Guide Summary of Results and Proofs on Fermats Last Theorem. (Sixth Paper)

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It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle.

He has been teaching at the University of Caen since In he wrote a thesis, "Elliptic Curves and Fermat's Equation. The text is accessible, without compromising the rigor of its mathematical exposition, to reasoned undergraduate students, at least so for the most part it can serve as the basis for various teaching courses.


It sets the whole discussion in a fascinating, generally educating historical context, thereby travelling - metaphorically speaking - through the centuries of mathematical history. No doubt, it is a true blessing that the English translation of this unique book is now at hand for a much wider public. We are always looking for ways to improve customer experience on Elsevier. We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit.

Almost all of the problems Fermat mentioned having solved were included in his work more than once, typically being restated as challenge problems which he then sent to various mathematicians with whom he was in correspondence.

4th Edition

However, FLT appears only once, in this margin. It is never again mentioned in any writings that Samuel was able to find. Assuming he truly had a long proof which was not incorrect, he would have likely written this down or discussed it with other mathematicians, as he did with essentially every other result he found. In fact, in his writings, we do find later references to special cases of the theorem see Wikipedia, Proofs of Fermat's Last Theorem for specific exponents.

However, he did send multiple letters, in , , and , containing this case as a problem. This was, after all, a private writing by an amateur mathematician who was just learning number theory. It was never intended to be communicated to others, and in his communications we can find no indication of such a claim. It's not clear what he would have meant by the note in the margin.

However, he was wrong, and very likely discovered this himself, possibly while trying to write down the proof. Exactly what this proof might have been is not clear. Many people since have failed to prove FLT in many ways.

Fermat's Last Theorem, Simon Singh -

Even that would have been far ahead of his time. But his error could have been something more mundane as well. Fermat who was just an amateur, albeit an extremely gifted one found a correct elementary proof of FLT which has since evaded thousands of mathematicians with more sophisticated technology and more complete understanding of number theory over a period of over years.

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He never wrote this down or communicated this result to any mathematicians, preferring to discuss only two specific cases. This can not be technically ruled out, but it seems highly unlikely, and the only evidence supporting it is a private note scribbled in the margin of a text by a man who was learning number theory for the first time. The first two possibilities both seem reasonable, while the third is almost completely absurd.

The Enduring and Revolutionary Impact of Pierre de Fermat's Last Theorem

This would not be the only case in which Fermat believed he had a result which was only completely proven later. The polygonal number theorem is another major case, which was only proven by Legendre for squares in , Gauss for triangles in , and Cauchy in general in Gauss in particular cast some serious doubts as to whether Fermat had a proof of this.

The Heart of Fermat's Last Theorem - Numberphile

The most popular guess is possibility 2, that Fermat had some sort of argument which was flawed but perhaps worked for some small exponents. It is simply not possible that Fermat discovered a proof which is equivalent to Wiles' proof. That would have been impossible; the concepts required to even understand Wiles' proof were not developed until the 20th century. There is no way that Fermat could have had anything approaching the now commonly-accepted proof.

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  • Your article, however, is a bit too short to be a good Monthly article. A line or two of explanation would really help. Can you write a meaningful paper shorter than 2 words?

    Fermat's Last Theorem

    Probably not. Still, I want to mention the following case report of severe writer's block, which contribute important zero words to the literature:. Also the following zero-word paper excluding the abstract makes an important point. Originally submitted to Nature Chemistry it did not make the cut for publication.

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    But the editors liked it so much that they covered it in their blog and their production team produced a print PDF for it.