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 …