A fun fact from Euclidean geometry that I thought was a wonderful enough gem to share. It’s standard, but it’s nowhere near any curriculum. I’ll try not to get too snarky about the curriculum.
Ptolemy vs Thurston in Hyperbolic Geometry and Topology, AustMS 2020
On 9 December 2020 I gave a (virtual) talk in the Topology session of the 2020 meeting of the Australian Mathematical Society.
I got problems – congruence problems
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.
University forever
I don’t have anything against people who want to stay at university as long as possible: this is, after all, my life. I think long term economic trends point in this direction though.
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.
A-polynomials, Ptolemy varieties, and Dehn filling, Melbourne June 2020
On 15 June 2020 I gave a talk in the topology seminar at the University of Melbourne, entitled “A-polynomials, Ptolemy varieties, and Dehn filling.”