AustMS2021 plenary profile – Richard Brent

This is the eighth 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?

 It’s hard to be sure, but I do remember being pleasantly surprised to learn that 1 + 2 + … + n = n(n+1)/2 – I don’t recall if I worked it out for myself or not. When a young boy (aged about 6) I used to amuse myself on long car trips by doing mental arithmetic, but maybe that doesn’t count as “mathematics”.

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

When I went to Uni (Monash, 1964-67) as an undergraduate I was undecided between maths, physics and chemistry, but I found that chemistry was too “ad hoc” and physics too “experimental” for me. Also, Monash had a great maths (and stats) department in those days – people like Gordon Preston, Zvonimir Janko, E. Strzelecki, Terry Speed, etc. So perhaps I decided to become a mathematician around 1966, in my third year at Monash. As a graduate student at Stanford (1968-71), I took courses from some great mathematicians (George Polya (in his eighties), Menahem (Max) Schiffer) but ended up graduating in Computer Science (which also had mathematicians: Forsythe, Golub, Knuth, etc). I then worked at the mathematical end of computer science for many years, and did not get a “real” job as a mathematician until the age of 58, when I became a Federation Fellow in MSI at ANU.

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

This paper improved on several earlier papers, and any further improvement would require proving (or disproving) the RiemannHypothesis. (Several other papers by Terry Tao are also amongst my “favourites”.)

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

Bernhard Riemann. I would ask him what he knew (or believed to be true) about the Riemann zeta function, but had not published.

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

A proof that P ne NP, or that the Riemann Hypothesis is true, or that the optimal exponent in the complexity of matrix multiplication is strictly greater than two, or […]. One attraction of mathematics is that there is never a shortage of interesting open problems!

AustMS2021 plenary profile – Robyn Araujo

This is the seventh 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?

I don’t have any very early mathematical memories, although my Mum has always proudly claimed that she heard me speak my first words as a toddler when I started to count out the clothes pegs in her laundry!!  (Apparently I was an avid watcher of Sesame Street as a young child, and my parents are convinced that I learned to count, and read simple words, from watching that).   But I do remember starting to take a serious interest in mathematics in early High School, as I had a truly fantastic maths teacher who gave wonderful explanations of mathematical concepts, so I started to appreciate the exciting possibilities of mathematics.

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

I never made a conscious decision to pursue mathematics, as such.  As an undergraduate, I initially got started in Engineering, but was a little disappointed with the amount (and level) of mathematics taught in my degree.  Bit by bit, I transitioned over into a more mathematical direction and then did a PhD in applied mathematics at QUT.

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

It’s hard to pick just one paper, but I’d love to highlight the extraordinary work of the German mathematician Karin Gatermann here [See eg ACM DL, ResearchGate -Ed].   Unfortunately, Karin passed away in 2005 while only in her early forties;  but Karin was an extraordinary mathematical pioneer in symbolic computation and toric geometry, and was one of the first mathematicians to identify deep connections between mass-action kinetics and toric varieties. 

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

If I had to pick just one historical mathematician, I’d probably pick Galois … I’d love to ask him where his ideas and insights came from, and how his mathematical thinking evolved.

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

I’d love to see a big breakthrough in the mathematics of the ‘Laws of Life’.  In many ways, the current state of biology and the life sciences is reminiscent of the state of physics 400-500 years ago.  Historically, biologists have shied away from ‘grand theories’ of nature, and have tended to focus more on details and reductionist approaches.  But things are changing, and there is now renewed hope that we may find the ‘laws of life’ in a similar spirit to the fundamental laws of nature in other areas of physics.

AustMS2021 plenary profile – Jennifer Flegg

This is the sixth 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?

I was listening to my parents talk about something and I interrupted them to ask my dad what a 15% discount meant. I remember his explanation of “one-tenth and then half that again” being really easy to follow. My dad says I then worked out what their discount was going to be (on my brother’s braces); but I don’t remember that I just remember his explanation of how to calculate 15%.  

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

I decided to become a mathematician in my first year of university. I was studying maths and economics in a double degree at the time; business because my parents were worried that I’d have no career options after finishing a maths degree on its own. I didn’t enjoy the economics much but loved studying maths at university and from then there wasn’t another career on my radar. 

  1. Name a favourite paper by a contemporary mathematician, and why (or more than one, if you can’t decide).
  • Jonathan Sherratt and James Murray, “Models of epidermal wound healing”, Proc Biol Sci. 1990 Jul 23;241(1300):29-36. doi: 10.1098/rspb.1990.0061. PMID: 1978332.

This paper started my love of mathematical biology and was the first that I spent many months looking over as part of a research project in my undergraduate degree. I wish I had time to look over papers now like I did this one.  

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

I don’t think I could go past having a chat with Alan Turing about his mathematical work of how biological shapes and patterns develop.  I’d probably have a few questions about cracking the Enigma code too 🙂   

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

Since what I work on is quite applied, this is difficult for me to answer in the way I’m assuming the question was intended. So, I’m going to take this question a bit differently and say that the ‘result’ I’d like to see is more structure/support around interdisciplinary work that involves mathematics and statistics.  

