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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
is in any way relevant why?
I have a feeling a lot of excellent math departments will be looking to hire this guy from Utah.
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
At least this Indian mathematician is still alive. :)
Even better, at least this Indian mathematician has a name.
If htis pans out as well as it looks like it will, this guy will be a full professor in no time flat.
Reject Fear - Embrace Hope
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.
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.
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?
BCS and Math busters, yeah! (Utah Alum, 2003)
Pretty exciting stuff! (Relatively speaking, of course :-)
If I remember correctly this can have quite an effect on the area of cryptography. I seem to recall something about one of Fermat's theorms in regards to RSA encryption. It's been awhile since I've studied it though so I'm not sure.
This is a direct quote from TFA.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
that Serre's Conjecture was already proven?
The best education consists in immunizing people against systematic attempts at education. - Paul Feyerabend
...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?
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
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
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.
This is the real problem beyond Fermat
an ill wind that blows no good
I remember in HS we once watched a play on DVD on Fermat's Last Theorem. It was called Fermat's Last Tango . It was a rather interesting thing seeing mathematics portrayed in a musical form, and to this day, I still recall parts of the lyrics.....
In undeveloped countries, the consumer controls the market. In capitalist America, the market controls you.
*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.
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.
love is just extroverted narcissism
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."
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 Indian descent).
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.
2 50 6530100.htm)
(http://www.hindu.com/2005/04/25/stories/200504
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?
Uh, where was he when he did this?
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
Besides neither one is what Fermat claimed to be his [never/loss documented] answer.
"I hate to advocate drugs, alcohol, violence or insanity but they've always worked for me" - HST
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?
What color is the sky in your world?
You better watch out, there may be dogs about . .
The article is in an Indian newspaper, I'm sure a Utah paper would stress the fact that he's at a local university ...
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.
hah DNF .. ive been waiting for that forever...
He did a little too much LDS at Berkely.
There is no such thing as 'chocohol' or 'workahol'.
Webpage of TIFR (Tata Institute of Fundamental Research) mentioned in the article.
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 the other hand, if he succeeds, they can crow "We were there first!" and quite possibly get first coverage of his success. From the mathematician's perspective, he's just commenting on his progress to someone who seems an interested observer. Too, by getting an interview, he's getting publicity which may lead to further funding to his coffers to solve the problem. That's... not wrong, albeit something which does not sing to my soul.
All in all, I think the article is reasonable if perhaps a bit misleading in title.
This sig has absolutely no significance and serves only to take up screen space and waste the time of the reader.
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)
This is pure psychobabble like something lifted out of Star Trek. And it gets modded up!
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
Here's my two part solution to winning the lottery:
1) Buy a ticket
2) Verify the winning number.
I have actually completed the first step.
I'm a little stuck on part 2), but I'm really poised.
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.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
Fermat claimed he found a truely remarkable proof for his theorem, but he also claimed that the margin was too small to contain it. The parent is a nice meme of that quote.
It takes a man to suffer ignorance and smile
Be yourself no matter what they say
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...
Hah! America is imperious to your weapons!
Get thee glass eyes, and, like a scurvy politician, seem to see things thou dost not.--King Lear
"Well, double dumbass on you!"
That's right. All your base.
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.
It's been at least a month since I last heard the "Some Indian math guy" meme...apparently people forgot it was supposed to be a joke about the lack of a name in the original article.
A mistake that this article, fortunately, didn't repeat.
tasks(723) drafts(105) languages(484) examples(29106)
do it.
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).
Yeah, I know he never thought it was great but I wonder how much pressure he felt to find Fermat's proof and not just one that worked. (As I'm sure you know) rumor had it Fermat solved it in a single page book margin, something that seems rather suspect leaving open the idea Fermat actually never correctly solved it.
I'm interested to see how Khare uses Taniyama-Shimura. Could FLT ever be proven without it?
Great reply 2nd_coming. Thanks again.
"I hate to advocate drugs, alcohol, violence or insanity but they've always worked for me" - HST
What is it with guys named Chandrashekhar and math?
