Don't Let Me Stop You

What the heck, you'll do what you want anyway.

Visit from Dr. Escultura

Posted by Dan Draney on February 21, 2006

We still consider this June, 2005, DLMSY post to be the definitive word on Escultura, Wiles, and Fermat’s Theorem. It includes a complete rundown on the “controversy,” links to other posts here and elsewhere on the topic, an explanation of Fermat’s Last Theorem, and why Dr. Escultura’s claims to have refuted the proof advanced by Dr. Andrew Wiles cannot be believed.

We promised ourself not to write anything more about this topic, but recently another one of our old posts drew some new comments from Dr. Edgar Escultura* himself. Since tomorrow is our blogiversary, revisiting the saga at this time can be justified for “historical” purposes, as well. Our HaloScan comments go away after a few months, so we have copied Dr. Escultura’s comments into this post to preserve them for posterity.

The real number system has a number of defects among which are the following:

1) most of its concepts are ill-defined and are, therefore, ambiguous, nonsense.

2) The trichotomy axiom is false (i.e., it does not qualify as an axiom) because the real number system has no natural ordering.

It follows that FLT as formulated is ambiguous, nonesense, the reason it could not be solved. The first crucial step in resolving FLT would have been to fix the real number system first which Andrew did not do. I did by constructing the real numbers (the decimals, specifically) on three simple consistent axioms yielding the new real number system without ambiguity and contradiction. Moreover, this new mathematical space yields countable counterexamples to FLT proving that it is false. For details of this resolution, see my thread, Contradiction-Free Mathematics, in the math forum Sci Math that started last Jan. 5. All of these is accomplished in over half a dozen papers also listed in the same thread. Together with applications including physics there are now over three dozen papers on the subject in refereed international journals listed in the same thread.

I encourage viewers to take their comments from the top not from the flat of their foot.

E. E. Esccultura [sic]
E. E. Escultura | Homepage | 02.11.06 – 9:37 am | #

The problem with this line of argument, as we explained in our previous post, is that it’s irrelevant. Fermat posed the problem in the integer number system, not the real number system. That’s where Wiles solved the problem, and that’s where any meaningful refutation of Wiles’s work must take place. As we wrote:

We will note, however, that Escultura’s “refutation” of FLT is only valid in the special mathematical universe he has created, at best. Since FLT is cast in the standard number system, disproving it by changing the rules is not much of a feat.

So whether or not this “new mathematical space yields countable counterexamples to FLT” really makes no difference. Redefining decimals? So what? Only integers are involved.

Apparently after reading some other posts here on the topic, Dr. Escultura* returned to leave two duplicate comments on the same thread:

All I have seen here so far are comments that miss the issue and focus on rumors and hearsay when the Manila Times headline of the April 1, 2005 article was quite categorical and unambiguous:

UP Prof Proves Princeton Man Wrong.

I explained in my previous post what the issue was and what I did and cited the publications where I accomplished this feat. No one is interested in those rumors anymore and this website will not thrive on them.

E. E. Escultura

He’s probably right in saying that DLMSY will not thrive on this topic. We won’t be quitting our day job just yet.

* Note that we can’t be absolutely certain these comments are really from Dr. Escultura. It’s possible that someone else is spoofing his identity. The comments were posted from IP addresses in the Philipines, however, and they do make the same arguments Dr. E. has made in in the Manila Times and numerous other venues.

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