This week the Australian Mathematical Society recognises the work of leading Australian mathematicians at its 64th Annual Meeting.
The virtual event, hosted by the University of New England, started today and saw the award of the AustMS Medal, the biennial George Szekeres Medal, the Society’s Award for Teaching Excellence, the Gavin Brown Prize, and the Mahony–Neumann–Room Prize. These prizes cover the breadth of contributions of mathematicians—from distinguished research of a mid-career researcher to sustained outstanding contributions; from teaching to a specific breakthrough publication in the last decade.
Later in the week the Society will award the B.H. Neumann Prize for the best student talk at the Annual Meeting, but until then there is a new podcast started by one of last year’s winners aiming to interview as many past Neumann Prize winners as possible.
In what follows I want to give a sense of what the medals were awarded for alongside the official citations. I also asked the winners some questions, you can see their answers below.
The AustMS Medal
The Australian Mathematical Society Medal is awarded to a member of the Society under the age of 40, for distinguished research in the mathematical sciences. This year the Medal is awarded to Associate Professor Luke Bennetts of the University of Adelaide for work on mathematics applied to geophysical problems, in particular wave-ice interaction and catastrophic ice-shelf disintegration in polar regions, and also ocean wave energy harvesting and acoustic metamaterials.
His papers are marked by a striking feature — relentless attention to making sure the mathematical models agree with field observations, measurements, and lab experiments; he is often involved in making the measurements or designing the experiments.
His mathematical modelling advances strongly contribute to integration of wave-ice interactions into large-scale coupled numerical models; he has implemented his theoretical developments into an international operational forecasting system and his modelling framework has been adopted by many international research teams. In 2014 he co-initated the Australasian KOZWaves conference series and, since 2016, he has been the Executive Committee Chair. He was awarded the Academy of Science 2016 Christopher Heyde Medal.
The methodology that Assoc. Prof. Bennetts creates was inspired by the polar regions, but because they are so important to the world’s atmosphere and oceans, it is also immediately applicable to the improvement of and contemporary research in world-scale, coupled, operational climate forecasting. His fusion of analytical mathematics with advanced computational methods empowers real-world, nonlinear, problems to be tackled, solved, and influence the field.
The official citation for A/Prof. Bennetts can be read here.
- What is your first mathematical memory?
LB: I clearly remember a maths test when I was six, in which the first to answer all questions gets a gold star. I was the first to the teacher with my answers, only to be told that I’d answered the wrong set of questions.
- What does this award mean to you?
LB: I interpret it as a sign my research is heading in the right direction. I hope I’ve got a lot of time remaining in my career, and there are lots of things I still want to achieve, including more promotion of mathematical sciences in the different disciplines I work in and to the public.
- What is one mathematical fact or idea you would wish the broader public to know?
LB: That equations are simply shorthand for words, and nothing to be scared of.
The AustMS Medal was established in 1981 and is awarded annually.
George Szekeres Medal
The George Szekeres Medal is awarded biennally for a sustained outstanding contribution to the mathematical sciences in Australia by a Society member. This year it is awarded jointly to Professor Nalini Joshi, AO of the University of Sydney, and Professor Ole Warnaar of the University of Queensland.
Professor Joshi
Nalini Joshi is Chair of Applied Mathematics and a Payne-Scott Professor. She is a world leader in the theory and applications of differential equations, contributing mathematical results that have impact in fields as diverse as particle physics, quantum mechanics, large prime-number distributions, and wireless communications. Her distinguished research record has led to numerous awards, including becoming the 150th Anniversary Hardy Fellow of the London Mathematical Society in 2015.
Nalini’s contribution to the Australian and international mathematical community is outstanding. To mention only a few positions, she was a Member of the Prime Minister’s Commonwealth Science Council (2014–2018), a Member of the Science in Australia Gender Equity Expert Advisory Group (2016–2018), and is currently the first Australian Vice President of the International Mathematical Union (2019-2022). She was the first mathematician to be awarded a Georgina Sweet ARC Laureate Fellowship (2012-2016). Nalini promotes mathematics to government and the wider community, and her work on creation of the SAGE initiative has resulted in influential actions and impact across the nation. Nalini has written over 100 peer-reviewed papers together with authored and edited monographs. Her outstanding contribution to mathematics is confirmed by numerous awards and positions.
The world around us is very fruitfully described by differential equations: these are equations between quantities that vary in time and space that also link their rates of change. Think of how heat flows in a unequally heated object: from the hot regions to the cold regions, and faster if the difference is greater. The easiest class to study consists of the so-called linear differential equations. Sound waves obey a linear DE, which is one reason why we can listen to music played by a band and pick out the different instruments playing at the same time—the sounds from the different instruments just add up, and our brains can recognise the individual distinctive tones, picking them apart again. Nonlinear differential equations, on the other hand, have solutions that are much more complex, like waves in shallow water. Unlike small ripples on the surface of a pond, which can expand and pass through each other, surf can behave in much more violent ways than a simple model would predict. The breaking of the crest of a wave is a breakdown, or singularity, of the simpler sinusoidal motion of the surface of the water out in the deep.
There are certain classes of nonlinear DEs with properties that put them on the boundary of what is nicely behaved. Nalini’s particular field of expertise is the collection of six Painlevé equations, discovered by various mathematicians in the decades either side of 1900, and named for the French mathematician Paul Painlevé. She has pioneered innovative methodologies in mathematics for describing these, and her deep understanding of nonlinear systems has enabled her to develop simple, precise definitions of functions, yielding descriptions that extend to the whole domain of existence. Nalini’s new methodologies have uncovered hidden information across multiple fields and sparked significant new research programs across the globe.
In addition to her research contributions and leadership roles, Nalini has worked tirelessly to promote mathematics to the wider scientific community and general public. She was instrumental in development of the Decadal Plan for Mathematical Sciences. She has been a panellist on the ABC’s Q&A and is frequently interviewed on mathematics education both online and on the radio. As mentioned above, her appointment as an officer of the Order of Australia in 2016 was “for distinguished service to mathematical science and tertiary education as an academic, author and researcher, to professional societies, and as a role model and mentor of young mathematicians.” In 2018, Nalini was awarded the Eureka prize for Outstanding Mentor of Young Researchers.
The official citation for Professor Joshi can be read here.
- What is your first mathematical memory?
NJ: When I was very young, I remember bouncing a ball and counting each bounce, getting to higher and higher numbers as I went. It seemed like the numbers could go on for ever and I never wanted to stop.
- What does this award mean to you?
NJ: I find myself overcome by a morass of emotions: surprise, pleasure, humility, gratification. It is the first award I’ve ever received from the Australian Mathematical Society. When I went to check on the list of past winners, I was surprised to see that I am the first person of colour in the list. (It is not the only award with this feature.)
- What is one mathematical fact or idea you would wish the broader public to know?
NJ: I want everyone to know that mathematics is a creative art made out of patterns with deep interconnections. It is as human and as beautiful as a sculpture or a painting, and built on strong frameworks of ideas that are like bridges and cathedrals. It is these frameworks that provide the scaffolding and language that enables science and technology. Come and join us.
Professor Warnaar
Ole Warnaar is Chair and Professor of Pure Mathematics at the University of Queensland. He is a leading expert in special functions, partition theory and algebraic combinatorics. He made a number of breakthrough contributions in each of these fields, often making use of techniques from a variety of different areas of mathematics to solve outstanding problems.
Ole Warnaar is a leading expert in his area and has made a number of significant breakthroughs, some of which now bear his name. Ole often uses techniques from different areas of mathematics to solve outstanding problems. He regularly publishes in the top journals in pure mathematics and is widely acknowledged by his peers as a leader in his field. Ole has also contributed significantly to academic life within the Australian mathematical sciences community. He was elected at a relatively young age to Fellowship of the Australian Academy of Science and throughout his career he has held several senior positions in the Australian Mathematical Society, and is its current incoming President-Elect. Ole is an outstanding supervisor and lecturer and an accomplished mathematician. The citation highlights six different examples, but here are just a couple.
Trigonometry, or rather the ratios of sides of right-angled triangles and logarithms are encountered by many people in high school mathematics, but they are just the simplest examples of what are known as special functions. There is no real accepted definition, but they cover a whole zoo of mathematical functions that arise in various settings, for instance in solving differential equations that describe electron positions in an atom (“spherical harmonics”), or the vibration modes of a drum skin (“Bessel functions”), or from inversion of the length of an arc around an ellipse (“elliptic functions”), to name a few. However, these functions also arise in abstract settings with special symmetries and in the study of prime numbers and their distribution. Trying to tame this zoo, by creating a general theory to cover at least some small section of it, plays a rôle in Ole’s research. One specific cited aspect of this effort is the creation of “The Warnaar Theory”, as it is called in the edited version of Srinivasa Ramanujan’s Lost Notebook, which gives a framework to explain some of the complex and beautiful formulas Ramanujan wrote down—without proof!—in the last year of his short life.
The official citation for Professor Warnaar can be read here.
- What is your first mathematical memory?
OW: That’s a tough one. Probably the first time I became truly aware of the existence of mathematics […] was in grade 1 at primary school in the Netherlands. I went to a Montessori school where all children were given a lot of freedom as to how they would spend their time at school. After about three weeks my teacher took me aside and suggested I would spend a bit more time (more than epsilon is what she had in mind) doing subjects other than maths. I do remember arguing with her about the futility of spending my time reading and writing. [For non-mathematical readers: ‘epsilon’ in mathematics usually stands for a very tiny quantity! -Ed.]
- What does this award mean to you?
OW: It’s of course a cliché, but it is an incredible honour to be awarded the Szekeres Medal. I very much admire the work of all of the previous winners, and am not sure I really deserve to be part of such an illustrious group. I am really happy that some of my own work has intersected with that of George Szekeres; I never met him so it is pleasing there is a mathematical connection.
- What is one mathematical fact or idea you would wish the broader public to know?
OW: I am quite sure none of my own mathematical ideas would pass the public interest pub-test. It would be wonderful, however, if the broader public had much more appreciation of the beauty of mathematics and the joy it can bring to its practitioners (as opposed to pain and misery). Incidentally, as under 18 Dutch female chess champion, my niece Alisha Warnaar was interviewed a few days ago for Dutch television about the Netflix series `The Queen’s Gambit’. Alisha commented on how well the show manages to convey the idea of beauty in chess. I think we are still some years off before Netflix will produce a miniseries about the beauty of mathematics, so all of us still have a lot of work to do in this regard.
The George Szekeres Medal was first awarded in 2002 and was named for Hungarian-Australian mathematician George Szekeres who, with his wife and fellow mathematician Esther Szekeres, fled Nazi persecution in WWII. It is awarded in even-numbered years.
Award for Teaching Excellence (Early Career)
The AustMS awards an annual Award for Teaching Excellence (Early Career), to recognise and reward outstanding contribution to teaching and student learning in the mathematical sciences at the tertiary level by an early career academic. This year the award goes to Dr Norman Do, a Senior Lecturer in the School of Mathematics at Monash University.
Norman’s approach to teaching combines a remarkably enthusiastic lecturing style, interactive approaches to tutorials, and initiatives targeted at students across the spectrum of mathematical proficiency. His contributions extend beyond the confines of the university to programs that provide mathematics enrichment for school students across the country.
After completing his PhD in Mathematics at The University of Melbourne, Norman was a CRM-ISM Postdoctoral Fellow at McGill University, an ARC Australian Postdoctoral Fellow at The University of Melbourne, and an ARC DECRA Fellow at Monash University, before settling into his current academic role. His research lies at the interface between geometry and mathematical physics.
Norman established and ran the AustMS Gazette‘s Puzzle Corner column through 15 instalments, and it is still running today, almost fourteen years later. You can find the collection of puzzles on his website. Norman is passionate about mathematics education, which shows through his university teaching and his initiatives to enhance the student experience. He has also contributed extensively to mathematics enrichment for school students and school teachers. He is currently a Director on the Australian Mathematics Trust Board, the Chair of the Australian Mathematical Olympiad Committee, the Director of the National Mathematics Summer School, and a member of the Simon Marais Mathematics Competition Problem Committee.
The official citation for Dr Norman Do can be read here.
- What is your first mathematical memory?
ND: I think that mathematical thinking and mathematical play is innate to humans, particularly young ones, and takes place in all sorts of contexts. So in that sense, I would consider many of my earliest memories to be somewhat mathematical, such as playing with blocks of different colours and shapes, counting lamp posts along the freeway from the back seat of the car, sorting the books on my shelf in order of height, wondering why the house next door was numbered two more than ours, and so on.
More explicitly though, I remember my grade two teacher giving me a grade four maths textbook and telling me to go lie down at the back of the classroom to read it while the rest of the class continued with their usual work. It seemed fun and special at the time, although I think that most teachers these days have better ways to motivate children interested in maths.
- What does this award mean to you?
ND: I am truly honoured and humbled by this award. I see so many inspiring and innovative maths educators in the community and it sometimes makes me feel that I am still only taking my first steps in teaching and that I have a long way to go. I spend quite a lot of time volunteering for educational organisations and initiatives, such as the Australian Mathematics Trust, the National Mathematics Summer School, and the Simon Marais Mathematics Competition. So I also see this award as recognition that the academic community can and should play a role in the greater maths education landscape, beyond the confines of the university.
- What is one mathematical fact or idea you would wish the broader public to know?
ND: I would want people to know that maths is more than what they might have seen at school, that maths can be beautiful, and that there is a satisfaction to be gained from the productive struggle one encounters when engaging with maths. On this last point, it seems to be commonly accepted that when people play sports, there will be times when they make mistakes, times when they lose and times when their bodies will hurt, yet we consider the process to be enjoyable! Why do so few people see maths the same way? (OK, so I’ve actually given three ideas here, rather than one… mathematicians aren’t always very good at counting!)
Gavin Brown Prize
The Gavin Brown Prize recognises an outstanding and innovative piece of research in the mathematical sciences published by a member or members of the Society. This year it is awarded to Associate Professor John Bamberg, Professor Michael Giudici and Professor Gordon F. Royle of the University of Western Australia, for their 2010 paper Every flock generalized quadrangle has a hemisystem, published in the prestigious Bulletin of the London Mathematical Society (link).
Their work is in the area of finite geometry—where there are only finitely many points and lines under consideration—which is closely related to the study of abstract symmetries and also has links to the theory of experimental design. The rules of finite geometry are almost the same as traditional 2d or 3d geometry, except that parallel lines are extended “off to infinity”, where they meet (much like the long, straight rails of a train track appear to do). In this artificial setup, where geometry works, but not quite as expected, the behaviour of familiar objects like the general four-sided quadrangle is a bit unusual. Their paper solved a problem that originally stumped mathematicians for 30 years and was even conjectured to not be possible until partial results in the 90s and 00s.
This paper is described in the citation as a “genuine paradigm shift” in its field. The methods used in the paper are described as a clever mix of geometric and algebraic techniques. This work not only settles the problem … but it is an enormous step beyond what was known previously. The assessors were uniform in their high praise for this paper, judging it to be, “very influential in the area of Finite Geometry”, “innovative and excellent research which solves a significant problem in its field”. One assessor described that this paper “has unquestionably had a big impact on the field. So completely have the authors answered the question they tackled, that there have been almost no publications on the subject since their paper appeared. In other words, rather than opening up an area, this has closed one down.”
The official citation for Bamberg, Giudici and Royle can be read here.
- What is your first mathematical memory?
JB: My second-grade primary school teacher taught us how to multiply a multi-digit number with a single-digit number. At home, I asked my mother about multi-digit vs multi-digit multiplication, and she taught me the algorithm. I then taught my second-grade teacher how to do this by demonstrating how to work out 33×34.
GR: My first memory of something mathematical (outside times-tables and arithmetic) that intrigued me was when I was about 13, and was taught how to use a slide-rule (showing my age here) to multiply large numbers by adding lengths on the logarithmic ruler.
MG: Aside from arithmetic, I remember our primary school headmaster coming into our year 5 class and doing logic puzzles.
- What does this award mean to you?
JB: Knowing that the field is very competitive, and seeing who has already won this award, is very humbling. The recognition of the work of our paper, particularly from the broader community, means a lot.
GR and MG: [ditto]
- What is one mathematical fact or idea you would wish the broader public to know?
JB: That mathematics beyond the school level is incredibly interesting. That there is very interesting mathematics that is accessible to the general public that is not taught in schools, and is very different to what is taught in schools.
GR: That not everything is known about mathematics, in particular that there are many mathematical problems, including some that are simple to state and of great practical importance, that are still unresolved. How often have I heard “but isn’t it all done” when explaining that I am still busy doing research even though it is not term-time.
MG: Maths is much more than dealing with big numbers.
- How did the three of you start collaborating?
JB: We owe a lot to the Australian Research Council, because the Discovery Project [grant] we got was the impetus to our partnership. I came back to Australia in 2009 and was employed by this grant.
MG: Whereas this was the first project that all three of us had collaborated on, John and I had collaborated previously on a project on 3/2-transitive groups. The main impetus on the collaboration of all three of us was Gordon moving from the [Computer Science department] to the maths dept.
The Gavin Brown Prize was established in 2011 and is awarded for a single article, monograph or book consisting of original research, and published within the 10 years preceding the year of the award.
Mahony-Neumann-Room Prize
This Mahony–Neumann-Room Prize, for outstanding contributions to the Society’s research publications, is fittingly named for the founding editors of the three journals published by the society: the Journal, the Bulletin and the ANZIAM Journal. This year, Professor Janusz Brzdęk of AGH University of Science and Technology in Kraków is awarded the Prize for his 2014 paper A hyperstability result for the Cauchy equation, appearing in the Bulletin of the Australian Mathematical Society (link).
The Cauchy equation is an innocuous formula for a function f(x), namely f(x+y) = f(x)+f(y), proposed in the 1820s by Augustin-Louis Cauchy. Assuming any kind of mild ‘niceness’ properties about f, the only possible answers are f(x) = cx, where c is a fixed number. Any solutions to the Cauchy equation not of this form are exceedingly complicated and ugly! Trying to understand the behaviour of functions that solve the Cauchy equation is thus quite difficult, and one can instead try to understand what happens when things are changed up a bit.
Professor Brzdęk proved in his paper a result about functions f that almost solve the Cauchy equation for ‘large enough’ inputs, namely that they in fact do solve the Cauchy equation on those inputs. To quote from the official citation: “The methods introduced in the paper are presented in a form that has been shown to be widely applicable and has influenced others working in this field with applications to many other functional equations and in more general settings. … This paper continues to be strongly cited as one of a growing number of examples of hyperstability, acknowledging the significance of the early application of the method to the Cauchy equation.”
The official citation for Professor Brzdęk can be read here.
The Mahony-Neumann-Room Prize has been awarded since 2014 and in each year the winner is chosen from one of the three Society journals on a rotating roster.
