My name is Tyler Murphy and I love puzzles. Currently, my favorite puzzle is Fermat’s last Theorem. I find it very fascinating that this one conjecture confounded the greatest mathematical minds in the world for over 300 years. It’s even more fascinating that the math required to prove the theorem ($\nexists a,b,c,n \in \mathbb{Z}/\{0\} \mid a^n+b^n=c^n, n>2$) didn’t exist for 250 years after Fermat made the claim that he had proven the conjecture.

I also love that most people think mathematics is a stale field with nothing more to discover. Fermat’s Last Theorem is proof against that. I love that this was proved in my lifetime. To me it represents the continually changing and dynamic world of mathematics. It’s like having special eyesight that allows me to see into a special and private world that permeates every aspect of our lives which most people will never glimpse or understand.

Today, most mathematicians believe that Fermat could not have had a viable proof. Even once the conjecture was proven in 1995 by Andrew Wiles, the search for a proof didn’t end. Today, the search is for a more concise proof, as Wiles’ proof was over 100 pages long. The current search is trying to find a proof for a theorem about numbers that only talks about numbers.

Here’s an interesting article about the most recent advancement in Fermat’s Last Theorem as well as some historical context.