Monday, May 09, 2005

Wiles, Escultura, and Fermat

We posted last Thursday about this story in Don't Let Me Stop You: Math Wars. Briefly, Dr. Edgar Escultura, a mathematician in The Philippines believes he has refuted some work of mathematician Andrew Wiles of Princeton Univ. The math at issue is a proof, by Wiles, of a 350-yr-old "theorem" of mathematician Pierre de Fermat.

A bit of an international kerfuffle has ensued, as Escultura received a letter, purportedly from Wiles, which was published in The Manila Times with a reply from Escultura. The thesis of the newspaper report is that Wiles' letter had "conceded an error in his proof," admitting that Escultura is correct.

However, as we pointed out last Thursday, the Wiles letter is clearly dripping with sarcasm. The full letter is in the previous post and the Manila Times article, but consider these excerpts:
Also I'd like to have the address of the guy who let you get a PhD 30 years ago. I'd like to discuss few things with him...[elipses in original]
Translation: "How in the heck did you ever get a PhD?"
Your work is incredible, I read all of it just yesterday and let me tell you I respect you.
Translation: "Your work is so simplistic that I read all of it in one day." There's more, but you get the idea. This is not a letter graciously conceding an error, and it does not say an error has been found. It only says:
I am going to review all my 'proof' which I am sure is wrong (thanks to you!).
Coupled with the rest of the letter, this is not an admission of error.

Now this letter may not have been written by Andrew Wiles; it well could be a forgery. Someone could be playing a joke at Prof. Escultura's expense. It is crystal clear, however, that this is not a case of Wiles admitting Escultura has caught him in an error.

Today the Manila Times article is still posted, without any follow up or correction. It's hard to believe that no one has pointed out the obvious sarcasm by now. Perhaps there is a cultural difference between the Philippines and America that makes the sarcasm less apparent.

On the math bulletin board,, Escultura joins in on this thread started by an anonymous jokester on April Fool's Day with this post:
It appears the search for a proof to Fermat's Last Theorem, a 350-year-old problem that has puzzled the greatest intellects in mathematics since its conception, is back underway. Professor Jack Vincenza of Iowa State University took out Andrew Wiles' proof for one last look "on a hunch," a 'hunch' which turned out to be fatal for Wiles and his beloved 'proof.'

"I remembered that the handwriting on one of the long divisions was nearly illegible and the ink was a little smeared," Vincenza said in a press release. Vincenza was tipped off by a conversation he overheard from a bathroom stall where Wiles and a student of Wiles were chuckling about 'pulling a fast one on all of those sorry S.O.Bs.' After working out the long division, Vincenza noticed the mistake. Wiles had, intentionally it seemed, not carried a '3.' "I've been waiting for an opportunity to bring that bastard to his knees for 11 years now," Vincenza said.

Wiles, who responded from Kuala Lumpur where he was preparing to sky surf between the Petronas Towers, said, "I'll show him and prove the Riemman hypothesis. Damn! I'll prove everything if I have to. Shit, I'll carry that three right to his door."

Prof. Escultura's reply two days later missed the April 1 aspect of the first post. Another poster cites the Manila Times article.

The Sassy Lawyer also has a post on this, along with several comments, including this one which is right on the money:
"Carla commented on 05-09-05 at 04:34 AM :
From the sarcastic letter from 'Wiles' (or someone purporting to be Wiles) and from what I've heard from other mathematicians, I think this is a hoax. Wouldn't something this revolutionary be cited by the scientific community? Not just in discussion groups but by professional bodies."
We take no definitive position on Wiles' proof vs. Escultura's refutation, lacking the necessary expertise. However, it's hard to see how Escultura's examples counter to the theorem in his own number system can be said to disprove Wiles' proof which is done in the standard number system. At most it would seem such examples could refute the proof in Escultura's number system. The MathForge thread contains links to Escultura's websites for those who want to read more about his theories for themselves.

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