This is the second in a series of interviews with the plenary speakers for the upcoming 65th Annual Meeting of the AustMS.

1. 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.

2. 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.

3. 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.

4. 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.

5. 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!

This is the first in a series of interviews with the plenary speakers for the upcoming 65th Annual Meeting of the AustMS.

1. What is your earliest mathematical memory?

My family moved from Israel to Uganda when I was 8 years old, and I started school there without knowing any English. Nakasero Primary School was at the time an old fashioned colonial British school, which offered very little help for pupils who did not know English. I was put in a class and expected to catch up on my own.
I well remember that the one subject that I was able to follow for the first few weeks was Maths: multiplication table and such matters. At that point I was grateful that math was a universal language!

2. What made you decide to become a mathematician, and when?

In my final year at high school I was seriously thinking about taking up physics. I tried to read some of the university physics texts but decided that I needed to better understand the math, and while doing it fell in love with the subject. I participated in a couple of local math contests and received a small fellowship as a result of winning third place in one of them, and I saw that as a sign that I had a future in the subject.

3. Name a favourite paper by a contemporary mathematician, and why (or more than one, if you can’t decide).

Some of Michael Berry’s papers and surveys are particular favourites of mine, as they have shaped my views of Quantum Chaos and its relation to Number Theory. In particular I can mention the survey:

• Berry, M V, 1983, ‘Semiclassical Mechanics of regular and irregular motion’ in Les Houches Lecture Series Session XXXVI, eds. G Iooss, R H G Helleman and R Stora, North Holland, Amsterdam, 171-271. (author pdf)

Michael Berry is a physicist, but much of his work is mathematical and I have drawn inspiration from his way of looking at nature.

4. What historical mathematician would you like to be able to talk maths with? What would you ask them?

I suspect that many of the great mathematicians are not great conversationalists.

5. What result would you like to see in mathematics in the next 10 years?

I would like to see a proof of the Riemann Hypothesis. But it may well take much more than 10 years.