## Going Beyond Fermat's Last Theorem 357

Posted
by
Hemos

from the advancing-the-field-of-knowledge dept.

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. "*
## Papers by Khare (Score:4, Informative)

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

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

## Re:And being Indian ... (Score:5, Informative)

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"."## Re:And being Indian ... (Score:5, Informative)

## Re:And being Indian ... (Score:4, Informative)

http://www.fiestasiesta.co.uk/history/jews.html

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

## Re:And being Indian ... (Score:2)

## Re:And being Indian ... (Score:2)

The word "algorithm", which a few of the fellow slashdotters might be familiar with, comes from "Al-Khwarizmi"...

## Re:More importantly (Score:3, Funny)

## Re:And being Indian ... (Score:3, Interesting)

## Re:And being Indian ... (Score:2)

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

## Re:And being Indian ... (Score:3, Interesting)

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

## Re:And being Indian ... (Score:2)

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)

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.

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

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.

## Re:And being Indian ... (Score:2)

## Re:And being Indian ... (Score:2)

## Re:America! Fuck yeah! (Score:2)

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

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

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)

## Don't be so PC (Score:4, Insightful)

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."

## Re:Don't be so PC (Score:2)

## A story (Score:5, Funny)

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.

## Re:A story (Score:3, Insightful)

## Re:And being Indian ... (Score:2)

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

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

## Re:And being Indian ... (Score:2, Informative)

## Re:And being Indian ... (Score:2)

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.

## Home town boy ... (Score:2)

## Re:Racist Double Standard in Society (Score:2)

Heck, you're the one assuming he's not Caucasian just because he's of Indian descent.Wrong. I'm assuming it also. Is that, ok? Why would i not assume it? Why don't you tell me what i should have assumed from the few facts i read in the headline?

Hey, look at that! RTFA and the picture shows an Indian guy who does not look Caucasian!

Anyway, I thought the Indian part was meaningless until i saw the article and noticed that he was still a citizen of India (and not a US citizen that came from Ind

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

## Re:Somebody give that man tenure, quick! (Score:5, Funny)

Oh wait.

## But... (Score:5, Funny)

> 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.

## Re:But... (Score:5, Funny)

## For those who don't get it (Score:2)

## Re:But... (Score:2)

## Isnt everybody? (Score:5, Funny)

poisedto 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.## Re:Isnt everybody? (Score:3, Funny)

## Re:Isnt everybody? (Score:2)

The problem with number theory for me is that they just dont add up.Try using The New Math.

## Re:Isnt everybody? (Score:2)

## Re:Isnt everybody? (Score:2)

## Re:Isnt everybody? (Score:2)

## Re:Isnt everybody? (Score:2, Insightful)

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

## Worried (Score:2)

(http://www.hindu.com/2005/04/25/stories/200504

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

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

## Re:What is it about? (Score:2)

Besides, this is kinda vaporware. Why is this even news? Why not talk about it once it's done?I was thinking the same thing. I'm poised to finish lots of projects myself (mostly linux programs).

## Re:What is it about? (Score:5, Funny)

## Re:What is it about? (mod parent up!) (Score:2)

So we can expect to see lots of elliptic curves and modular functions in DNF... Does this mean they're going to use that new Imaginary engine instead of the Unreal engine?

## Re:What is it about? (Score:2)

Now I have to wonder - was the moderator trying to be nice & bump up your karma my moderating you "informative", or was the moderator totally clueless and thought "hey, this person sounds intelligent - I better mod it informative"

## Poised? (Score:5, Funny)

I mean, I'm

poisedto win the lottery. He's actually doing things.## Re:Poised? (Score:5, Funny)

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)

## Re:Only (Score:2)

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.

