Essays In The Foundations Of Mathematics, 2nd ED.

Essays In The Foundations Of Mathematics, 2nd ED.The content of this second edition is identical to that of the first, except for two additional essays and an elaboration in Richards paradox. The first of these, which would have to be considered the jewel in any crown, supplies the missing demonstrations of Fermat's last theorem. They are short and easy to read, but they took a very long time to find: twenty five years for me, almost eighteen hundred years for mankind, not counting Fermats lost

The content of this second edition is identical to that of the first, except for two additional essays and an elaboration in Richard’s paradox. The first of these, which would have to be considered the jewel in any crown, supplies the missing demonstrations of Fermat's last theorem. They are short and easy to read, but they took a very long time to find: twenty-five years for me, almost eighteen hundred years for mankind, not counting Fermat’s lost proof. As I explain below, the Wiles proof is not allowable.

The other essay addresses the so-called formula of Euler, and shows that it cannot possibly be true. How did it ever gain currency? Did both Cotes and Euler commit a procedural error that went undetected? It is possible, but highly unlikely. I can think of only one other cause, and that is that the entire concept of imaginary numbers is invalid, that there is no such thing as a square root of negative unity.

Consequently all problems that rely on imaginary numbers for their statements are false problems, and all proofs that rely on imaginary numbers, such as Legendre's proof of the irrationality of pi, Gauss’s proof of the so-called fundamental theorem of algebra, Lindemann’s proof of his corollary concerning the transcendence of pi, and Wiles’s proof of Fermat’s last theorem, are, through no fault of the gentlemen’s, false proofs.

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