Andrew J. Wiles of Princeton University revealed during a meeting at the University of Cambridge that he had solved Fermat's last theorem. This problem, one of the most famous in mathematics, was posed more than 350 years ago, and its roots extend back to Pythagoras himself. Since no oxen were available, Wiles's listeners showed their appreciation by clapping their hands.
But was the proof of Fermat's last theorem the last gasp of a dying culture? Mathematics, that most tradition-bound of intellectual enterprises, is undergoing profound changes. For millennia, mathematicians have measured progress in terms of what they can demonstrate through proofs-that is, a series of logical steps leading from a set of axioms to an irrefutable conclusion. Now the doubts riddling modern human thought have finally infected mathematics. Mathematicians may at last be forced to accept what many scientists and philosophers already have admitted: their assertions are, at best, only provisionally true, true until proved false.
This uncertainty stems, in part, from the growing complexity of mathematics. Proofs are often so long and complicated that they are difficult to evaluate. Wiles's demonstration runs to 200 pages-and experts estimate it could be five times longer if he spelled out all its elements. One observer asserted that only one tenth of 1 percent of the mathematics community was qualified to evaluate the proof.Wiles's claim was accepted largely on the basis of his reputation and the reputations of those whose work he built on. Mathematicians who had not yet examined the argument in detail nonetheless commented that it "looks beautiful" and "has the ring of truth."
Absolute Certainty?
Friday, May 28, 2004
Thursday, May 27, 2004
To see how much the intellectual landscape has changed, consider the words of President Woodrow Wilson in 1922, asked what he thought about Darwinian evolution. “Of course like every other man of intelligence and education I do believe in organic evolution. It surprises me that at this late date such questions should be raised.”
Compare that with Tony Blair’s reaction to news in 2002 that a state-funded school in north-east England was teaching creationism in biology lessons: “In the end, a more diverse school system will deliver better results for our children.”
How Mumbo-Jumbo Conquered the World
Compare that with Tony Blair’s reaction to news in 2002 that a state-funded school in north-east England was teaching creationism in biology lessons: “In the end, a more diverse school system will deliver better results for our children.”
How Mumbo-Jumbo Conquered the World
Thursday, May 20, 2004
WSJ readers say Fox News has "most accurate" Iraq reports
Wall Street Journal
Readers are asked: Which cable news network provides the most accurate depiction of the events in Iraq?
The results at last look, with 3,976 votes:
CNN 1115 votes (28%)
Fox News 2452 votes (62%)
MSNBC 409 votes (10%)
Wall Street Journal #3180.1
Wall Street Journal
Readers are asked: Which cable news network provides the most accurate depiction of the events in Iraq?
The results at last look, with 3,976 votes:
CNN 1115 votes (28%)
Fox News 2452 votes (62%)
MSNBC 409 votes (10%)
Wall Street Journal #3180.1
Wednesday, May 19, 2004
There are two main human sins from which all the others derive: impatience and indolence. It was because of impatience that they were expelled from Paradise, it is because of indolence that they do not return. Yet perhaps there is only one major sin: impatience. Because of impatience they were expelled, because of impatience they do not return.
A belief is like a guillotine, just as heavy, just as light.
------kafka
and here is one of his essays.
Kafka: Paradise
A belief is like a guillotine, just as heavy, just as light.
------kafka
and here is one of his essays.
Kafka: Paradise
Tuesday, May 11, 2004
But Americans and their allies must understand that Iraq is not a pragmatic society when it comes to religion, culture and sexual mores. It is never acceptable to touch a woman and then come back later to express regret or, worse, offer money. In their culture, Iraqis would accept money and a public apology for the killing of a family member. But in matters of honor — sexual assault, for example — an apology is accepted only when it comes with the head of the perpetrator. Those who are unable to pay such a price had better not commit the offense in the first place. This is why Bush's appearance on Arab TV last week was insulting and meaningless. He can never have enough money to cleanse the shame that his soldiers inflicted upon the Iraqi prisoners, and no words can do this either.
Los Angeles Times: Official U.S. Reaction Compounds the Rage
Los Angeles Times: Official U.S. Reaction Compounds the Rage
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