Humans have known how to multiply natural numbers for a long time. In primary school you learn how to multiply numbers using an algorithm which is often called long multiplication, and it was known to the ancient Babylonians. But it’s

## From Liouville geometry to contact geometry

(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.

## Lovely Liouville geometry

(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.

## Emmy had a theorem (mathematical nursery rhyme #2)

In the spirit of previous work in abstract algebra, I have, erm, adapted another nursery rhyme.

To the tune of “Mary had a little lamb”, a discussion of Noether’s theorem.

## Golay Golay Golay (Top of the autocorrelation world)

In 1949, Marcel Golay was thinking about spectrometry. Here’s what happened next…

## Topological entropy: information in the limit of perfect eyesight

Entropy means many different things in different contexts, but there is a wonderful notion of entropy which is purely topological. It only requires a space, and a map on it. It is independent of geometry, or any other arbitrary features — it is a purely intrinsic concept. This notion, not surprisingly, is known as *topological entropy*.

## Abstract algebra nursery rhyme

In the spirit of hilariously advanced baby books like Chris Ferrie’s Quantum Physics for Babies, I have taken to incorporating absurdly sophisticated concepts into nursery rhymes.

## Limitless as that space too narrow for its inspirations

In which I recall, via neurologist Oliver Sacks, some musings of Sylvester from 1877 on the limitlessness of mathematics.

## The Brain makes Contact with Contact Geometry

It’s always nice, intellectually, when two apparently unrelated areas collide. I had an experience of this sort recently with an area of mathematics — one very familiar to me — and an ostensibly completely distinct area of science. On the

## “The beauty of mathematics shows itself to patient followers” — The work of Maryam Mirzakhani

The recent passing of Maryam Mirzakhani came as a shock to many of us in the world of mathematics. Together with Norman Do, we attempt to share something about Mirzakhani’s work.