I recently had the pleasure of delivering a Lunchtime Lecture to the students attending the 2023 AMSI Summer School.

Back in my wild undergraduate days, I attended the 2010 AMSI Summer School at La Trobe University in Melbourne, so it’s pretty obvious that I jump at the opportunity for the trip down memory lane.

This year, I thought long and hard about what a young mathematical me would want to hear. From this, I came up with the following slide deck.

Probably, without my smooth vocals on the overlay, the slides may seem to lack cohesion so I’ll give you the narrative.

I think that pretty much everybody who attends an AMSI Summer School is at the tail-end of a maths degree and therefore can pretty much do whatever they want.

Often, an idea will grab hold of them and they will wander down that path.

For me, this path was prime numbers, and I discuss the idea that first made me want to be a number theorist. This pushed me to go and do my PhD in number theory.

I’m a disloyal mathematician, however. I find plenty of exciting ideas and I follow them. This took me into a career as a trader (and now educator) at Optiver and it also drives me to learn all sorts of new things on the side (machine learning, bioinformatics, etc.).

My message at this point is at follows: it’s never too late to change fields. If you find yourself interested in quantum physics, go for it. Sure, maybe it slows down your publication count in the short-term, but the more engaged you are, the faster those ideas will come.

I then drift onto what I think the markers of a successful mathematician in both academia and industry are (and please post a comment if you think I’m missing something):

Reads and speaks mathematics.

Uses old ideas in new ways.

Has a grip on technology.

Plays the game properly.

The remainder of the talk sheds more light on each of these, starting by saying: don’t let old G. H. Hardy discourage you from exposition – so much good comes from this.

If you have any questions about the slides, let me know. Hopefully, there is something useful in there for you.