Media that can be recorded and distributed can be recorded and distributed.
-kfg
I have a remarkable proof to this assertion but the web page is too small to contain it.
an ill wind that blows no good
I was pleasantly suprised to find that a book about a mathematical proof would be one of the most interesting books I've ever read.
It's really a series of biographies of mathematicians who contributed to the solution over the 350 years it went unsolved.
http://www.amazon.com/exec/obidos/tg/detail/-/038Like Sophie Germain, who in the 18th century gained admittance to the misogynist Ecole Polytechnique by taking over the identity of a former male student.
Her brilliance ultimately lead to her exposure, but by then the patriarchy could not deny her.
An anonymous member of the Longhorn team has stated that the proof will be included in Longhorn. Other problems to be solved by Longhorn are perpetual motion and cold fusion.
"Of the six (trigonometry functions), five seem to be essentially Arabic in origin; only the sine function was introduced into Islam from India."
/ Islamic%20astronomy.htm
http://faculty.kfupm.edu.sa/phys/alshukri/PHYS215
I have to add, while the role of Islamic science in preserving and transmitting knowledge from Greek, Egyptian, Chinese and Indian
societies was important, it wasn't the only one. Muslim scientists did a lot of ground breaking work in astronomy, medicine, geometry and algebra.
Abu Bakr al-Razi (844-926) made the first connection between bacteria and infection.
Omar Khayyam better known as a poet, made significant contributions to the solution of cubic equations
by geometric methods involving the intersection of conics.
Nassereddine al-Tusi is credited as the founder of modern trigonometry, separating it from astronomy.
Google for more if you are interested.
As a side note, any time you hear a scientific type term starting with 'al' it came from Arabic. That
includes algebra, algorithim, alcohol, alkali
It has been known for decades that electrons can only inhabit certain discrete shells of probability about the nucleolus of an atom. Similarly for the nucleolus, the protons and neutrons can only take up certain desirable configurations. We don't know all the details of how this comes to happen, but the laws of geometry and topology govern it, perhaps as a result of actions taking place in dimensions above the normal 3+1. This might give us another tool in predicting what these stable configurations might be on the elementary particle scale, whether they are electron orbits, or atomic nucleolus configurations, or quark bindings in mesons. This is what I was trying to say. Maybe I said it poorly, I was trying to be concise. Maybe this is still a string of fancy sounding words with no common thread to you.
I appreciate the kind words from StillNeedMoreCoffee in this mater. I was trying to be vague enough to include the possibility that it might have implication in Quantum Computing. In trying to be as general as possible perhaps I muddy my meaning and message. The reference to near Infinite was indeed a reference or guess has to how these possible configurations are settled into, by some not yet understood quantum mechanical operation that allows many things to be tried in parallel before deciding on the optimal solution and collapsing into it.
As to the Karma Whoring accusation, having looked at your log, you post often and get points, are you a Karma Whore? What would be the difference between us? I have had Excellent Karma for over two years. I care little for Karma and post to try to state opinions and get feedback. Feedback that is corrective or informative is the best. Yours would not pass that test.
If wanting to have a thread of discussion with others on my take of things is Karma Whoring then so be it. I would have thought this was the whole reason for Slashdot.
You make me sad. On the other hand you have challenged me to explain myself better, but I doubt that was your intent.
Letter To Iran
Well, wonder no more!
LDS=Latter-day Saint, abbreviation of The Church of Jesus Christ of Latter-day Saints, based in Utah. The guy in question is at the University of Utah.
I'm not sure if that was the joke, but you said you didn't know what LDS is.
He's a better joke, though:
What do you get if you cross LDS with LSD?
A high-priest!
Sam
blog.sam.liddicott.com
Parent may have been refering to a moment from Star Trek IV:
"William Shatner (Kirk): Oh, him? He's harmless. Part of the free speech movement at Berkeley in the sixties. I think he did a little too much LDS."
See here.
