Professor Joe Gani (1924-2016), mathematical statistician

I loved my time in Britain. I didn't care much for the corruption that was rampant in Egypt, and it was for me an enormous liberation to go to a country where things were done properly. As a foreign student I had to report to the police once a month, but otherwise I just loved it. I used to go to the theatre every weekend, and I saw Shakespeare, Bernard Shaw – you name it, I saw it – and some Restoration comedies, which I very much enjoyed. [laugh]

What direction did your studies at Imperial College take?

I enrolled for a degree in mathematics, but it was actually a degree in applied mathematics. For example, I never heard about measure theory until I left Imperial College, but we had a very solid bunch of applied mathematical courses. Analysis was basic, but we had also electrodynamics, quantum theory, hydrodynamics, a whole range of applied mathematical topics. One of my favourite lecturers was George Barnard, a statistician. He and Emlyn Lloyd (with whom, incidentally, I still correspond at Christmas) were very influential: they were excellent lecturers and they got me interested in statistics. But basically at that stage I would have considered myself a kind of applied mathematician.

How did you perceive statistics as a science, at that time?

Well, I had some very general ideas. It wasn't until I'd finished with my degree that I became more interested in statistics. I obtained my bachelors degree in 1947, and the following year I decided to do a Diploma of Imperial College, equivalent to a masters degree. I did my diploma under the supervision of George Barnard, who was extremely helpful, and I began to think of statistics as my preferred applied mathematical subject.

Moving to academic life in Melbourne

You went to Melbourne before you came to the Australian National University (ANU), didn't you?

Yes. My father had died in 1947, in Cairo. I'd gone back for a brief visit after that. The situation of most foreigners in Egypt had got worse after the war. Nationalism became a very strong force, and foreigners who had been the backbone of the middle class in Egypt were not so well looked upon and began to leave. Also, in 1948 the United Nations recognised Israel. My mother wrote to me from Cairo that year, 'Things are very bad. Jewish people are having trouble. Your brother Maurice has been arrested for being a Zionist. Get us out of here!'

One of my fellow teachers at the English School had been Grace Drummond, from Western Australia, who had since come to London to do a masters degree in education. We had kept some contact, and she agreed to sponsor the family if we went out to Australia. I approached Hyman Levy, the head of the department at Imperial College in mathematics, and he agreed to write a letter to Tom Cherry, the Professor at Melbourne. At that time it was difficult to recruit mathematicians, and Cherry agreed to take me on as a lecturer in mathematics in his department. So I flew from London through the United States to Sydney and then to Melbourne, while my mother and two younger brothers took a ship from Port Said to Western Australia.

Well, because my mother had been left some money by my father, we could afford to buy a house in Melbourne for us all. I looked at the paper and found some advertisements for estate buildings. One was in Moorabbin. So I just went off, out to Moorabbin – I had no idea about property, never having owned or bought anything – looked at the weatherboard houses there and thought, 'Oh, they're all right.' The house was priced at about £1800 Australian and my mother had more than that, so I clinched the deal and came back to the university. And my friend Betty Laby[?], who was the assistant to Tom Cherry in computation, came to me and asked how I had got on. I replied, 'I've bought a house.' 'What? You idiot! You didn't look at anything else?' 'No, I just went and saw this house and bought it.' [laugh]

As it happened, the house was quite adequate. My mother took the train across from Perth with my brothers, and established herself in Moorabbin. I had rented a room not far from the university, in Carlton, and it was fine. I spent my week there and taught at the university, and went for weekends at home. My mother had these oriental attitudes about hospitality and we had lots of friends around, and parties over the weekend. It was a very pleasant time.

Tell us a little about the department in Melbourne.

The department was run by Tom Cherry and his offsider, Russell Love. The Australian universities had originally been based on the Scottish model, where the professor was a kind of professor-god. In Scotland, apparently, he received the money for the department and paid his lecturers and assistants himself. In Melbourne you all got your salary direct from the administration, but there was a very strong authoritarian structure. Being a rather rebellious young man, I didn't take very kindly to that, but I stuck it out for a couple of years.

Cherry was always very correct and highly respected, but I decided that I would like to get a PhD if possible, and I left Melbourne at the end of 1950, after about two and a half years. Going back to Britain on the Orontes took forever.

Were there any statisticians in Melbourne, or people who became statisticians?

Yes. Maurice Belz was an associate professor in the mathematics department, and he taught some statistics there. In 1948 he broke away and created his own department, and later he became a full professor. Geoff Watson was one of his people, Evan Williams also was with him, and I gave a few lectures in the Department of Statistics on a kind of honorary basis.

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Mixed experiences in Britain and Australia

What happened after you left Melbourne for Britain?

