- Escultura has "refuted" Wiles' proof of FLT
- A phony guestbook entry on Escultura's web site is from Wiles
- This guestbook entry represents some sort of admission by Wiles that his proof is "wrong"
- It doesn't really matter whether the "Wiles" note is a real concession or not
Has Escultura Refuted Wiles' Proof of FLT?The answer is clearly, "No." A valid refutation would have been big news in the world of mathematics and science, as big as the original proof was. The silence of the media on this "news" has been deafening. Other than The Manila Times no reputable publication has accepted Escultura's claims to have done so. In as much as The Times has already admitted that Escultura himself is the only source they have consulted on this issue, all this does is raise the question of whether The Times should be considered "reputable."
We have read all the entries on this topic in discussion groups and blogs that Google finds in English and French. We have yet to see someone with a strong math background who accepts Escultura's "refutation" as fact. Those posters who initially proclaimed the proof refuted did so entirely on the basis of the alleged "letter from Wiles" in the Manila Times.
As noted previously, Escultura is not claiming that Wiles' proof is wrong in the normal number system. Instead he claims that the number system itself is "flawed" at its foundations and that Wiles made a "blunder" in formulating his proof in the standard number system. Escultura asserts that individual axioms of standard mathematics are "wrong." To correct these "problems" Escultura constructs his own number system, and it is in this alternate universe that he finds Wiles' proof of FLT is not valid.
Alternative number systems can be of use in special circumstances. However, validity or invalidity of a theorem/proof in one system says nothing at all about the alternative systems. Furthermore, if Escultura has indeed built a better mousetrap, the world of math has yet to beat a path to his door.
To the extent that Escultura has published his "refutation" in reputable, peer-reviewed journals, he has staked his claim. Wiles's proof was heavily scrutinized before and since its publication in a prestigious, peer-reviewed journal. Time and other professional mathematicians will be the judge of who is correct, if there is even any real disagreement beyond which number system to apply to FLT.
Are the Escultura Guestbook Entries from Wiles?The answer is almost certainly, "No." There is no evidence at all that these were written by Andrew Wiles. In emails to Alecks Pabico Wiles has denied writing them, denied having seen them before Pabico directed him to them, denied ever having visited Escultura's web site, and denied even knowing what a "guestbook" on such a site is.
The original Manila Times article quoted a "letter" supposedly from Wiles. Later this was downgraded to an email, and eventually it turned out to be a guestbook posting on Escultura's web site. Letters are more verifiable than emails, and emails are more verifiable than guestbook entries.
There is absolutely no verification process for making guestbook entries on the site, so the notes attributed to Wiles could have been written by anyone with access to the Internet. We were able to create the following guestbook entry:
Name: Richard M. Nixon
Referred By: Just Surfed In
Comments: I am not a crook.
Did the Writer(s) of the Guestbook Entries Admit Wiles' Proof is "Wrong?"Again, the answer is "No." The guestbook contains many entries that are cruelly sarcastic and insulting to Dr. Escultura. Apparently someone thought it would be "funny" to pretend to be Wiles and pretend to concede "error" to Escultura. Unfortunately, the Internet is home to many such people. However, whoever wrote those guestbook entries is most certainly not an admirer of Dr. Escultura, nor is the writer in any way conceding any error.
Evidently Dr. Escultura believes that the guestbook entries were from Wiles. He may have thought the writer was sincere. He may have recognized the sarcasm and decided to play a little joke of his own by publicizing the message through The Manila Times.
Does It Matter Whether or Not Wiles Conceded? We can't really improve on Alecks Pabico's comment in the PCIJ thread:
I disagree that the authenticity of the guestbook entries made by the 'Andrew Wiles' poster is irrelevant as far as the Manila Times story is concerned, especially in light of the repeated denials from Prof. Wiles himself.We can understand Dr. Escultura's desire to vigorously defend his work by all the means at his disposal. However, we think he would be wiser to admit that there is no reason whatsoever at this point to think that the guestbook entries are from Wiles.
Because having proven the messages to be dubious, to say the least, there's nothing newsworthy to report here. There's no story at all. Dr. Escultura's refutation of Wiles's proof to FLT is old hat. Diaz's article even mentions it: 'In 1998 he published his formal refutation in "Exact solutions of Fermat's equations (A definitive resolution of Fermat's last theorem)" in the Journal of Nonlinear Studies, Vol. 5, No. 2, pp.227-254.
The Manila Times is not doing itself any good by pretending that the original story was accurate and giving full backing to Dr. Escultura's claims. If they are paying any attention at all, the Times editors must realize they erred in publishing the phony "Wiles letter" without even attempting to validate it. No doubt they hope to avoid an embarassing retraction and believe everything will soon blow over and be forgotten. Perhaps they are right. However, by letting Dr. Escultura continue to make these claims in their paper they are prolonging the problem and destroying their own credibility.
Technorati: Wiles, Fermat, Escultura, mathematics, hoax, press misconduct, Manila Times