I have long been fascinated by Fermat's Last Theorem and greatly excited by Andrew Wiles' proof. I have wanted for a long time to explore the history of the problem and also the amazing proof by Wiles.
Just this week, for example, I learned that another mathematician is about to provide a very significant result that builds on the work done by Wiles. For those interested this mathematician, Chandrashekhar Khare, has a home page here: http://www.math.utah.edu/~shekhar/. After I get to Wiles' proof, I will attempt to also analyze Khare's result.
This blog will be an effort to trace the history of Fermat's Last Theorem and work through the details of the second version of Wiles's proof. Fermat has been called the Prince of Amateurs (Bell, Men of Mathematics) so I hope it is appropriate that this blog is also run by a mathematical amateur.
My goal in this blog is to present a set of proofs in a style very much like Euclid. Each proof presented will either rely on a previous blog or rely on a set of identified postulates. I am not a professional mathematician so I may make mistakes. I am hopeful that other participants will provide useful comments to keep the quality of this blog up.
The solution to Fermat's Last Theorem embodies a large part of the history of mathematics including many of its major results and many of its most famous persons. This blog will start with Fermat. For the most part, it will follow a historical flow, going from Fermat to Euler to Gauss to Kummer, etc.
It would be a shame to trace the history of the proof without also looking at the lives of the mathematicians involved. Some blog topics will explore the life and achievements of the participants of this story.
I look forward to people adding their comments and corrections to the biographies and the proofs. I think that this is one of the most exciting stories in all of mathematics and a blog is a great way to explore it.