Saturday, August 21, 2004

The snobbish Manila Times
The editorial staff of the Manila Times must have a very high regard for the intelligence of their readers. How else can we explain their decision to hire Prof. Escultura as a columnist (who, incidentally, is a townmate)? Just a fortnight ago, the professor was explaining in prose a proof of Fermat's last theorem; today, he is educating his graduate students on the dead ends of mathematics, which he says are foundations, number theory, real and complex analysis, abstract algebra, topology and category theory. (Don't ask me, I have no idea what those are.)


aa said...

Prof Escultura's prose on Fermat's theorm for that paper, is I think, incongruous. Should be in technical or science journals.


E. E. Escultura said...

Two Fatal Defects in Andrew Wiles’ Proof of FLT

The field axioms of the real number system are inconsistent; Felix Brouwer and this blogger provided counterexamples to the trichotomy axiom and Banach-Tarski to the completeness axiom, a variant of the axiom of choice. Therefore, the real number system is ill-defined and FLT being formulated in it is also ill-defined. What it took to resolve this conjecture was to first free the real number system from contradiction by reconstructing it as the new real number system on three simple consistent axioms and reformulating FLT in it. With this rectification of the real number system, FLT is well-defined and resolved by counterexamples proving that it is false.

The remedy for the real number system is given in the paper, The new real number system and discrete computation
and calculus, Neural, Parallel and Scientific Computation, 17 (2009), 59 – 84. The counterexamples are given in
the article, Exact solutions of Fermat’s equation (Definitive resolution of Fermat’s last theorem), Nonlinear Studies,
5(2), 1998, pp 227 – 254.

2) The other fatal defect is that the complex number system that Wiles used in the proof being based on the vacuous concept i is also inconsistent. The element i is the vacuous concept: the root of the equation x^2 + 1 = 0 which does not exist and is denoted by the symbol i = sqrt(-1) from which follows that,

i = sqrt(1/-1) = sqrt 1/sqrt(-1) = 1/i = i/i^2 = -i or

1 = -1 (division of both sides by i),

2 = 0, 1 = 0, i = 0, and, for any real number x, x = 0,

and the entire real and complex number systems collapse. The remedy is in the appendix to the paper, The generalized integral as dual to Schwarz distribution.. In general, any vacuous concept yields a contradiction.

E. E. Escultura

E. E. Escultura said...

Reply to Bart van Donselaar’s article, Edgar E. Escultura and the inequality of 1 and 0.999...

1) The reason Bart van Donselaar cannot see why 1 and 0.99… are distinct is he looks at them as concepts in one’s mind and missed what David Hilbert already knew almost a century ago that such concepts are ambiguous being unknown to others. 1 and 0.99… are distinct objects in the real world like orange and apple and to write the equation orange = apple is simply nonsense.

2) He could not understand why I “claim” that FLT is false and Wiles’ proof is incorrect since he says the proof is admired Worldwide (actually only four or five mathematicians do). I hope he has seen my article, Two fatal defects of Wiles’ proof of FLT, posted in several blogsites and websites.

3) He claims that constructivists have not found hard evidence of defects in standard mathematics. The evidence is just under his nose: Felix Brouwers’ counterexample to the trichotomy axiom, Putnam and Benacerraf, Philosophy of Mathematics, Cambridge University Press, 1985 and my own version in, The new real number system and discrete computation and calculus, Neural, Parallel and Scientific Computation, 17(2009), 59 – 84.

4) He claims mathematicians (he probably means some mathematicians) are happy with traditional mathematics. I wish them continued bliss of innocence.

5) He doubts that I have solved the gravitational n-body problem. I did in the paper, The solution
of the gravitational n-body problem, Nonlinear Analysis, 30(8), Dec. 1997, 521 – 532; the journal is a
publication of Elsevier Science Ltd. based there in Amsterdam.

6) He claims he can compute with nonterminating decimals. His claim is based on unclear thinking. Can he add sqrt2 and sqrt3 and write the precise sum?

7) He also cannot understand why it is impossible to verify whether a nonterminating decimal is periodic or nonperiodic. Clue: the digits are infinite and we cannot look at all of them to check.

8) I notice lately, that Wiles’ supporters have done massive promotion of his proof including publication of some books about it. It will not prosper unless they address my specific criticisms of the proof point blank.


The article is not well thought out and uses rumors and gossips. It quotes Alecks Pabico an amateur journalist who lost his job as a journalist for commenting on an issue he knows nothing about and writing about it that he posted in blogsites and websites across the internet.

Bart is unsure of his ideas, makes claims he cannot verify and resorts to name-dropping which makes me doubt if he, like Alecks, understands what he is writing about.

E. E. Escultura