks*
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.
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.
You can't add pianos and telephones.
With this kind of progress, we should have FTL engines by the end of next year.
Being Indian is totally irrelevant to the story
*sigh*
But the story isn't using "Indian" in a racist way. It's merely an addition, perhaps to shed some "interesting" light on his background outside of his area of research. Not everything that mentions somebody's ethnicity is racist.
You sound like one of those overly-PC people who make things difficult for everyone, just for the sake of trying to live up to some misplaced "holier than thou" moral code.
Person1: "See those kids playing? One of them is my niece."
Person2: "Which one?"
Person1: "The black-haired one."
Person2: "There are six of them."
Person1: "The one in the blue shirt."
Person2: "That leaves four..."
Person1: "Ummm, the one with the sandals..."
Person2: "Three..."
Person1: "...and the red ball."
Person1: "Oh, you mean the black girl? Cute kid."
That may be true, but you'll never truly understand Algebra until you read it in its original Klingon.
Too late, the San Francisco 49ers already drafted him.
Oh wait.
Yes, it's just you.
5 06 530100.htm
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/2005042
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.
Kill, Tux, kill!
http://www.fiestasiesta.co.uk/history/jews.html
Great ideas often receive violent opposition from mediocre minds. - Albert Einstein
Waiting on a math major to give a long-winded set of analogies to make this somehow releevant to the masses....
If religous zealots don't believe in Evolution, then why are they so worried about bird flu?
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).
"There are a dozen opinions on a matter until you know the truth. Then there is only one." - CS Lewis (paraprhase)
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.
I am the Alpha and the Omega-3
We need to find some Weapons of Math Instruction...
That's right. All your base.
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 (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. The proof was flawed.
3) No, the Riemann hypothesis (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...
I heard a better story, but I have no idea if it's true or not.
There was a guy from Jamaica who had to go to the hospital for some reason, and he was driven there by his friend. When filling out the forms, he neglected to fill out the race field, and the receptionist nurse told him that he should check African-American.
He tried to explain to her that he was neither African nor American, even showing her his passport. Eventually he had to point out his (white) friend, who as coincidence has it was of South African descent and an American citizen. An African American, so to speak.
Regrettably, I don't remember how the whole thing ended.
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).