Professor John Stillwell sits in the back of the bistro wearing a bright orange shirt, somewhat illuminated further by the sun’s rays. He talks with great excitement as he explains his family history in relation to Graduate House: he is the grand-nephew of Frank Stillwell, of the Stillwell Room. “I knew him as a child though not very well because he was a rather stern and quiet man. He wasn’t very good with children,” says Professor Stillwell.

Frank and his three sisters were all graduates of The University of Melbourne. Frank, who studied geology in the early 1900s, was invited to the Mawson Expedition to Antarctica in 1911. After voyage, Frank Stillwell filled in for Mawson at The University of Adelaide while Mawson was on a speaking tour and subsequently went on to become a well-regarded geologist.

Frank’s three sisters were also graduates of The University of Melbourne. The oldest was Effie who a young John Stillwell did not know, because she passed away when John was eight years old. She had gone to India for decades as part of a missionary organisation, where her objective was to be a doctor for Indian women who were not allowed to see male doctors.

Frank’s sister Florence was a chemistry graduate and became the first woman to gain thence a Master in Chemistry degree. The third sister, Olive, completed an Arts degree and also went to India where she became head mistress of a School in Calcutta. She returned to Australia in the early 40s when India was approaching Independence.

“I knew Florence and Olive the best. Florence was the only one who married although she didn’t have children but she liked children and used to hold parties at her house for all the children in the Stillwell family,” he says.

“She also gave me a lot of her books. I still have them. Science books and also literature. She had an eclectic taste in reading, so I’ve sort of inherited the taste for both science and literature from her.” And as the tale unfolds, it turns out that both Effie and Florence were good at mathematics: Effie came top of the State of Victoria at the end of year 12 in 1894 and Florence was second in 1896. Like this mathematical streak, the Stillwell family seems always to have had a relationship with The University of Melbourne, Professor Stillwell having been a student here, as was one of his sons. “It’s been almost continuous really through the generations,” he says.

He gained a Bachelor of Science degree studying chemistry and physics. In the end, however, the family love and natural talent for mathematics led him to choose a career path in this field, as did his interest in Gödel’s Incompleteness Theorem which more or less establishes that mathematics is not complete and thus statements in the language of number theory can neither be proved nor disproved.

Professor Stillwell explained that as an undergraduate student, he was lucky to have had rather indulgent teachers and professors who let him pursue these specific interests for both his honours and masters theses. Though not at that time offered as specialty subjects, these academics facilitated an education that stemmed from his interests – possibly the best thing that teachers can do – and supervised him in a manner that allowed his exercise of academic independence.

John admits, “I had a very good education in calculus and the ideas around calculus. I didn’t realise this until later when I met students in America who didn’t have this background.”

“There were two professors – Love and Cherry. Nominally Professor [Eric Russell] Love was pure mathematics and Professor [Thomas MacFarland] Cherry was applied mathematics but they had both come through Cambridge in the time of G H [Godfrey Harold] Hardy who was a legendary teacher and mathematician, but also a fellow who wrote textbooks and educated students very rigorously,” he says. “He thought English mathematics needed a kick in the pants and had not kept up with the latest trends in France and Germany and he thought he could lift it to that level by teaching calculus very rigorously, which he did. My Professors inherited this attitude and they passed it onto me.”

This sound and comprehensive education in mathematical analysis, particularly the relationship between logic and analysis, led eventually to his research interest these days. However, when he went to graduate school at Massachusetts Institute of Technology (MIT) he found himself floundering with many subjects. Though adept at mathematical analysis and logic (as he had essentially self-taught for the latter) he had a lot of trouble with algebra and topology.

“I dropped out of topology and I got a C in algebra which is virtually a fail,” he says. “I was carrying this burden because I liked the idea of topology. In fact, when I was a first-year student [at The University of Melbourne] we had a Professor from Germany called Professor [Felix] Behrend who also came from this very rigorous and deep school of mathematics and he believed in teaching students hard stuff.”

“One of his other innovations – and I suspect it was his idea – was to have first year students give talks to the other students and staff at lunch times. I gave a talk on topology because I thought this is a fun subject. I’d read a little bit about it and it was intuitive, things about knots and twisting shapes and seeing how far you can distort things, so you can give a nice talk on this with a lot of pictures, and I was excited about the subject in first year but they didn’t teach it at The University of Melbourne.”

When he began at MIT and had the opportunity to learn topology he found that it was entirely different from what he had expected. He was very disappointed, failed the subject, gave up on it and pursued logic.

