Maths and Musings – Cantor's Archive

Series

The Basel Problem: 1+1/2² + 1/3² +… = π²/6

Solving the Basel problem, using an elementary introduction to Fourier series! Part 0: Motivation, some History, and Welcome! Hello and welcome! We are going to be tackling a beautiful problem, the ‘Basel Problem’. It was posed in 1650 by Pietro Mengoli, and it took 84 years to solve it, when

Analysis

The Chessboard Puzzle and the Mathematics of Invariants

Here we crack a tricky yet simple problem at the intersection of computer science and mathematics. It also gives a lovely insight into how…

Complex Analysis

Euler’s Fabulous Formula

Here we investigate and understand the brilliant formula which unlocks the power of complex numbers.

Logic

What is the Axiom of Choice?

Here’s a fun 2-minute guide to the infamous Axiom of Choice, one of the stranger mathematical curiosities.

Analysis

Mathematics Analysis For Coders

An intro to mathematical analysis, using ideas familiar to coders

Prime Numbers

Erdős’ Proof of the Infinitude of Primes

Let’s take a look at an unusual proof that there are infinitely many prime numbers.

Arithmetic

The Fundamental Theorem of Arithmetic

Over 2,300 years ago Euclid proved the Fundamental Theorem of Arithmetic. Now it is our turn.

Differential Geometry

The Gauss Bonnet Theorem and an Introduction to Spherical Geometry

A visual introduction to Spherical geometry, a geometry where triangles’ angles don’t sum to 180.

Dynamic Programming

Exploring Monotone Subsequences With Dynamic Programming in Python

When computer science and dynamic programming meets math

Erdős

A Theorem of Erdős and Szekeres

A Theorem by two mathematical greats, which anybody, no maths experience required, can understand! An amazing, and beautiful, result…

Combinatorics

A Combinatorial Curiosity

A beginner’s guide to combinatorics, and using it to solve a rather tricky question.

Calculus

The Fundamental Theorem of Calculus

The beginner’s guide to proving the Fundamental Theorem of Calculus, with both a visual approach for those less keen on algebra, and an…