## Proof of Progress (Score:2)

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

## Re:Only (Score:2)

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)

Wikipedia page [wikipedia.org] for Serre conjecture

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

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

## Serre Conjecture (Score:4, Interesting)

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

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

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)

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

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

## Re:Every day... (Score:2)

## Re:Every day... (Score:2)

## Re:Every day... (Score:2)

## Re:Every day... (Score:2)

## Re:Every day... (Score:2)

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

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)

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

*ducks*

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

No! no! Introduce a Lemma!

Ya that's it, Proof by Counter-Example, that's the way I like it.

## not trolling but (Score:2)

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.

## Re:erm (Score:2)

What color is the sky in your world?

## Re:erm (Score:3, Interesting)

## Re:not trolling but (Score:2)

Difference in opinion about

## Incredible!!! (Score:4, Funny)

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

## While it's interesting ... (Score:2)

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

## Hmmm... (Score:4, Insightful)

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

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)

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...

## Re:Slashdot and mathematics breakthroughs... (Score:3, Interesting)

## A little exposition (Score:5, Informative)

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).

## Re:Another one? (Score:2, Insightful)

At least this Indian mathematician is still alive. :)Even better, at least this Indian mathematician has a name [slashdot.org].

## Re:Explanation needed (Score:4, Informative)

Wikipedia page [wikipedia.org] of the theorem

I don't follow the field close enough to know its relation to Serre's multiplicity conjectures [wikipedia.org].

## ha (Score:2)

In 1961, Jean-Pierre Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra.I mean, obviously.

## Re:Explanation needed (Score:2)

I thought Fermat's Last Theorem was proved not so long ago by someone else, using some sort of complex geometry concepts. Can any expert confirm this or explain why this is relevant?Like Hollywood - the sequel doesn't have to have anything to do with the original. You just need the name that people know, like Fermat's Last Theorem. I can see it now:

Fermat II: The Serre Conjecture, starring Keanu Reeves as Chandra Khare (he looks Indian enough), a simple mathmetician from Utah. Just when thought it was

## Re:Explanation needed (Score:2)

Fermat II: The Serre Conjecture, starring Keanu Reeves as Chandra Khare (he looks Indian enough), a simple mathmetician from Utah.Did you see the life of Buddha starring Keanu Reeves as good ol' Siddhartha himself?

It was somewhat less than convincing.

## Re:Explanation needed (Score:2)

## Re:Explanation needed (Score:2)

I am fairly certain that Wiles's proof is not the same as Fermat's as some of the concepts used to prove it were not around in Fermat's time.Given that it took Wiles years to prove it, and several mathematical techniques that were unknown until the 1960s (eliptic curves), I think you can be more than fairly certain.

I do not, however, know if this proof could have been the one given by Fermat.We'll have to wait for the proof, but I seriously doubt it.

In my mind the most likely case was that Fermat tho

## Re:Explanation needed (Score:2)

The problem currently stands that proof to Fermat's Last Theorem can only be given by some very complicated math that maybe 1% of the population could understand.I think you could probably make that

1% of mathematicians. I tried reading the 186-page book as an undergrad. Got through page 4 and then realized I wasn't cut out to be a theoretical mathematician.## Re:Explanation needed (Score:3, Interesting)

Can any expert confirm this or explain why this is relevant?Yes, Fermat's Last Theorem was proven by Andrew Wiles in the early nineties.

This result would (apparently) supply another proof. Like the first, it would rely on quite complex and modern mathematics, but a slightly different sort than before.

The thing is that Fermat's Last Theorem is not especially important to mathematics; it's mostly a historical curiosity. However, it is a simple enough equation that anyone with a smattering of mathematics

## Re:encryption (Score:4, Informative)

That's not only not the famous Fermat Last Theorem but it's also trivially provable with basic number theory.

Tom

## Re:GO UTES (Score:2, Funny)

Go Gators.

## Re:GO UTES (Score:2)

three(projected) number one draft picks this year: Alex Smith in football, Andrew Bogut in basketball, and of course Chandrashekhar Khare in mathematics! (Utah Alum, 1984)## Re:GO UTES (Score:2)