I stayed in Britain for about a year. I managed to get a job at Birkbeck College, where the professor was Cyril Offord. I began to teach there, but I needed to get an appropriate visa. My Egyptian passport ran out in 1951, and I went to the Egyptian Embassy in London to renew it. I was totally entitled to a renewal but they started making difficulties – 'Oh, you will have to go back to Cairo and do things from there,' and so on – and I realised it was probably connected with the fact that my brother Maurice had been arrested as a Zionist. But I wasn't going back to Cairo, no matter what happened.

The embassy informed the Home Office that I was now stateless, and I got an extremely polite letter saying, 'The embassy informs us that you are now a stateless alien, and if you do not leave this country by such-and-such a date we will deport you.' [laugh] I looked at this and thought, 'To hell with it!' so I wrote back equally politely, 'Thank you very much. No need to do that. I shall deport myself.'

Fortunately, I still had my visa for Australia, but for about 18 months after I came back I could not get myself an academic job and so I did all kinds of odd jobs. I was a client of the Commonwealth Employment Bureau in Melbourne; I'd go along and look at the jobs on offer. I had nine different jobs, and gradually climbed from doing manual labour to clerical labour. Eventually I became a schoolteacher in Victoria, teaching mathematics and science for a while to recalcitrant farmers' boys in the Wimmera.

During that period I matured a lot, I think. After all, basically I was a middle-class boy who had been brought up in a middle-class home. I didn't know anything about blue-collar workers, but I found out about them. It was a very formative experience. I learnt a lot about life in general.

Well, I kept applying for academic jobs and didn't get any. I wondered why, because my credentials were pretty reasonable. Then, when I applied for a job at the University of Tasmania, the registrar took pity on me and sent me back the references. And one of them was from Tom Cherry – who had heard me say rash things like, 'Oh, I'm glad Mao Tse-tung has got hold of Beijing. He was much better than Chiang Kai-shek.' He had written, 'Joe Gani is a good lecturer, he does his work competently, but he has Communist sympathies.' In those days, that was the kiss of death!

Realising what had happened, I decided to confront Cherry. I went to him and said, 'I've been trying hard to get an academic job, and I simply can't get it. Do you think people's politics have any influence on that?' Without tackling him directly and saying, 'I know what you've written,' I got him to realise that one's political views did not really affect the issue. After that I applied for three jobs and was offered all three, and I realised that Cherry had thought it over and decided to be a bit kinder.

I liked Cherry, and we enjoyed a pretty good relationship personally. But those were the days of Menzies, and people with leftist tendencies were not exactly favoured. Anyway, we later became even better friends.

So, Joe, after your labouring and worldly experiences in Victoria you went to Western Australia to work.

Yes. I was offered a job in Perth by Larry Blakers, and another offer was a commonwealth postgraduate scholarship at the ANU. I took up the job with Blakers and stayed there for a year, and at the end of 1953 I took up the ANU scholarship under Pat Moran.

Blakers was an interesting man, and we became very good friends. His main difference was that having been trained in the United States he was used to having Jewish colleagues, he was used to people of different views and different attitudes. He was a very broad-minded man, and he helped me tremendously. His view was, 'The better educated my staff, the better it is for the department,' and so he welcomed my going to the ANU. He gave me two years off to get my PhD.

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Getting launched on a PhD

Would you like to tell us about that ANU period?

Yes. I arrived by train at the Kingston station, in Canberra, with an enormous suitcase containing all my worldly goods. But there were no taxis, nothing. An elderly lady passing by in a car saw me sitting on my suitcase and said, 'Do you think you need a lift?' I said, 'That would be very helpful. I need to go to Brassey House' – where scholars at that time were accommodated. It turned out that she was Lady Frankel, the wife of Sir Otto Frankel, with whom I later became very friendly. She drove me to Brassey House and I took up residence, and the next morning I turned up in Pat Moran's department, was given a room and began my time as a postgraduate student.

Pat Moran was in many ways a very good supervisor, full of ideas, but he had a hands-off policy for supervising students. He would come around and say, 'Look, there's a very interesting paper, you should read it.' So you would read it. 'There's a very interesting book by Feller. You should definitely read it.' So you'd do that, and then you'd wait for the thunderbolt of inspiration – which never came [laugh]. I spent eight months reading widely, thinking, 'I'll get an inspiration soon.' But none came.

Things changed by accident. Pat Moran asked me to read a 1946 paper by HR Pitt, 'A theorem on random functions with applications to a theory of provisioning', in the Journal of the London Mathematical Society, volume 21, pages 16–22. He had been working on the theory of dams and I was familiar with his theory, and when I read this paper I realised that in a sense there were similar problems. I saw how I could make the connection, and how I could improve on a couple of things – and these things were the subject of my very first paper, 'Some problems in the theory of provisioning and of dams', in Biometrika, volume 42, 1955, pages 179–201.

Well, once I'd seen that research was about making connections, improving what had been done slightly differently before, I was launched. But it took me eight months to get there, during which I'd nearly given up hope and Pat Moran, I think, was beginning to regard me as a dead loss. After I made this jump, I never looked back.

You met Ted Hannan at about this time.

