“Send me your rotation

let's focus on good definitions...”

Fermat's Proofs

A collection of some Fermat theorems and how they were eventually proven. These are the beginnings of modern number theory.

Basel's Problem - New proof and some calculus

Sorry for the long hold up on another post. This new post is a result on my investigations on a proof of \(\zeta(2) = \frac{\pi^2}{6}\) by Daniele Ritelli. Yes, it's another post on something Euler solved first. But I did things different this time around: I discussed …

Euler's Pentagonal Number Theorem

Today, I'll prove Euler's Pentagonal Number Theorem and show how he used it to find recurrence formulae for the sum of \(n\)'s positive divisors and the partitions of \(n\). This post will be based on two papers I read last week: “An Observation on the Sums of Divisors” and …