On 7 December 2020 I gave a (virtual) lecture at the Australian Mathematical Olympiad Committee’s School of Excellence on congruences.

## From Here to Hensel

Here’s a nice maths problem, which I thought it would be fun to discuss. The question doesn’t involve any advanced concepts, but it leads on to a very nice result called Hensel’s lemma.

## Return of the Euler-Fermat theorem

A long long time ago, in a galaxy far away, I wrote up an account of the Euler-Fermat theorem for school students.

## Topology: The shape of space

Monash Open Day in 2020 was a purely online affair, thanks to COVID. I recorded a video talking about Topology: The Shape of Space.

## Sitting out the math wars

Very few professional mathematicians have been involved in the “math wars”, and when they have, they have not always inspired confidence. I wondered why.

## Not human, but inhabited by humans: writing mathematics

Mathematics can be written in many ways. One approach, very popular with professional pure mathematicians, is to write as little as possible. But there should also be others.

## “I liked doing what I wasn’t supposed to do”: the life and mathematics of Karen Uhlenbeck

In September 2019 I gave a talk about the life and some of the mathematics of Karen Uhlenbeck, the great mathematician and first woman to win an Abel Prize. This was a Monash LunchMaths seminar.

## Breakthroughs in primary school arithmetic

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, but it’s called “long” for a reason! Recently, a new paper purports to give an algorithm to multiply faster.

## 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.