Professor Stillwell then completed his PhD on infinite computations and in 1970 started as a lecturer in Mathematics at Monash (a position that he had been promised after a Monash Professor saw one of John’s presentations during his masters year) a post that he kept for 31 years until 2001 when he felt that the things he was interested in were not taught as much. Why the shift in subjects offered? Mathematics, he felt, became more of a service subject for engineers and other scientists. “When I started, mathematics was ‘king’. You could teach almost everything you wanted in mathematics because for some reason the 60s brought mathematics to the pinnacle of the sciences. It was gradually put in its more minor place over the decades.”

It was around this time that Professor Stillwell had begun corresponding with someone from the University of San Francisco who was writing a book and sending John chapters for his opinion. Everything fell into place. That fellow became an Associate Dean, the Dean was a mathematician, and they wanted to hire John. “I thought this has happened at just the right time, so I went over there to try it out for a semester and said yes, I’ll join you.”

He started in 2002 and has been there ever since for one semester a year. “Part of the reason they wanted me was because of the books I had written. In turn, I wanted to continue writing books and thought that if I have one semester of teaching, in the other semester I can spend time writing.”

“It has worked out very well. It’s a pleasant university to work in and a pleasant city to live in. My wife and I go there for one semester each year and spend most of the rest of the year in Melbourne, which we also like. I’m really happy that it’s turned out this way. It took a long time.”

From a student of mathematics to a teacher of mathematics, I ask if he sees any evident differences between learning mathematics, teaching mathematics and even writing about mathematics. “Teaching maths is the best way to learn maths,” he says. “As a student, I was not a very good learner. I would write detailed notes and the lecturing style in the early 60s typically was that the lecturer would write everything on the board, so I’d simply copy it down. I would feel a little frustrated that I didn’t understand it at the time, but I would look at my notes afterwards and gradually it would sink in.”

From a student of mathematics to a teacher of mathematics, I ask if he sees any evident differences between learning mathematics, teaching mathematics and even writing about mathematics. “Teaching maths is the best way to learn maths,” he says. “As a student, I was not a very good learner. I would write detailed notes and the lecturing style in the early 60s typically was that the lecturer would write everything on the board, so I’d simply copy it down. I would feel a little frustrated that I didn’t understand it at the time, but I would look at my notes afterwards and gradually it would sink in.”

He would read books if he was interested in the subject, finding that reading about the subject would help him learn just as quickly as he could from lectures. This meant that when it came to Professor Stillwell teaching, he empathised and sympathised with students and any difficulties that they had with understanding complex mathematical principles. He would take the pressure off by drawing diagrams by way of explanation. In so doing, he realised that although his greatest efforts were going into teaching the students, he was, inadvertently, learning more himself.

As Professor Stillwell has taught across the antipodes, it was interesting to gain his perspective on some of the differences between Australia and America, but in order to maximise the wonderment quotient the conversation veered towards whether mathematics differs among cultures, alien cultures.

In a presentation entitled ET Math: How different could it be for the SETI [Search for Extra-Terrestrial Intelligence] Institute, the research organisation founded by Carl Sagan and Jill Tarter, Professor Stillwell talked about whether intelligent aliens would have the same basic ideas about numbers and geometry as us, and, if they did, whether they would express these ideas in the same manner. “If we’re trying to recognise alien signals it’s often thought that we should look for signs of mathematics in the signal. The talk was showing that even some of the basic maths that we do, like a times b equals b times a can be interpreted in many different ways (see diagram below),” he says. He takes a notepad in front of him, clicks the pen and begins creating a diagram. He draws two rectangles.
“Obviously it’s the same rectangle. Then I played with the idea a bit and showed that a times b equals b times a can be arrived at in other ways — so aliens who didn’t have eyes, for instance, this wouldn’t occur to them, probably. But if they could count, they could talk about the numbers 1, 2, 3, 4, 5 and they could come to the idea of addition, then they could come to the idea of multiplication and through a rather tortuous process they could prove that a times b equals b times a.”

So if the situation ever arose of talking to aliens who don’t have eyes they might think of a times b equals b times a in an entirely different way because we know at least two different ways of talking about it. “If you’re looking for mathematics in alien signals you’ve got to be prepared to think of very different ways of interpreting signals,” says Professor Stillwell.

Understanding the historical background of a field is how you can immerse yourself into a certain topic area, from interpreting alien signals to provability.

In his books, Professor Stillwell expresses the importance of understanding the historical background of today’s mathematics. “This not only makes it more interesting, but I seldom appreciate a subject until I know where it comes from,” says Stillwell.

“I think this is true of many students too. They want to know why is this important. If I tell them where it came from very often they understand better why it’s important.”

“The world of today certainly runs on mathematics. We are constantly using technology which ultimately depends on mathematics, particularly electronic technology. But mathematics is very satisfying in the sense that you’re mastering a certain field of thinking. Mathematics is learning how to think, in a certain way – an accurate and logical way and there’s always a need for accurate logical thinking,” he concludes.