Oh yes. Ted Hannan also came to the ANU in 1953, in May. He came from what was the nucleus of the Reserve Bank of Australia: Nugget Coombs, who like Blakers had a broad view of things, sent him as a research fellow to work under Trevor Swan. The story goes that Pat Moran saw Ted in the library reading a mathematical book and asked why. Ted said, 'Well, I love mathematics,' to which Pat replied, 'You shouldn't be in economics. You should be with me in statistics,' and he got him transferred.

Ted was self-taught, essentially, in mathematics. He had done a degree in commerce at the University of Melbourne, with one course under Schwerdtfeger in mathematics and one course in statistics under Belz, and that launched him. He knew much more mathematics than I did, he was much more learned.

We became very good friends. I recall that in about 1954 I had to have a wisdom tooth out. It was a fairly difficult operation and my jaw swelled out and so on. Ted said, 'You can't look after yourself. Come home to me.' So he and Irene looked after me and fed me liquid food for a couple of days until I got better and went off again.

Ted and I both finished our degrees in 1955, after which he became a research fellow under Pat. In 1959 he became the first professor of statistics at the then Canberra University College, which in 1960 became the ANU School of General Studies.

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Life in Canberra: papers, plays and marriage

So, after the initial eight months, your research went well and you produced a number of papers.

Absolutely. Once I saw what needed to be done, I began to work on a couple of lines. One line was dams, reservoirs, following Pat's work. He published a paper in 1954, 'A probability theory of dams and storage systems', in the Australian Journal of Applied Science. (Later, in 1959, he wrote a book also, The Theory of Storage.) This was, in a sense, a sub-branch of queuing theory.

The other line was inference in Markov chains. That was originally motivated by a paper of Pat's, 'Estimation methods for evolutive processes', in 1951, in the Journal of the Royal Statistical Society, Series B, volume 13, 141–146.

Was that influenced by Pat's developing interest in mathematical genetics?

It preceded it, but yes, Pat's interest in mathematical genetics was also very influential on me. I read his book The Statistical Processes of Evolutionary Theory, 1962, Oxford University Press, with very great interest.

What about your life at ANU? Did you continue to live at Brassey House?

No, University House opened in February 1954. I was at the opening ceremony where the Duke of Edinburgh gave a speech welcoming us and so on. Brassey House had been more than adequate, but University House was at a level of luxury unknown to most of us! [laugh] I lived there because, as an unmarried graduate student, I was compelled to.

We used to have lots of entertainment, including plays that various students got together to put on. For example, Alan Boyle and I translated a play of Pirandello's, Man, Virtue and the Beast. I have a marvellous poster for it, showing John Carver (who became an eminent physicist and a Fellow of the Academy), his wife Maggie, and me – in the play, actually. To our great surprise, it was an enormous success.

This poster also reflects your inclination to an artistic career.

Well, ah, I'm what the French call an artiste raté – or, you might say, an artiste manqué. [laugh]

That was a wonderful time, very nice. University House in those days was the social centre. We used to have our meals there, and all that I learnt about demography, in which I am quite interested, was learnt at the lunch table as I spoke to people like Mick Borrie and Norma McArthur, who were in the Department of Demography. It was a very good time. People mixed much more, and the university was small enough to form a reasonably cohesive social group. It's too big now: you hardly know people in the Mathematical Sciences Institute, let alone other departments.

You became married during those ANU years.

Yes. I met Ruth Stephens, my wife, at a party. We could never agree exactly when it was. She maintained it was in early 1955; I kept saying it was at a Christmas party in 1954. It doesn't matter, but we met at a party and we became very good friends. It wasn't long before we got engaged – if I recall correctly, in May of 1955. We were married in September 1955, at the end of my graduate studentship.

I lived at University House until I got married, and then I went and lived in a house that Ruth had rented in Ainslie.

I left the department after graduating, and I was able to get a Nuffield Fellowship. And again Larry Blakers showed enormous generosity, allowing me another year's leave. He had the American idea. In the United States, staff, faculty, are free to do pretty much what they like, so long as they don't need to get paid from the source. So if, for example, you could get a year as an invited professor in another university, they would willingly let you go because they felt this added to their kudos. Such an idea was not at that time very current on the Australian scene.

So off we went to Manchester for a year. There I came under the influence of Maurice Bartlett (very famous as a statistician), especially through his book on stochastic processes. He was the person who got me interested in epidemics, which became a very great part of my research interest later on.

A beneficial period in New York

You also spent some time at Columbia?

Yes. From Manchester I went back to Western Australia, and our first child, Jonathan, was born there. In 1959 I got an offer to go to Columbia as an associate professor, and for the third time Blakers showed his immense generosity and let me go. So Ruth and I lived for a year on West 99th Street, pretty much in the middle of Manhattan Island, and I used to walk to the office at Columbia, at 127th Street.

