- What is your earliest mathematical memory?
My earliest mathematical memories come from my years at primary school. Things that stand out are the colourful Cuisenaire rods, which all the kids enjoyed. Then there was the rote learning of the times tables up to 12 x12 which was fun as a group chanting activity, like singing songs. I clearly recall our initiation to long division, which was generally hated, although I didn’t mind it in moderation. Lastly, I recall that we had to do written calculations in non-base 10 units, for length, area, volume, speed, currency, etc. That was later removed from the primary school curriculum but, looking back, it is perhaps surprising that most students were able to manage it quite well.
- What made you decide to become a mathematician, and when?
At primary school I was very interested by mathematics and science, and I seemed to have an aptitude for it, but at that time, where I grew up, no child would have imagined they were going to become a mathematician. I was absolutely enthralled by watching the first lunar landing, which really sparked my interest in gravity. So I just naturally drifted towards focussing on mathematics and physics and, by the time I was 14, I had decided that I somehow wanted my career to involve those fields.
- Name a favourite paper by a contemporary mathematician, and why (or more than one, if you can’t decide).
- Penrose, R., 1965, “Gravitational collapse and space-time singularities”, Physical Review Letters, vol. 14, no. 3. pp. 57–59, 1965.
The contemporary mathematical physicist Prof Sir Roger Penrose proved an astonishing singularity theorem in 1965. He showed that, in very general circumstances involving isolated gravitating systems undergoing gravitational collapse, a trapped surface will form, inevitably leading to the formation of a singularity – the heart of a black hole. This result demonstrated that singularities in black holes should be a common feature of our Universe, and yet no candidate for a black hole had been identified at that time. The international astronomy community were in denial about the result, and even Einstein himself would have been shocked to see this consequence of his theory. This incredible breakthrough earned Roger the 2020 Nobel Prize in Physics.
- What historical mathematician would you like to be able to talk maths with? What would you ask them?
I would love to be able to chat with Emmy Noether. She was an extraordinarily gifted mathematician and mathematical physicist with great vision of connections between different branches of mathematics. I would ask her how she became interested in exploring the mathematics behind the then recently presented general theory of relativity due to Einstein. I would also ask how the insight she gained with this work led her eventually to the creation of the deep principle known as Noether’s Theorem, one of the most celebrated results in mathematical physics.
- What result would you like to see in mathematics in the next 10 years?
The famous singularity theorem due to Roger Penrose actually proves that, in very general circumstances involving isolated gravitating systems undergoing gravitational collapse, a trapped surface will form and thus there will exist an incomplete, causal geodesic. The theorem does not actually prove the existence of curvature singularities as the name suggests. The “completion” of this singularity theorem to prove the existence of curvature singularities has proven to be an intractable problem for more than 50 years. I would love to see that problem cracked in the next 10 years, and I would love to be part of the solution!