Elliptical Curve Photo

Click here to see a picture of an elliptical curve mentioned in the Andrew Wiles video

3-5 switch

Andrew Wiles was having trouble making some connections with his proof, until he figured out this little "trick" the three-five switch. This is covered in chapter 11 of Nigel Boston's book about the proof of Fermat's last theorem. When dealing with an infinite number of possibilities you have to be able to count them. The idea of counting something infinite may sound like it is not possible, but it is as long as what you are using is countable. For example the integers and natural numbers are infinite countable sets, where the reals are an infinite uncountable set. The three-five switch aided in the countability of sets.

Pictures of some of the important people involved.

Yutaka Taniyama

Goro Shimura

Andrew Wiles

Kenneth Alan Ribet

Taniyama–Shimura–Weil conjecture

Andrew Wiles proof that all that all rational semi stable elliptic curves are modular which, in particular, implies Fermat's Last Theorem. This is the proof of the Taniyama-Shimura-Weil conjecture which can be found here. Kenneth Alan Ribet is the one who found the link between Taniyama-Shimura-Weil and Fermat's last Theorem. This is contained in his proof of the epsilon conjecture, and thereby proved that Fermat's Last Theorem would follow from the Taniyama-Shimura conjecture.

Andrew Wiles

Fermat's Last Theorem is one of the most famous problems in the history of mathematics. Pierre de Feremat said "I have a truly marvelous demonstration of this proposition that this margin is too narrow to contain.". Until 1995 there was not a proof of this theorem, although many had attempted, and some began to believe that it was impossible to prove. In case you are not familiar with Fermat's Last theorem it is stated here.


Andrew Wiles is the one who eventually proved this theorem. He said that it was his lifelong dream to prove this theorem. Here is a video that was made describing how he solved it.
Andrew Wiles Video
Andrew Wiles orriginal proof of the theorem had some gaps in it that were later corrected by him and Richard Taylor. The proof is published in two papers in May of 1995
Modular elliptic curves and Fermat's Last Theorem
Ring theoretic properties of certain Hecke algebras

FIrst Blog

This is our blog for CSCI 140. We love this class!