Our second child, Miriam, was born in December 1959, and Ruth was delivered of the child at Columbia Presbyterian Hospital. I remember it quite vividly. Ruth was very methodical – she'd prepare the bag and everything – and the idea was that on the day she felt birth pangs we would go out and get a taxi, and she would go to the Presbyterian Hospital at the end of the island.

The day came, we got up and I took Jonathan by the hand and we walked downstairs. It had snowed overnight and we couldn't get a taxi. (We did find a taxi which had overturned at the end of our street.) So Ruth set off bravely to the underground station, and I can see her walking with her bag, waving to us. She got to the hospital safely, and the baby was delivered. All went well.

In those days children were not allowed to see their mothers in hospital. But fortunately I had a cousin, Rachel Gani, living in New York, and she agreed to come with me. She looked after Jonathan, I went in to see Ruth and the new baby, Miriam; and then I looked after Jonathan while Rachel went in to see Ruth.

I had a very interesting time at Columbia. The man who ran the department was Herbert Robbins – a very famous statistician, slightly eccentric but very, very clever. Others in the department included TW Anderson, who later moved to Stanford, and a colleague of mine, Harold Ruben, who went later to Montreal.

When I got back to Western Australia I was more or less well established. I was able to create a department, which later was run by Uma Prabhu and still later by Terry Speed. So the time in America did launch things, for which I owe Blakers an enormous debt.

At that time you became interested in his great interest, the development of mathematics in Australia.

Yes. Blakers was the person who pushed for the development of the Australian Mathematical Society. During one of the summer holidays he toured the whole of Australia in his big American car, persuading various professors of mathematics that it was time to form the society. And so the Australian Mathematical Society was founded in 1956, and with him I was one of the founding members.

Blakers was a man of very broad ideas. He brought to the Australian scene a whiff of American enterprise, and we owe him a great deal.

Was that the time when you wrote your book?

Well, my book The Condition of Science in Australian Universities was published a bit later, in 1963. But it started because Blakers and I wrote a paper together on Australian mathematics, and I carried on the interest and got more ambitious. My wife was very displeased with me at the time, because I'd go in the morning and work all day in the office, then come home and write this book. She kept saying, 'It's not right, you know. We don't have any family life.'

And you had three young children at the time.

Ah yes [laugh]. Eventually I did write another book. I edited books and collaborated and collected material for books, but I didn't write another book until one with Daryl Daley, Epidemic Modelling: An Introduction, published after my wife had died.

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Birth of the Journal of Applied Probability

You went back for a while to the ANU.

Yes. I was building up the department in Western Australia, and invited both Pat Moran and Ted Hannan to visit. When Pat Moran saw that I was building up the department he thought it would be nice to get me to help build up the department at the ANU, so he offered me a job there as a senior fellow. Somewhat reluctantly, I left Western Australia at the end of 1960 to come to the ANU. The department flourished – Joe Moyal joined, Pat Moran was there, and I think Geoff Watson was there for a while before he left to go to Toronto. Ted Hannan was at the School of General Studies, and there was very close collaboration between his department and Pat's. In a sense, we felt like one group.

At ANU did you continue your research?

Yes, and I helped Pat build up the department. I think I was influential in getting Peter Finch to join.

In about 1962 I got some study leave, and Ruth and I went to Britain. I was offered space at University College, London, where Maurice Bartlett had become the professor. He was helpful as usual, and also I met Toby Lewis and we became good friends. I did some work on epidemic theory while there.

In Britain I took the opportunity of sounding out a variety of colleagues about the possible creation of a journal of applied probability. Pat Moran, myself and others working on applied probability problems were having some difficulty in getting papers published. Applied probability lies between statistics and theoretical probability, being the application of probabilistic methods to real-life problems. If you wrote a paper in it, you'd send the paper to Biometrika, the recognised statistical journal, and they'd send back a polite letter saying, 'Too much probability. We're a statistical journal.' You would then send the paper to the Proceedings of the Cambridge Philosophical Society, who took exactly the opposite tack, 'This has got too much statistics. We can't publish it.' So I thought we should have a journal in applied probability.

At that time there were two journals publishing probability in general, the German Zeitschrift für Wahrscheinlichkeitstheorie and the Russian Teoriya Veroyatnostei. They both published papers verging on the applications, but they were mostly theoretical probability. So I did some homework. I went through Mathematical Reviews to see how many papers could be classified as applied probability, and it looked pretty obvious that there were enough papers to feed a journal which specialised in that area. I sounded out my colleagues and many of them were very enthusiastic. I enlisted the help of such people as Ted Hannan and Pat Moran, who agreed to join as associate editors if I was able to launch it.

I came back to Australia thinking, 'Well, that's wonderful. Let's start this journal.' So I went and tried to get help. I tried the Australian Mathematical Society: no, nothing doing. I tried the Australian Academy of Science: no, they wouldn't help. The Statistical Society wouldn't help. Basically, I think they were a bit intimidated by the challenge. They weren't used to the idea that somebody in Australia could start an international journal. And when I went to Pat for help with the ANU, he was tepid. He had agreed to join as an associate editor, but he wasn't going to do anything about it.

