Category Archives: Uncategorized

This was inspired by a discussion with James Aaronson outside the Chapel. We were contemplating group theory and automorphisms (specifically, trying to determine whether there exists a group of size strictly larger than with only two automorphisms), and eventually considered the … Continue reading →

A recurring general theme in mathematics is of a property being true of three objects when considered pairwise, but not true of the entire set. For example, earlier we considered non-trivial mutual friends, and how a simple graph is not sufficient … Continue reading →

Some people have recently been discussing Eric Weinstein*, who has proposed a 14-dimensional theory of everything known as Geometric Unity. The media attention is possibly as a result of the trivial difference between his surname and that of the patent office clerk responsible … Continue reading →

The Sierpinski triangle is a surprisingly ubiquitous mathematical object. Rather than describing what a Sierpinski triangle is, I may as well show you a picture of one. Essentially, it consists of three identical copies of itself, scaled by a factor … Continue reading →

I’m not sure exactly how to motivate a discussion of the Hoffman-Singleton graph, except perhaps by beginning with the following problem from the October 2011 edition of the Advanced Mentoring Scheme: This problem seems quite innocuous at first, and one would … Continue reading →

Two open problems about the distribution of the primes have been solved within about 24 hours of each other, namely the ternary Goldbach conjecture and a weakened form of the twin prime conjecture. Let’s look at these in approximate chronological … Continue reading →

Some of my favourite books were written by Douglas Adams. (Indeed, my forename was actually named after his surname, rather than my Biblical namesake or the Greek word for ‘indestructible’.) Although I personally prefer the Dirk Gently books, I have … Continue reading →

There are several mathematical heuristics (it’s difficult to call them proofs), which are non-rigorous in the best of cases and sometimes seemingly insane. For example, Euler’s ‘proof’ that the sum of the reciprocals of the primes diverges at an asymptotic … Continue reading →

In Einstein summation convention, repeated indices are summed over. For example, . If a Kronecker delta has two different suffices, we can ‘contract’ them as follows: , whereas . Vishal Patil considered contracting English words in this manner. For example, … Continue reading →