SIMO Retiree Blog

Introduction Etienne here. Some of my favourite proofs in mathematics are those that connect two seemingly unrelated subfields together. A well-known example of this is Andrew Wiles' proof of Fermat's Last Theorem, which uses a special connection between elliptic curves and modular forms. In this article I'll demonstrate some bizarre proofs using topology, the study of continuous transformations, in the field of combinatorics, the study of discrete objects.

(Zhao Yu here.) It's been a long time since I've touched olympiads and I have a really bad memory, so today I'll try something different and talk about something unrelated to olympiads. I will talk about 3 interesting facts that follow from the theory of elliptic curves . I will not be precise, and I will black-box many things. The point is just to give you a taste of elliptic curves and hopefully this will motivate you to learn the actual theory in the future!