I got a bit fed up, frankly, and decided I'd have to try elsewhere. I had met David Kendall in Britain during my sabbatical and he had been very enthusiastic, and now he wrote that I should go and talk to the London Mathematical Society. So I flew to London, chatted with the Council of the Society, and within an hour had convinced them to help.

We needed, we assumed, about £4500 sterling to get the thing started. With that we could run the journal for a whole year, even if we didn't make a single sale. I had raised half of it in Australia. I contributed, Norma McArthur contributed, and so did Ted Hannan. But we needed another half, and the London Mathematical Society provided it with pleasure, with ease. I came back to Australia and announced that we had the funds, we could do it.

At about this time you moved to Michigan, didn't you?

Well, things became a bit difficult for me within the department. Perhaps Pat decided that I'd grown too big for my boots. Anyhow, relations were a bit strained – never unpleasant, but uncomfortable.

At that time I got an offer from Ken Arnold, the chairman at Michigan State University, in East Lansing, and so we pulled up our roots and left. I got established at Michigan State, where Uma Prabhu (of the University of Western Australia) joined me. And so did Chris Heyde, almost immediately after finishing his studies at the ANU in 1963. That was his first job.

We tried to build up stochastic processes, but regrettably we met with a lot of resistance from the better-established Bayesians and statisticians. Ken Arnold gave us all the support he could, but in American universities everything is done by vote, and we were outnumbered. We got voted down once too often.

Wasn't this the time, though, when the first number of the Journal of Applied Probability appeared?

Yes. I had been preparing the journal at Michigan. My young assistant Alice Spier helped me a lot, and the first issue of the journal eventually came out in June 1964.

I should explain that the term 'applied probability' came originally from the 1995 Proceedings of the Seventh Symposium in Applied Mathematics of the American Mathematical Society, which were entitled Applied Probability. That was, as it were, the initial use of the term, which was then taken over by Maurice Bartlett. He published several books with Methuens in a series in 'statistics and applied probability'. Bartlett made the term popular, and I used it in the title of the Journal of Applied Probability.

I have here a copy of the first issue, which bears a signature by Ted Hannan. As the editor-in-chief for a while, I had the full series of the journals, as did Ted because he was one of the editors. When Ted died in 1994, I gave my series away to a college in Africa or somewhere and I took over his lot.

Would you like to read us the names of the editors at that stage, for posterity?

The editors were Maurice Bartlett, R Bellman, David Cox, A Dvoretzky, Peter Finch, John Hajnal, JM Hammersley, Ted Hannan, Sam Karlin, David Kendall, Motoo Kimura, Pat Moran, Joe Moyal, Yuri Prokhorov, Alfred Rényi, George Reuter, L Schmetterer, Laurie Snell, Lajos Takács and Geoff Watson. It's quite a collection of very well-established people in probability.

And perhaps the names of the authors of that first issue, as well?

They were Uma Prabhu, Harold Ruben, Lajos Takács, Joe Gastwirth, Julian Keilson, Peter Finch, Warren Ewens, AW Davis, Peter Brockwell, Ora Engelberg and Chris Heyde. They're all well known, all big names in the area.

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Sheffield, home of the Applied Probability Trust

We must be coming now to the beginning of your years in Sheffield.

Yes. I started in Sheffield in 1965 and went on to 1974. It was one of the happiest times in my life. Ruth bought a house on Riverdale Road, in west Sheffield. The northern part of Sheffield is rather industrial, but the western part is more rural, full of trees and very attractive. She made the house into a very warm, comfortable home. Our children were basically educated in Sheffield, and in fact developed North Country accents [laugh].

I was very impressed, watching from a distance the parade of eminent people to spend time in Sheffield. They included a number from Australia and New Zealand. Would you like to amplify on this continuing connection?

Well, it was very helpful to me. As a result of my connection with Australia, whenever an ANU PhD was ready I would hire them. Sue Wilson, Malcolm Clark, a lot of Australians came through Sheffield. Terry Speed was there for a while.

David Vere-Jones?

Ah, David Vere-Jones visited. He wanted to get a job as a professor, and so we got him a job within the Manchester–Sheffield School. That was an interesting story, actually.

In 1967 Peter Whittle, the professor at Manchester, was offered the more prestigious job of professor of operations research at Cambridge. He took off, and many of the department went with him or got jobs elsewhere. Manchester was left denuded except for Richard Morton (who later came to Australia, to CSIRO).

The vice-chancellor at Manchester offered me the job. But I felt it was unfair to Sheffield to leave after only two years, so I came up with the bright idea of a joint Manchester–Sheffield school of probability and statistics. We would have a joint masters degree, and people would be seconded from Sheffield to help fill the gap until Manchester could build up again. To my enormous surprise, the Manchester people agreed to it!

