Thursday, May 12, 2005

P vs NP is for kids...

In our humble corner of the mathematical landscape we jump excitedly at each new proof that P = NP, P != NP, or even P = RP?. But for the brave souls who patrol the vast expanses of sci.math, much more enjoyment is to be had.

Dave Rusin maintains a page of some the "many delights available through the internet". Among them, the daring exploits of one Edgar Escultura, mathematics professor in the Phillipines, who slayed not one, but two mighty mathematical dragons.

In 1998 (search for Escultura), he disproved Fermat's Theorem, demonstrating that "trillions upon trillions" of numbers satisfying the equation exist. A lesser man would have balked at the existence of a contradictory proof; Prof. Escultura is not one of those men. Faced with a cruel and unrelenting system of numbers that mocked him, he invented a new one !

When Wiles announced his proposed solution of the problem in 1993, Escultura pointed out his main error as lack of knowledge of recent mathematical discoveries, particularly, the uncertainty in the behavior of large numbers and in dealing with infinite mathematical systems such as the natural numbers.

But Prof. Escultura is no one-trick pony.
 
Earlier, Escultura captured the last stronghold of physics with his
solution of the gravitational n-body problem posed by Marquiz de
Laplace at the turn of the 17th Century. [...] His paper, The Solution of the Gravitational n-Body Problem, is published by the journal, Nonlinear Analysis, Vol. 30, No. 8, pp. 5021 - 5032, Dec. 1997. The paper earned for him international recognition: membership in the American Association for the Advancement of Science; the 25-member Core of Experts which is the leading body of the International Federation of Nonlinear Analysts (IFNA); the Editorial Board of IFNA and the Global Organizing Committee of the Third World Congress of Nonlinear Analysts 2000 (WCNA 2000), 19 26 July 2000, Catania, Italy; and organizer and chair of the international mini- symposium on the topic, The El Niño
and its Impact: Drought and Turbulence, during the Congress.
Chair of a conference on El Niño ? member of AAAS ? Give the man a cookie !

p.s Why bring this up now ? For some reason, his "disproof" of Wiles' theorem has been doing the rounds on some blogs recently, prompted by an article in the Manila Times.
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