In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

These are my latex'd lecture notes for different courses from the mathematics bachelor at EPFL. They most certainly are full of typos and errors, the only reason this repo is public is so that I can ...

Bernhard Riemann was a man with a hypothesis. He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed. A ...

The following lecture notes are taken during my year in Part III of the MASt Pure Mathematics course in the University of Cambridge. You can download them via the ...

First let’s start with a very obvious question our students are going to have… What is geometry? Geometry is one of the oldest sciences and a branch of mathematics. It focuses on shapes and their ...