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 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.

## “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.

## Tutte meets Homfly

I’ll tell you about some extremely clever methods to tell graphs and knots apart, involving polynomials: the Tutte and HOMFLY polynomials. And they’re closely related.

## Holy h-principle, Batman!

In which I attempt to explain some of the ideas behind the h-principle.

## Every world in a grain of sand: John Nash’s astonishing geometry

After the recent tragic death of John Forbes Nash Jr, many tributes have been paid to this great mathematician, who was made famous by the movie “A Beautiful Mind”, and much has been said about his work on game theory. But less has been said about Nash’s other mathematical achievements.

## Paranoid defence controls could criminalise teaching encryption

You might not think that an academic computer science course could be classified as an export of military technology. But under the Defence Trade Controls Act – which passed into law in April, and will come into force next year – there is a real possibility that even seemingly innocuous educational and research activities could fall foul of Australian defence export control laws.

## Why your calculator (and computer, and phone…) is a weapon

The Australian government may have classified your calculator — and phone, and computer, and every electronic device you own — as military weapons.