Thursday, May 12, 2005

Escultura and Wiles III

We have two previous posts on this topic: here and here. However, judging from the traffic on the blog and elsewhere, there is still considerable interest.

Fermat's Last Theorem (FLT) is that for the equation:
x^n + y^n = z^n
there are no non-zero, positive integers for x, y, and z that satisify it for n > 2. This was incorrectly stated in the original article in the Manila Times quoted in the first post on the subject on this blog.

The letters to the editor of The Manila Times include this letter from Roy C. Choco, dated May 10. The copious "[sic]" references were added by the paper. Considering that newspapers routinely edit letters from readers silently to remove these kinds of errors, we surmise that the media in The Philippines are every bit as receptive to constructive criticism as those in the US. Here is Mr. Choco's letter in its entirety:
"I was reading your on-line edition on Thursday (May 5) when I came upon the story about Prof. Edgar Escultura proving the proof advanced by Mr. Andrew Wiles and Richard Taylor on Fermat's last theorem was incorrect. The story is at the very least incomplete and most probably untrue.

First, according to the theory, the refutation of the proof was published in 1998 and was greeted with much discussion on the Internet. A casual Google search on the terms 'proof Fermat's last theorem' yielded websites that only discuss the proof as presented by Mr. Wiles and Mr. Taylor. No mention has been made regarding Mr. Escultura nor his supposed refutation. Did your reporter, Mr. Rony V. Diaz, even made [sic] this kind of cursory search?

Second, according to the story, Mr. Wiles conceded an error regarding his proof and will be reviewing all his proof. But the e-mail was addressed to Mr. Escultura. There is no independent verification of this 'supposed' concession was made [sic]. Did The Manila Times even tried to contact Mr. Wiles regarding this assertion by Mr. Escultura? Nothing in the article leads me to believe that asking Mr. Wiles nor other mathematicians was even considered.

Third, who even said that Mr. Escultura actually refuted Mr. Wiles's proof [sic]? Who or what body was the source of this story? Whom did this person/body/ experts/ decide that Mr. Escultura was correct [sic]? To whom should the readers actually try and validate veracity of the story [sic]?

So The Times ran a story from no-one that was verified by nobody [sic]. Is this the king of journalism [sic] that The Manila Times practices [sic]?� I expected more from your paper.
Obviously, English is not Mr. Choco's native language. However, every one of his points are right on the money. His logic is solid, and his arguments are well-constructed. Mr. Choco missed the sarcasm in the letter attributed to Wiles, but he has plenty of company on that score. Considering the language barrier, even if he suspected sarcasm, Mr. Choco probably would have hesitated to raise that in a public forum.

So what does The Manila Times have to say in response?
"The source of our information, including the letter of Dr. Wiles, was Dr. Escultura. We did not have any reason to doubt him. Escultura published his refutation of Wiles's proof and counterexamples to Fermat's last theorem in: (1) Proceedings of the Second International Conference on Dynamic Systems and Applications, Atlanta, 1995. (2) Exact solutions of Fermat's equation, Nonlinear Studies, 5(2), 1998. (3) Mathematics of the new physics, Applied Mathematics, Computation (138(2), 2001. (4) New mathematics and physics, Applied Mathematics, Computation, 139(2), 2003.

More discussions on the FLT can be found in: (1) Usenet Archives, (2) Archives of Mathforge.Net and (3) Archives of news group Sci Math, among others on the subject.

The editors who published Escultura's refutation and counterexamples are V. Lakshmikantham (USA), M. Sambandham (USA) and M. Scott (USA). Mathematicians who acknowledged and/or congratulated Escultura were R. Agarwal (USA), editor, Archives of Inequalities and Applications; G. Osipenko (Russia), editor, Electronic Journal of Differential Equations; Xilin Fu (China); L. Kusmina (Russia); V. Gudkov (Latvia). "
So we learn a couple of important things here. The letter attributed to Dr. Wiles was, as we suspected, supplied by Dr. Escultura. As Mr. Choco suspected, the paper did no fact checking at all before publishing the story. Furthermore, they still feel no need to check the critical fact of the story, namely the authorship of the purported "concession" email.

Without the "confession" from Wiles of his "error," there's really no story here. Dr. Escultura has been publishing his work on the topic for years in the places cited above, on his own web site, and in The Manila Times. The whole "sizzle" of this story is the Wiles "concession." It absolutely required a verification that the letter was actually from Wiles and that he was in fact abandonning his previous positions on the topic.

We don't suggest that Dr. Escultura faked the email, in fact we are certain he did not do so. However, it is not enough to "trust" him on this. Spoofing an email to make it appear to come from someone else is easily done. It's quite clear no one has checked the email header for evidence of spoofing.

Furthermore we don't believe for a moment that this email letter represents any sort of acknowledgement by Dr. Wiles that Dr. Escultura has refuted his work. We doubt that Wiles had anything to do with the letter, but it is absolutely clear that whoever wrote it was not doing so out of respect for Dr. Escultura's work.

As for the references cited for the work itself, postings on MathForge or Usenet groups prove nothing at all, as will be obvious to anyone who has read such groups. Conference proceedings are not peer-reviewed publications. Math is not our field, so we are not familiar with the journals "Applied Mathematics, Computation" or "Non-Linear Studies," but we have no reason to doubt their legitimacy.

If you're scoring this at home, that's Choco 1, Manila Times 0.

Some other discussions on this topic can be found here and here.

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