UP Math prof proves Princeton man wrong

Edgar Escultura, a prof­essor of mathematics at the University of the Philippines, proved that Andrew Wiles’ proof of Fermat’s last theorem is false.

In 1993 Andrew Wiles of Prince­ton University announced at a lecture in London that he had proved Fermat’s last theorem (FLT). This is a conjecture by the French mathematician Pierre de Fermat in 1637 that for any integer n greater than 2, Fermat’s equation that claimed xn + yn = zn has no solution in integers x, y z except 0 which satisfies the equation.

Integers are whole numbers like 8, 73, 1,257, etc. Since that time mathematicians and amateurs had been trying to find a proof but failed.

When Wiles made the announcement it was celebrated around the world. In Chicago, for instance, mathematicians marched on the streets in euphoric celebration.

Escultura, who had been working on the problem since 1992, disputed Wiles’ claim and inserted his refutation in the appendix to his book, Diophan­tus: Introduction to Mathematical Philosophy. He went on to present his results at the Second International
Conference on Dynamic Systems and Applications in Atlanta in 1995.

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. Since then Escultura has published over two dozen papers on the
subject, and its applications to physics, in international scientific journals.

Escultura’s refutation sparked much discussion on the Internet that has spilled over to other fields such as physics, astronomy, cosmology, intelligence, learning, chaos, turbulence, gravity and nonlinear analysis.

He took the position that the failure to resolve the problem for over 360 years reveals the inadequacy and defects of foundations, number theory and the real number system. He undertook a thorough critique-rectification of these fields and found, among others, that the real number system in basic algebra, the foundation of mathematics, is defective. Specifically, two of its axioms (the trichotomy and completeness axioms, for those who took basic algebra in high school and college) are false.

Escultura went on to overhaul the real number system and reconstructed it without these false axioms using only three simple axioms instead of 12. The result is a new real number system that is free from defects and contradictions, finite and enriched with new numbers that have important applications for physics.

Using the new real number system Escultura constructed many counterexamples to FLT showing that it is false.

by: Rony V. Diaz

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Escultura was a former math and science editor and columnist of The Manila Times. He also taught math at The Manila Times School of Journalism.

He is currently working with Bernard Ziegler of the University of Texas at Houston on the new calculus based on Escul­tura’s real number system.

Ziegler and Escultura will also collaborate on a new nonstandard analysis, a subject on which Escultura has published many papers in peer-reviewed international journals.

Source: As posted in Balik Pinas Online Group