Introduction
The proof of the Taniyama-Shimura conjecture, or modularity theorem, has been one of the most important breakthroughs in modern math. It’s been used to prove Fermat’s last theorem and provides a rich new way to analyze elliptic curves. As a CTF player, the ubiquity of elliptic curves and their associated problems makes understanding their theory crucial to solving cryptography problems.
Unfortunately, you might notice that modern math is really complicated. If you’re looking to self study the Taniyama-Shimura conjecture, buckle up, because there’s going to be a lot of background info you’re going to need to build.
What is the Taniyama-Shimura Conjecture?
In short, for every elliptic curve, there exists an associated modular form.