Suddenly there I was, the head of the Manchester–Sheffield School of Probability and Statistics. The first thing I did was to second one of my best men in Sheffield, Chris Heyde, to go and run the Manchester group. And I persuaded Richard Morton, who was negotiating to leave for the University of Essex, to stay on so that we would have someone who knew how things were done. Between him and Chris Heyde, and the people we then recruited, Manchester came up again and became independent and quite strong.

The Manchester–Sheffield School still survives today, but in a different form. The statistical groups from the Universities of Salford and Keele joined with it, and it has served its purpose. That interesting experiment worked very well.

The Applied Probability Trust editorial office still remains in Sheffield.

Yes, and we were lucky that the first person to run the office was Mavis Hitchcock, an extremely capable, very strong woman.

We were very lucky altogether with the Applied Probability Trust. Although we didn't expect it to launch itself from the beginning, it very rapidly became completely independent and has been financially successful. There were four trustees, Daryl Daley, Chris Heyde (who, regrettably, died on 6 March of this year), Søren Asmussen, who is now the editor-in-chief, and myself. We perpetuate ourselves: trustees appoint trustees to replace them. It seems to be working. Long may it last – you never know with these things!

Just before we pass on from Sheffield: you've had a long-term connection with Klaus Dietz.

Yes. Klaus was a student in Germany and wrote to me at Sheffield. He was interested in epidemics, and could he come and work for a while? So I invited him, he came over and he made an excellent impression on me. I got him interested in problems on epidemics and he later went on and became an authority in the field. I visited him at Tübingen, and he is a very highly respected man in the area. A charming man. We still correspond.

I'd like also to bring in Partha – KR Parthasarathy. He was an Indian who came to us in Sheffield and became a lecturer. He was so bright that he soon progressed through senior lecturer to reader, and then when Manchester had a vacancy for a professor in mathematics I recommended him strongly. They did appoint him and became extremely pleased, because he was absolutely brilliant. He later went back to India and became a Fellow of the Indian Academy of Sciences, and is very highly respected. He was one of our success stories. Actually, he's retired now.

Of course retired in the sense that you and I are retired, yes.

That's right. Retired but active! [laugh]

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The CSIRO years

How did it come about that you returned to Australia, specifically to the CSIRO?

That was very interesting. Early in 1973, Alf Cornish, the head of the then Division of Mathematical Statistics at CSIRO, died. Victor Burgmann, who was responsible for the division, went headhunting in Europe and Britain. He visited Britain and talked to various people – to John Nelder, to David Cox, to me – and asked us to apply. I told him quite frankly, 'My experience of Australian universities has not been brilliant. I don't think I'd like to go back to Australia.'

They appointed John Adair Barker, an Australian at IBM in San Jose, California. He came out to head the division, lasted a couple of months and went back to IBM. Victor Burgmann then came on a second tour of headhunting. He didn't get very far. So he said to me, 'Look, you're an Australian' – I had become naturalised in 1954, before I got married to Ruth – 'will you come out and do a review of the division? We obviously need changes.' And I came out in about February 1974.

In order to review the division I travelled everywhere. They had nine locations, in Melbourne, Sydney, Canberra, Adelaide (the headquarters), Perth, Brisbane. My report said, in effect, 'The Division of Mathematical Statistics has so far concentrated on biometry and application to agricultural problems in Australia, but Australia has moved on. It has now become an industrialised country, and you need to have a broader spectrum of interest. You need operations research, mathematical modelling, applied mathematics, computational mathematics. And, without stopping your work on biometrics, on agricultural statistics, you should broaden the field of inquiry.' Then I went back to Sheffield quite happily. Six months later I got a letter saying, 'The executive have decided to accept your report in toto, but we think you're the only man who can do it.' I was hooked!

I talked to Ruth. She was always very keen on Australia, even though she had been born in York and brought up in London and Manchester, and I myself felt this was my chance to do something for my adopted country. So we decided to return to Australia, and I came in about September 1974. Ruth stayed on in Sheffield until the children's school ended in July 1975, and I flew back every three months to keep in touch with the family.

So I came out to Australia – and bought a house. Ruth had made me promise that I would not buy a house until she came out. But a house came up in Deakin, in the same street as the house we had got when I joined the ANU in 1960–61. I rang up and said, 'Ruth, there's this house, all our neighbours are still there, it'll be wonderful.' 'Don't you dare buy that house!' [laugh] I twisted her arm, and eventually she made me promise that if she didn't like the house we'd sell it and we'd get another one.

When she came out with the family, she looked at the house and she didn't like it [laugh]. So I said, 'Well, you have a choice. Either we can leave or you can modify this house.' She decided she would modify it. She spent as much modifying it as I spent to buy it, but in the end she was very pleased with it. That's the house I now live in, and everywhere I go there is a whiff of her. She enlarged our living room, she modernised our bathroom and kitchen, she did wonders. It became a modern house. That was a very happy time at home.

How were things going at the CSIRO?