The mere fact I know this may mean I'm not getting a date with anyone not in a Troi costume for a year or two.
Tweet, tweet.
thank you for reminding me of a million exam nightmares. No, really.
Where's James Harris when you need him?
yee-haw, fellow Utes on slashdot!
I was looking over the name and it rung a few bells, however, our quantum mechanics geeks in here might remember a certain law about the creation of black holes known as Chandraskhar's Limit Not related apparently, but worth reading up on. Does the name just build geniuses or something *peers around warily*
I like losing arguments, it just means that I can take your point and make it my own.
Can someone give a short explanation of this conjecture -- small enough to fit in the margin of a book, say?
But, I wanted socialized health insurance!
To expand on this comment: http://science.slashdot.org/comments.pl?sid=147252 &cid=12338367
n Caucasian ( P ) Pronunciation Key (kô-kzhn, -kzhn)
adj.
Anthropology. Of or being a major human racial classification traditionally distinguished by physical characteristics such as very light to brown skin pigmentation and straight to wavy or curly hair, and including peoples indigenous to Europe, northern Africa, western Asia, and India. No longer in scientific use. See Usage Note at race1.
http://dictionary.reference.com/search?q=caucasia
Wow! It seems that not only whites are Caucasian, but Egyptians and other North Africans, Arabs, and Indians are too! Gee, isn't it funny how some words actually have specific meanings!
The road to hell is paved with good intentions.
There's no disputing the invention of Zero as Indian (AFAIK), but I seem to recall reading that algebra was considered "created" in the Islamic world when they began to substitute "symbols" for numbers.
"1000-post-a-day" - about 1 in 6 people on the planet are Indian?
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
considering race doesn't exist except in the minds of ignorants, this doesn't seem to be an issue.
Wonder Woman Where Did You Go Without Us? SOMEWHENELSE I GUESS!! Chandrashekhar Here's the true story of Sophie Germain, an 18th-century woman who assumed a man's identity in order to pursue her passion -- attempting to prove Fermat's Last Theorem. http://www.pbs.org/wgbh/nova/proof/germain.html
If you're not cheating you're not trying.
It is ridiculous to blame the present state of Islamic nations on the Mongols or the Crusades.
First off, the USA did not even exist when the Mongols or Crusades happened, yet, has easily surpassed the greatest achievements of the middle east within a scant two hundred years. Americans did, after all, put a man on the moon.
Secondly, the Japan and Germany were both completely destroyed during World War II through its bombing campaigns, and those nations both have bounced back. The Mongols did not fire bomb Baghdad.
To have a scientific society, you have to have some pre-requisites:
a) You have to accept scientific findings when they clash with religious findings. You have to admit that whatever holy book you believe in is not the only source of knowledge, and -gasp- is probably wrong. Even the Communists could manage that one, which is why despite Russia going to hell in a handbasket economically, they beat the USA into space.
b) You have to have a society which accepts open communications on scientific matters, as a minimum, and encourages open communication altogether. Again, even under Russian communism, they could communicate relatively freely about matters of science. But more so in western nations can scientists communicate, and that is why the west leads in technology.
Islamic societies do not have these prerequisites.
Religious leaders have real political power, and Islam, religious leaders hold that, because Islam is a "practical religion", they can rule on all aspects of life. Every time someone says anything, you get some two bit cleric tossing out a fatwah or declaring a jihad about topics that they aren't remotely qualified to speak to. In the west, if someone asks a question, the thing to do is to run an experiment and find out. In Islam, the thing to do, is ask a cleric, who makes something up.
Islamic societies have achieved nothing despite vast investment.
The transfer of American money into the middle east is one of the largest transfers of capital in human history. Since the end of World War II, America has purchased probably close to 20 trillion dollars worth of oil from the middle east. Where has all this money gone? Are there new technology centers in the middle east? Is the middle east producing any new drugs to fight disease with? Is the middle east even a banking center? Nope, no and no. Instead, they just sit on that oil and take their money and just waste it, the same way they sat on world trade routes and wasted their money when they were a great empire.
