Fermat's Last Theorem : Unlocking the Secret of an Ancient Mathematical Problem
Fermat's Last Theorem Unlocking the Secret of an Ancient Mathematical Problem Author:Amir D. Aczel Over three hundred years ago, a French scholar scribbled a simple theorem in the margin of a book. It would become the world's most baffling mathematical mystery. — Simple, elegant, and utterly impossible to prove, Fermat's Last Theorem captured the imaginations of amateur and professional mathematicians for over three centuries. ... more » For some it became a wonderful passion. For others it was an obsession that led to deceit, intrigue, or insanity. In a volume filled with the clues, red herrings, and suspense of a mystery novel, Dr. Amir Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph.
From formulas devised for the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt. Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, Fermat's Last Theorem brilliantly combines philosophy and hard science with investigative journalism. The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down.« less
This was an interesting discussion of all the efforts by many individuals to solve this problem. The problem is so simple that a high school student might think they could solve it by finding an exception to the rule but clearly it is not. A^2 + B^2 = C^2 or 3^2 + 4^2 = 5^2. Fermat says he can prove there are no solutions for cubes or higher that result in all integers. The final solution that is presented is very complicated and totally lacks mathematical elegance. Certainly not something Fermat would have come up with. Maybe there is more to come on the subject
Edgar E. reviewed Fermat's Last Theorem : Unlocking the Secret of an Ancient Mathematical Problem on
I just want to point out that Wiles' proof of Fermant's last theorem has two fatal defects:
1) 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.
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
V. Lakshmikantham Institute for Advanced Studies
GVP College of Engineering, JNT University