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Diophantus Of Alexandria: A Study In The History Of Greek Algebra (1910) Hardcover – June 2, 2008
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I am not a member of the community of mathematicians. I am only a hobbyist. Nevertheless, I am convinced that professor Andrew Wiles' attempt* to solve "Fermat's Last Theorem", brought that important problem to the forefront and also resurrected interest in this amazing and mysterious book. Mathematics and mathematicians owe Professor Wiles a great debt which will eventually be recognized. I am totally in the dark as to what: Iwasawa's theory is, what modular forms are, what Galois representations are and what the Shimura-Taniyama conjecture is. None of these mathematical: theories, conjectures, forms, ideas nor techniques existed in the 1600's. I do not nor would I ever question the importance, validity, accuracy, nor the correctness of Professor Wile's achievement.
Diophantus's book (text book) is wonderful if one wants to learn about Greek mathematics by puzzling through and by attempting to follow how he solved a lot of complex, complicated algebra problems. It is a scholarly book. Heath briefly goes through the histories of the various translations. He covers in some detail the development of the uses of many various Greek mathematical terms and many of the various pertinent ancient mathematical symbols. Then comes his translation of the book (the problems and their solutions - many of techniques which "D." employed remain mysterious. After all, "book 2 (chapter 2) problem #8 continues to remain the clue to "Fermat's Last Theorem" 's proof - if there ever was one expressed in the mathematics of Fermat's time. Diophantus's book is for the truly dedicated scholars and hobbyists who may still be searching for a proof for "F.L.T" couched in the mathematics of his time.
*Marilyn vos Savant ( with all due respect to Dr. Wiles' work) in her book , "The World's Most Famous Math Problem", points out that Dr. Wiles' proof is not Fermat's claimed proof.