I had seven years with CSIRO, between 1974 and 1981. The general consensus was that it went brilliantly. We instigated the agreement between the universities and CSIRO for the visitors program, which incidentally is still alive today as the CMIS [CSIRO Mathematical and Information Sciences] Visitor Program, and we invited everybody. People in CSIRO still come up to me saying, 'Oh, that was the first time I met David Cox, when you brought him out,' or, 'It was the first time I heard John Nelder giving a talk,' 'It was the first time John Tukey came out and talked to us.' So the programs were very good.

We did broaden our area. For example, recently in CSIRO they celebrated the 60th birthday of Frank de Hoog, a very eminent mathematical modeller, basically an applied mathematician, who has done wonders – he modelled the BHP blast furnaces and saved them millions, and did many other very good things. Yes, we expanded our purview, we did everything that we said we would do.

Chris Heyde joined you early in the year?

Yes. Chris had been a reader at the ANU but he joined me and became assistant chief. He was very, very good, and helped to develop all sorts of things. We had a splendid time.

But at the end of seven years, as usual in the CSIRO, there was a review. By that time, the head of the institute which contained our division – renamed as the Division of Mathematics and Statistics (DMS) – was John Philip, who was also the Chief of the Division of Environmental Mechanics. He was a difficult character, and although our relations were polite we didn't get on particularly well.

He put himself at the head of the committee of review. We thought we'd done brilliantly, and Paul Wild, who was then the head of CSIRO, agreed. But the review, when eventually it came out, was schizophrenic.

The first part said, 'This division has become internationally renowned. It has done extremely well, blah, blah, blah. It has done all that we had asked of it.' Part two said, 'Unfortunately, that's not what the government wants. What it wants is a more commercially oriented enterprise. It wants a return to the more consultative aspect of before.' We had become a very strong research as well as consultative unit. They wanted a kind of return. I have no idea to what extent the views of John Philip influenced that.

Anyhow, in essence I was told that I had to change policy. Well, I'm not a very easy person to twist, and my attitude was, 'For seven years I've gone before my troops and told them they must do research, they must bring out papers, as well as consulting. Now I'm supposed to tell them, "No, I'm sorry, we're going to go back." I'm not going to do it.'

Ruth was very upset, because our children had grown here, we had a nice house, we'd made friends. She said to me, 'Don't be so stiff-necked. All the other chiefs have agreed to the new policies. Why don't you agree?' And I kept saying, 'Ruth, it's not going to work.'

Anyway, she was a very loyal wife, and when I resigned and went off to the University of Kentucky she followed me faithfully. And, to do her credit, four years later when she could see what had happened – Chris Heyde was acting chief for a short while, he was followed for a couple of years by Terry Speed, who then went to Berkeley, he was followed by Peter Diggle, who lasted a full year and then went off to Lancaster – Ruth came to me and said, 'I hate to have to say this, Joe, but you were right.' [laugh] The only time in my life that my wife admitted to not being correct!

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A return to academia

So you left CSIRO and went back to academia?

That's right. Having decided to leave CSIRO, I was going to resign totally, but Paul Wild (a very gentlemanly person) said to me, 'Don't do that. Resign from being chief, but stay with CSIRO on leave, and then come back later and complete a few weeks with CSIRO, after which you can retire honourably at the age of 60' – which is what I did.

I went to America, to a couple of conferences, trailed my coat a little and got a couple of offers, one from the University of Kentucky and one from Colorado State University. I chose to go to the University of Kentucky, and stayed there for four and a half years. That was a reasonably happy time. We enjoyed living in Lexington, a very lovely town. And the department went quite well. I had a very cooperative dean of the Faculty of Science, who agreed that all statistics must be taught by statisticians. So we always had plenty of students.

I taught several courses and I built up the department. I got a promise of $50,000 for a consulting laboratory – and although it never quite eventuated, Dick Kryscio (who has been head of the department for a while) came to join us and he began consulting with the medical school, et cetera. I taught statistics for nurses, both men and women, and enjoyed that quite a lot. They were not mathematically prepared, but they were very charming persons. And in Kentucky I had my first experience of going to an American football game, which I didn't understand one bit!

What caused you to move to Santa Barbara?

Somehow word got around that I was building up the department in Kentucky very nicely. Quite out of the blue I got an offer from James Robertson, a mathematician at the University of California at Santa Barbara. They had two people who taught statistics within the mathematics department, Sreenivas Jammalamadaka and Milton Sobel, and they wanted to create a department. They hoped that somebody would come and build it up, and then break away from the maths department.

So, although I had been happy in Kentucky, I left and went on to California. Actually, Ruth preferred Lexington to Santa Barbara, saying that Lexington was a more 'normal' sort of city and Santa Barbara was a city inhabited by retired millionaires: 'You know, Joe, the only reasonable people in this town are the Mexicans. All the others are artificial.' [laugh] But Santa Barbara was a beautiful town and the campus was very attractive.

