(Roughly) Daily

Posts Tagged ‘Fermat’s Last Theorem

“I have had my results for a long time, but I do not yet know how to arrive at them”*…

 

Fermat

Andrew Wiles gave a series of lectures cryptically titled “Modular Forms, Elliptic Curves, and Galois Representations” at a mathematics conference in Cambridge, England, in June 0f 1993. His argument was long and technical. Finally, 20 minutes into the third talk, he came to the end. Then, to punctuate the result, he added:

=> FLT

“Implies Fermat’s Last Theorem.” The most famous unverified conjecture in the history of mathematics. First proposed by the 17th-century French jurist and spare-time mathematician Pierre de Fermat, it had remained unproven for more than 350 years. Wiles, a professor at Princeton University, had worked on the problem, alone and in secret in the attic of his home, for seven years. Now he was unveiling his proof.

His announcement electrified his audience—and the world. The story appeared the next day on the front page of The New York Times. Gap, the clothing retailer, asked him to model a new line of jeans, though he demurred. People Weekly named him one of “The 25 Most Intriguing People of the Year,” along with Princess Diana, Michael Jackson, and Bill Clinton. Barbara Walters’ producers reached out to him for an interview, to which Wiles responded, “Who’s Barbara Walters?”

But the celebration didn’t last. Once a proof is proposed, it must be checked and verified before it is accepted as valid. When Wiles submitted his 200-page proof to the prestigious journal Inventiones Mathematicae, its editor divvied up the manuscript among six reviewers. One of them was Nick Katz, a fellow Princeton mathematician.

For two months, Katz and a French colleague, Luc Illusie, scrutinized every logical step in Katz’s section of the proof. From time to time, they would come across a line of reasoning they couldn’t follow. Katz would email Wiles, who would provide a fix. But in late August, Wiles offered an explanation that didn’t satisfy the two reviewers. And when Wiles took a closer look, he saw that Katz had found a crack in the mathematical scaffolding. At first, a repair seemed straightforward. But as Wiles picked at the crack, pieces of the structure began falling away…

How mistakes– first Fermat’s, then Wiles’– reinvigorated a field, then led to fundamental insight: “How Math’s Most Famous Proof Nearly Broke.”

* Karl Friedrich Gauss

###

As we ponder proof, we might we might spare a thought for Josiah Wedgwood; he died on this date in 1795. An English potter and businessman (he founded the Wedgwood company), he is credited, via his technique of “division of labor,” with the industrialization of the manufacture of pottery– and via his example, much of British (and thus American) manufacturing.

Wedgwood was a member of the Lunar Society, the Royal Society, and was an ardent abolitionist.  His daughter, Susannah, was the mother of Charles Darwin.

 source

 

What’s (the) matter?…

 source

On the heels of yesterday’s film recommendation, another… albeit somewhat different:  Stanford physics professor, Leonard Susskind, one of the fathers of string theory, articulator of the Holographic Principle,  and explainer of the Megaverse, has a gift for making science accessible… a gift that is on display in this lecture, “Demystifying the Higgs Boson“:

(email readers, click here)

###

As we say “ahh,” we might spare a thought for Pierre de Fermat; he died on this date in 1665.  With Descartes, one of the two great mathematicians of the first half of the Seventeenth Century, Fermat made a wide range of contributions (that advanced, among other fronts, the development of Calculus) and is regarded as the Father of Number Theory.  But he is best remembered as the author of Fermat’s Last Theorem.* Fermat had written the theorem, in 1637, in the margin of a copy of Diophantus’ Arithmetica– but went on to say that, while he had a proof, it was too large to fit in the margin.  He never got around to committing his proof to writing; so mathematicians started, from the time of his death, to try to derive one.  While the the theorem was demonstrated for a small number of cases early on, a complete proof became the “white whale” of math, eluding its pursuers until 1995, when Andrew Wiles finally published a proof.

* the assertion that no three positive integers ab, and c can satisfy the equation an + bn = cn for any integer value of n greater than two

 source

Written by LW

January 12, 2013 at 1:01 am

%d bloggers like this: