Bhabha is a great lover of music, a gifted artist, a bril-liant engineer and an outstanding scientist. He is the modern equivalent of Leonardo da Vinci.

Introduction: Professor J (Joachim) Hyam Rubinstein, who was born in Melbourne, Australia, in 1948, is a pure mathematician at the University of Melbourne. He is especially well known internation-ally for his contributions to the algorithmic theory of 3-manifolds (see his student Ben Burton’s Regina suite of software), and particularly for his work on Heegaard splittings, minimal surfaces, shortest networks and special triangulations of 3-manifolds. However, he also has a number of other mathematical interests, notably applications to fields as diverse as underground mine design, machine learning and finance.

Recognition of Hyam’s work includes his election as Fellow of the Australian Academy of Science, and award of the Academy’s Hannan Medal and the Australian Mathematical Society’s George Szekeres Medal. He has provided extensive leadership to the mathematics profession in Australia, including as President of the Australian Mathematical Society, as Chair of the National Committee for the Mathematical Sciences, and as Chair of the Working Party for the National Strategic Review of Mathematical Sciences Research in Australia. From July 11 to 22, 2011, a workshop and conference in his honour, jointly titled “Hyamfest: Geometry & Topology Down Under”, were held at the University of Melbourne.

Peter Hall: Thank you, Hyam, for agreeing to this interview. I wonder whether we could start by talking a little about the family from which you came, and about what motivated you to become a mathematician.

Hyam Rubinstein: My father was a publisher and printer. He founded and operated York Press, which was situated in Faraday Street in Carlton, near Melbourne University. In the 1920s, when my uncle came to Australia from Poland to assess opportunities for the family, Carlton was the Jewish centre of Melbourne. The uncle bought a local Jewish newspaper, and my father’s father, who was a Yiddish scholar, produced the newspaper’s Yiddish edition. My father developed the enterprise into one of both publishing and printing.

My father had commenced an Engineering degree in France (at that time it was difficult for Jewish students to undertake university studies in Poland), and had a life-long interest in things mechanical. For example, when he had the money he would purchase new machinery for the printery, and periodically he travelled back to Europe (specifically, to Heidelberg) to visit trade shows where the latest engineering advances in the printing profession were displayed. However, he was very much occupied with the business, and following the conven-tions of that period, he left a great deal of the role of parenting up to my mother.

PH: Please tell us a little about your mother.

HR: My mother was a brilliant woman, and in today’s era would likely have had a particularly successful career as a scientist. She topped the Victorian state school examinations in science, and she entered university at age 16. Indeed, she was asked to repeat year 12, to avoid being only 15 years old in her first year at university! This gave her an opportunity to study more of the humanities at school, and she won awards for this, just as she had for Science. She successfully completed an MSc degree at Melbourne University in physical chemistry, but subsequently raising six sons (I had five brothers, but no sisters) restricted her further career.

In her 40s she taught at high school for a period, and in the 1960s she completed a second University of Melbourne MSc, this time in Biology, an area that had long interested her. She was particularly fascinated by the genetic basis of disease, especially schizophrenia (one of my brothers was diagnosed with schizophrenia). She became an assistant in the department of psychiatry at the University of Melbourne. She worked there from about age 55 to age 70, publishing about 12 papers, edited many books and conference proceedings and encouraged all her sons to study science.

PH: That is fascinating. What courses and careers did your brothers choose?

HR: Five of us went to Melbourne Boys High School, and the other to Mount Scopus Memorial College, an excellent Jewish school in Melbourne. In order from the oldest to the youngest, they were Martin, David, me, Jeff, Simon and Ian. Jeff and I studied at Monash University. The others took undergraduate degrees from Melbourne. Martin went on to Berkeley, where he studied analysis with Stephen Diliberto. He joined IBM, where he worked for 20 years in New York; he didn’t bother completing his PhD. He has now retired and lives in Melbourne. David, who has suffered from schizophrenia since his 20s, studied physics at Melbourne and engineering at Swinburne. Jeff became a musician and has made his career in the UK. Sadly, Simon passed away two years ago after a battle with cancer.

Simon majored in Statistics, was a professional gambler for a while, and eventually followed our father into the printing business, where he was very successful. Ian is the family’s “black sheep” — he is the only one to have had a conventional career! He studied accounting at Melbourne University and now sells accounting software.

PH: You have a son and a granddaughter, I think.

HR: Yes, my son Ben was an undergraduate at Melbourne University, studying Engineering and Science and majoring in Software Engineering and mathematics. Ben and I have a most enjoyable collabo-ration in machine learning — his area of expertise, since there are some aspects using geometry and topology — my area. He did an MSc here, and a PhD at Berkeley, both in Computer Science. The PhD was supervised by Peter Bartlett, an Australian. Ben now works for Microsoft in Silicon Valley, and his daughter was born about a year ago. His wife Juliet is also Australian, and completed her BSc/BE at Melbourne and a PhD in Electrical Engineering at Berkeley in Lithography.

My wife Sue and I married just after my honours year at Monash. She did an honours degree in Biochem-istry, and later a graduate degree in Accounting. She was the accountant for my father’s printing works for many years, which meant she could often come with me during academic trips.

PH: Next we’d like to learn about your own career!

HR: As an undergraduate I was strongly influenced by Terry Speed, now internationally known as a statisti-cian, but who did his PhD in lattice theory and Boolean algebra at Monash. Terry was completing his PhD, and lecturing, when I was an undergraduate there. He encouraged me to go on and do a PhD.

At about this time I began to form views on the connections between mathematics and its applications. Today I feel that we sometimes overemphasise theory. It becomes too much of an end in itself, and we must continually ask ourselves who else is interested in our work, from other areas of science and technology, as well as other areas of mathematics. Moreover, I believe that we need to fight against the elitist nature of mathematics, to make it more accessible and less of a priesthood for the initiated.

I went to Berkeley to do my PhD. Initially I planned to study algebraic topology, but after two years I found it was rather too technical for my taste. I considered doing a PhD in dynamical systems, but ended up working in geometric topology with John Stallings. I was fortunate to have had a very strong mathematics training at Monash, which meant I could complete the Berkeley coursework component within two, rather than the usual three, years. I then spent 18 months on my thesis, and in 1975 I was able to return to Melbourne to a postdoctoral position.

Simon Rosenblat, known for his work in fluid mechanics, was Head of the Mathematics Department in those days, and he could see the connections between his area and mine. I read about bifurcation theory, which was Simon’s interest at the time, and went along to his learning group, but we never actually published together.

My postdoctoral appointment ran for two years, at which point there were significant budget cuts in Australian universities. I was concerned about my prospects, and considered retraining into engineering, but luckily I received a three-year contract to teach in the mathematics department. This was later converted into a tenured position. I had been promoted to senior lecturer in the last year of the contract.

In 1980 Leon Simon, who had obtained his PhD at the University of Adelaide as a student of Jim Michael, was appointed to Melbourne University from Stanford. Leon attracted a great many outstanding visitors, and suddenly the department took on international dimen-sions it had not seen before. There were many seminars and lectures — it was a wonderful time! However, two years later Leon moved to a Chair at the ANU, so much of this came to an end. Leon suggested that I apply for the Chair of Mathematics that he had vacated; I would not have done this without Leon’s encouragement. I applied and was successful, and became a Professor of Mathematics here at the age of 34.

Leon also got me interested in the minimax method — he had a PhD student who showed that for the 3-sphere with any Riemannian metric, there was an embedded minimal 2-sphere. Leon encouraged me to work with Jon Pitts, who had pioneered the minimax method during his PhD with Fred Almgren at Princeton. Pitts and I extended the minimax method to general Riemannian 3-manifolds, constructing many explicit minimal surfaces. Later I used a combinatorial minimax technique to establish the 3-sphere recogni-tion algorithm and with Jaco showed that many results using minimal surface theory could be obtained using a simpler, piecewise linear theory of minimal surfaces.

PH: Leon obviously dispelled some of the isolation from which Australia suffered at that time, at least in pure mathematics. How have things changed?

HR: Yes, in the 1970s, and into the 1980s, Australia was very isolated. The main areas of research in pure mathematics were analysis (here I include PDE), discrete mathematics and algebra. Areas such as geometry and topology had a low profile. While there was a flowering of pure mathematics in Australia in the 1980s and early 1990s, unfortunately, from the mid 1990s to the present, pure mathematics has been struggling. Of course, it has shared this difficulty with other areas of the mathematical sciences, particularly applied mathematics and statistics.

Nevertheless we still attract extraordinarily talented undergraduate students here in Melbourne, although the numbers are probably about the same as they were 30 years ago; they haven’t increased proportionately with the population. To some extent the network of a few good schools, training for the Mathematics Olympiads, etc., is still in place, but there have obviously been many challenges. For example, Australia, and Melbourne in particular, has a substantial need for well trained and highly motivating mathematics teachers. Sadly, the number of schools teaching mathematics at a high level has probably decreased in the last 30 years, even though the population has increased substantially.

PH: Yes, you and I have had many discussions on the challenges facing mathematics in Australia. Would you like to summarise what you see as the main issues?

HR: In the university sector the problems afflicting mathematics in Australia are largely traceable back to changes made to the relative funding model in the mid 1990s, after the election of the Howard govern-ment. For example, the relative funding model has led, in many instances, to mathematics being taught by non-mathematicians in Australian universities, because departments in other fields earn more money per student to teach it.

Additionally, competition for international fee paying students has had a significant negative impact on mathematics. The students that Australia has needed to take from abroad, in order to compensate for the loss of government funding, have usually not been able to study much mathematics in our universities. This has impacted negatively on our capacity to fund mathematical sciences departments, and on how mathematicians are perceived within universities.

More generally, the funding model that Australia has adopted, where departments are financed on the basis of the quantity of students they teach rather than the quality of the courses they deliver, has had a signifi-cant, negative impact on scholarship. Our colleagues in the US, where funding is not tied nearly as closely to the number of backsides on seats in each year, are particularly surprised by the Australian approach.

In both teaching and research the mathematical sciences are low cost but also low revenue, and the latter aspect means that they cannot serve as significant money earners for universities. Moreover, there is the usual problem that mathematics can be the most difficult subject that students are studying. We tend therefore to be viewed unfavourably, or ignored, by many university managers.

Going beyond these problems, I feel that we need to strengthen our connections to engineering, as distinct from science. Engineering addresses issues that need immediate solutions, and I think we have much to offer there. For these reasons, and others, it is detrimental for mathematics to be seen only as part of science, and not from a wider viewpoint.

In Australia the nature of our society means that the main types of industry (primary production, both agricultural and mining) don’t provide as much added value as a different industrial base might. For example, the quantity of sophisticated manufacturing is not high in this country. In this sense, our abundance of natural resources is something of a handicap to the development of parts of our economy. Exceptions include portions of the biomedical sciences, which are internationally competitive and well resourced. However, Australia has few engineering or high-level manufacturing companies involved in significant research and development. Our industry demands job-ready graduates, and does not appreciate what mathematically trained graduates can do.

On the other hand, the Australian economy is particularly open and internationally competitive, and these assets should be able to be harnessed to bring about change, given appropriate leadership from government.

PH: What does the immediate future hold for mathematics, and for you, at Melbourne University?

HR: IBM has recently opened up a major research facility in Melbourne and is now engaged in recruiting mathematical scientists. Hopefully this is a sign of more such developments in the future in Australia. I am engaged in a project with a group of engineers and mathematicians to develop algorithms and software for the efficient design of access networks in underground mines. The future of the mining industry will involve automation and optimisation, so it is a great area for mathematical applications.

PH: Finally, do you have any advice to give to students today?

HR: I urge young students to always consider taking as much statistics, operations research and computer science as you can, to complement your mathematical skills. There are excellent opportunities for students beyond universities and we need to always direct students to be aware of these.

PH: Thank you very much, Hyam.