It's time for Islamic countries to stop blaming their failures on everyone else but themselves.
This is my sig.
So much nonsense that its hard to know where to start...
1) My mention of the Mongol invasion was simply a statement of historical fact. You implied that it was Islam which stopped Arab scientific progress. I INFORMED you that:
a) Arabs started progressing scientifically AFTER they became Muslim, not before
b) Arab scientific progress WAS more or less stopped in its tracks after the Mongol invasions.
Those are facts. Easily researched. So, in conclusion, I do not agree with your assertion that Islam was the reason for stagnation.
Whether you approve of how the Arab world handled the aftermath of the Mongols is neither here nor there.
2) I did not blame the current state of the Muslim Ummah on the Mongols or the Crusades. I put those events into their proper historical perspective. They happened, they had a profound and lasting effect. Thats called history.
Your logic is faulty if you imply from that that I was arguing that this excuses the current state of the Muslim world. I didn't even broach that topic.
3) Each dominant civilisation stands on the shoulders of the dominant civilisations which preceeded it. The Egyptians built on the Mesopotamians. The Greeks built on the Egyptians. The Romans built on the Greeks. The Arabs built on what the Greeks, Chinese and Indians provided. Europe built on the advances made by the Arabs.
At each stage, the rate of progress increases. Civilisation and technological prowess, generally speaking, tends to follow a linearly upward path.
Consequently, comparing the rate of progress made by the US is misleading - tantamount to dishonesty. They built on the foundations others had laid (see above, as well as the British).
The successor dominant civilisation to the US will themselves, in all likelihood exceed the rate of progress achieved by the Americans.
4) "You have to accept scientific findings when they clash with religious findings"
Really? Are you actually aware of a significant instance where Islam actually contradicted scientific findings?
Or are you just assuming that because Christianity (to take an example) was incompatible with many facets of scientific progress over the centuries (Copernicus, Galileo, etc), that the same must be true of Islam as well?
An ignorant assumption.
5) "In the west, if someone asks a question, the thing to do is to run an experiment and find out. In Islam, the thing to do, is ask a cleric, who makes something up."
This is just so stupid that I hardly know how to respond.
6) "It's time for Islamic countries to stop blaming their failures on everyone else but
themselves."
I wasn't. To paraphrase (for your benefit), I would propose that its time for people like you to stop heaping half-baked, false accusations against Islam and Muslims when you are so ignorant of the matters at hand.
In conclusion:
You have 2 paths you can follow.
1) Realise that your world view is not as informed as you thought it was, come down off your pedestal and learn some more before spouting nonsense. You may become a better person for it.
2) Stay in your current blinkered mindset. Keep persuading yourself that you are not a bigot. Continue to associate with like minded people who will make you feel better about your beliefs. Keep your TV tuned to Fox News 24/7. You'll feel better about yourself - even if it is all hogwash.
In either case, there really is no point in arguing the matter further with people like you. So, lets stop here.
I should also mention that my criticisms are equally valid for Christianity to. They are universal. For example, christian fundamentalist efforts to ban teaching of evolution, efforts to reject the results of carbon or radioisotope dating, or to control cultural values through the government, are just as damaging to American democracy as Islamic clerics are to the prospect of democracy in Iran.
I asked a cleric point blank, on the pro-islam web site, why there was no separation of church and state in Islam, and he said flat out it that it was because no seperation was necessary as Islam was a practical religion and the Koran held all the truths. This is the same kind of answer that we get from our own fundamentalists here and the results of that are generally non-conducive to science.
I've long argued that a democracy in the middle east is possible and have supported President Bush's efforts to bring Democracy to Iraq. On the other hand, those who are against the idea of democracy in the middle east generally believe that arabs are "animals" and are incapable of forming an elected government. I reject that position and I say, yes, I do think that arabs can build a democracy, but I say that knowing that those arabs working to do so are bringing with them a new kind of islam that addresses some of the criticisms that I have mentioned.