AustMS2021 plenary profile – Gang Tian

This is the fifth 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 mother was a mathematician who made outstanding contributions to Hilbert’s 16th problem. When I was between 5 and 6 years old, she gave me some logical problems. One of them was to find bad ball by balance, say you have 9 balls, one of them is bad, but you do not know this ball ball is heavier or lighter, the problem is to find this bad one by using balance three times. The maximum number of balls one can do is 13. I found it was interesting. 

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

I like mathematics since very young. I decided to become a mathematician when I was in college. One reason is its beauty, the other is its simplicity in some sense, for instance, unlike many other disciplines, I can do mathematics in a rather independent way. 

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

There are a number of papers I enjoyed reading and studying. A particular one is Perelman’s first paper on Ricci flow. It solves some long-standing problems on Ricci flow in an elegant yet simpler way. Moreover, it led to solving the Poincaré conjecture and so on. 

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

Maybe skip this question. Of course, being a geometer, I have the highest respect for Riemann. 

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

I would like to see a fundamental progress on understanding smooth structures of 4-manifolds, such as the smooth Poincaré conjecture for 4-manifolds, through geometric methods.

AustMS2021 plenary profile – Emily Riehl

This is the fourth 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?

Not the earliest memory but an early memory is being absolutely delighted by Louis Sachar’s Sideways Arithmetic from Wayside School. Problems include EGG + EGG = PAGE, SHE+EEL = ELSE, etc.

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

I’ve loved math my entire life and had decided to become a mathematician by mid high school, when I started learning about proofs.

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

John Bourke’s and Richard Garner’s “Algebraic weak factorisation systems I: accessible AWFS” is absolutely beautiful and on a topic very close to my heart. 

Though I also have to mention the delightful “Homophonic quotients of free groups” by Jean-Francois Mestre, René School, Lawrence Washington, and Don Zagier, which everyone should read immediately.

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

I’d love to hear Emmy Noether describe the insights that lead her to modern algebra.

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

I’d like to see a variant of homotopy type theory which actually computes, includes higher inductive types, and has semantics in any ∞-topos. Mike Shulman has proven that traditional homotopy type theory (without higher inductive types) has semantics in any ∞-topoi, but we’re still working on understanding the semantics of the new experimental “cubical” versions of homotopy type theory which have constructive proofs of univalence.

AustMS2021 plenary profile – Joaquim Serra

This is the third 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?

Something I remember well is spending a long time trying to solve a problem which required solving a quadratic equation, by only “rules of three”. The teacher had given it to us so that we failed, in order to motivate the coming lessons on quadratic equations.  I was stubborn enough to find, after hours, a solution using only rules of three. I was very proud about it until I learned what a quadratic equation was,  how easily it was solved

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

I always wanted to do Physics, but then I went to the Physics and Maths olympiads and  I performed rather poorly in the Physics ones, so I decided to try Maths.

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

The paper “Regularity of flat level sets in phase transitions” of Savin is one of the first papers I read  and among my favorites since then. I remember struggling to understand some proofs at the beginning, but at the same time finding the interplay between PDE and geometry of the level set very beautiful.

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

Gauss, who gave deep pure results with the most useful practical applications. After he was updated on today’s state of the art of knowledge, I would ask him what is his opinion on Machine Learning and its implications for Mathematics

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

Many of them! For instance, the classification of stable solutions  (stable critical point of the energy) of the Allen-Cahn equation in three dimensions.  Or the Cartan-Hadamard conjecture (isoperimetric inequality with Euclidean constant on spaces of nonpositive sectional curvature). 

AustMS2021 plenary profile – Susan Scott

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.

  1. 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.

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

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.

  1. 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.

  1. 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!

AustMS2021 plenary profile – Zeev Rudnick

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!

  1. 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.

  1. 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.

  1. 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.

  1. 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.

Credit: Copyright C.J. Mozzochi, Princeton N.J

Winners of the scienceXart school photography competition

This year is the 100th anniversary of the International Mathematical Union, and in honour of this the Australian Academy of Science chose the theme ‘spot the maths’ for this year’s scienceXart competition. The competition was open to school students of all ages, with winners chosen in several year-level brackets: Foundation–Year 3, Years 4–6, Years 7–9 and Years 10–12. There was also a separate category dedicated to statistics. The winners can be seen at this link.

Open for entries from 28 June to 25 September, the competition engaged students with the mathematical sciences and highlighted the inherent creativity of maths. The competition received close to 1000 submissions from students all around Australia. The judging panel and Academy shortlisting team enjoyed the high quality and creative submissions that combined maths and art.

Dr Julia Collins of Edith Cowan University was on the judging panel and said “I was blown away by both the quality of the winning photos and also the creativity of how these students had seen unexpected mathematics in the world around us. From the spirals in shells and plants to circles made by falling raindrops and the hexagons in bubbles and beehives. Or the symmetry in a chairlift, the number patterns in playgrounds, and the wonderful visual statistics of swallows on a fence.”

The student who won each bracket will receive a STEM-related prize pack for themselves and their class.

Dr Collins noted that “The winners should be very proud of their achievements, and I encourage everyone to take a look at the shortlist of impressive photographs. I can’t wait to see what the 2021 competition will bring!”