Abstract: I am sure everyone knows what Fermat's Last Theorem states. I will give you some historical perspective on attempts to prove it (probably prove some cases as well !!). It will lead us to the need for new ideas and connections – elliptic curves and modular forms. I will give you a brief introduction to the beautiful world of these objects, and how they ultimately led to the proof of FLT by Andrew Wiles. No background needed except basic stuff from the Algebra qual course.