IF the experiments in Iraq and Afghanistan succeed, then yes, we can look back and view it as a turning point where Islamic states began to move towards modern times. But, barring those two nations, there is not much movement. There is no free press in Saudi Arabia or Iran. There is no wide open internet in Iran.
This is my sig.
Hmm, what do we have here?
Completely irrational ravings, replete with half-truths and outright lies. You are just shouting from the 'raving anti Muslim' hymn book, without any realisation that much of what you say is completly untrue.
There is so much nonsense in what you say, and such bile in the world view behind it, that I just cannot even start to refute it. Its like trying to convince a committed Nazi why they shouldn't regard Slavs and Jews as sub-human. No matter what one says, they wouldn't get it.
You didn't even understand what little I tried to convey. I don't love the Taliban - never said that I did. Reforms in Iran? You have no clue about what society is actually like in Iran, or what level of empowerment the people there do or do not have.
Being deeply ignorant about a subject or a people isn't great - but noone can know everything about everything. However, being deeply ignorant about a people, and simultaneously holding strong and harsh views about them is simply unconscionable.
In a sick sort of way, you really are as much of a fundamentalist as those you despise. You started off by lauding the scientific spirit as one which holds knowledge and the quest for knowledge as everything. And yet you cannot bear to subject your own world view to an examination by the facts.
Here's one fact to throw a spanner in your works. Digest this, and see how it fits in your perspective on things.
Some of the Prophet (peace be upon him) most famous sayings:
"The ink of the scholar is more holy than the blood of the martyr"
"You should go even to the walls of China for learning'
"The man who educates 2 daughters has built a wall in between himself and hell"
I dare you to dip your toe in the water and educate yourself about the reality of Islam and Muslims, before you continue to preach nonsense about them.
Do that with an OPEN MIND (as all good scientists would), and then preach what you like. Until then, keep your opinions to yourself.
Whatever I say to you simply goes in one ear and out the other - with no processing in between. There is only so much I can say to a brick wall. This conversation is at an end.
Ok, some quotes from the Koran, which I incidentally read.
"Slay them wherever you find them. Drive them out of the places from which they drove you. Idolatry is worse than carnage"
"Prophet, make war on the unbelievers and the hypocrites and deal rigorously with them. Hell shall be their home: an evil fate."
"Men have authority over women because God has made the one superior to the other, and because they spend their wealth to maintain them. Good women are obedient"
Look, the Koran is an old book and riddled with as much contradiction and cruelty as the Christian bible. But obviously most Muslims are just people , and can interpret the goodness within it for themselves and arrive at a just society. God imbues every Muslim with a soul, not just the Mullahs, so, in light of that, why should not God decide that only a special set of "mullahs" should hold political power? Why should the interpretation of the Koran by a bad Mullah be better than the good works of a good Muslim citizen? Who is closer to the divine, the Ayatollah Khoemini that ordered so many people killed that opposed Islam, or, the westernized Islamic student that might cure cancer and save millions of muslims? Who would have more of a right to lead a nation? A man that has memorized the Koran or an economist?
Look, if the people of the middle east democratically elect a fundamentalist Islamic state and decide for themselves that they would rather not have as much technical or economic progress in order to satisfy their spiritual goals, that's fine. Just don't go blaming the West for making that decision, that's all!
This is my sig.
One part of Serre's conjectures was proved some time ago by Ribet and Edixhoven, and this was used as part of the proof of Fermat's Last Theorem. I have found on the web that the recent proof of some cases of Serre's conjecture is currently being explained by Edixhoven in two talks "On Serre's conjecture in level one [Khare, Wintenberger, Dieulefait]", at: www.math.leidenuniv.nl/~gabor/geom_sem.html, and by Ribet in: "The modularity of some mod p Galois representations": "I will sketch the main ideas of recent preprints of Khare-Wintenberger and Dieulefait that allow one to establish certain cases of Serre's conjectures", at: http://www.cms.math.ca/Events/summer05/abs/Plenm.h tml