I began building up the department and got a large number of people to join. It grew very rapidly and very soon became one of the top three statistical establishments in the California system. On the whole, my faculty was very cooperative. But I had some difficulties with the older-established staff, who felt that power had been removed from them, you know: 'And who are all these newcomers?' This again brought attention to the disadvantages of the vote going with the majority, whether they're right or wrong. But on the whole it went quite well.

We lived in Santa Barbara for a good number of years, and when I turned 67 I decided to retire. But the provost, David Sprecher, said, 'Oh, you can't do that. You've got this enormous contract with NIH and it's bringing in $50,000 in overheads to the university. You can't retire. Come to Santa Barbara one term out of three each year. You'll remain on the books, you'll get paid for that term, we can retain the contract. And the contract comes to an end when you turn 70; you can then retire.' So from 1991 we lived in Canberra, where I had kept the house, and we went Santa Barbara for three months each year. I would teach, do whatever was necessary and come back. In July 1994 I retired from Santa Barbara and became a visiting fellow at the ANU.

Was that, effectively, the end of your teaching career?

Yes. I taught a little bit at the ANU, an honorary course, and also there was a fixed appointment when I was a paid visiting fellow for a couple of years. The money that was offered was minimal but it helped with travel. The rest of the time I have been an honorary fellow.

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Perpetuating and sharing statistical science

How have you been spending your retirement time?

I went on working at the ANU. I've got a fairly well established routine, like clockwork. My neighbour Richard Cornes, who is the Fred Gruen Professor of Economics, knows that, and when he wants a lift he comes out at exactly 8.30 a.m. and I pick him up, and we drive in together. I get to the ANU at about 8.45, when you can still get a parking space. In my office I answer my emails, and then my time is divided basically into three parts.

The first part is editorial duties. I still edit The Mathematical Scientist, one of the four journals of the Applied Probability Trust. That takes a couple of hours each day. Papers come in, I've got to find referees, I've got to sometimes referee papers myself.

The second part is mentoring younger people, for example Linda Stals, a senior lecturer. We often collaborate on papers; I help her with one or two things. Belinda Barnes, who now works for the government, used to work for the Research School of Biological Sciences. She comes in and I talk with her about her problems. We've now got a routine: when she needs something, I go for the Encyclopedia of Statistical Sciences, photocopy the relevant parts, hand it over to her. So mentoring is a good part of my time.

The third part of my time is research. As I've got older I've got stupider, but I still enjoy doing research. So, although none of my ideas are earthshaking, I continue to work on epidemic modelling. For example, in the last year I was very lucky: one of my former students from Santa Barbara, Randy Swift, came over to spend a sabbatical here and we published quite a large number of papers together. The last paper is 'A simple approach to the integrals under three stochastic processes', which is going to appear in the Journal of Statistical Theory and Practice very shortly. So I continue to publish.

You have a good publication rate for someone who's retired: about seven papers a year. In fact, not too many mathematicians would publish seven papers a year.

Well, what else have I got to do? [laugh] They do say that it keeps the brain active. Without being falsely modest, I don't think any of my recent work is worthy of a Nobel Prize but it keeps me interested. And it keeps me abreast of what's going on.

Looking back, then, what are your favourites amongst your own writings?

There was a paper of which, technically, Ruth should have been shown as an author, 'A simple method for determining the proportion of lymphocytes in the four phases of the DNA cycle', which was in the Bulletin of the Institute of Mathematics and Its Applications, volume 11, 1975, pages 70–74. In that paper we looked at the various cycles in DNA. She told me about the situation, explaining it in terms understandable to the layman, and then I worked on it and she helped to set me right on a variety of points. I kept urging her to join me as an author but she was very modest and just wouldn't agree to it. So there is an acknowledgement to her but she left me as the sole author. That's one of my favourite papers.

The other one was a paper presented to the Fifth Berkeley Symposium and published in 1967. That was basically the solution of the differential equation for the general stochastic epidemic. It was a very strong mathematical paper, in which I solved what had until then been an unsolved equation.

More recently I have worked a lot on HIV – for example, I've got several papers on HIV modelling, some of them with Sid Yakowitz. And a recent paper that I am fairly pleased with is 'A simple approach to birth processes with random catastrophes', authored with Randy Swift, in the Journal of Combinatorics, Information and System Sciences.

What do you think are your most influential papers, the papers that are perhaps more than 20 years old and continue to be cited?

Ah, I would imagine most of my work in epidemic theory. The book that I wrote with Daryl Daley, Epidemic Modelling, published in 1999 by Cambridge University Press, contains a compendium of all the work that we did in epidemic modelling, and I think it's been reasonably influential. My information is that it has been recommended as a book for masters courses and is fairly popular, still selling. These things usually have a life of between five and 10 years, so within a couple of years it will probably be dead. Daryl is talking about a revised version. I don't think I'll live to see it [laugh] but it doesn't really matter.

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The legacy of Ruth Stephens Gani

Your wife Ruth was also a scientist and an author of scientific papers. Did she influence the direction of your research towards the biological?

She definitely did. She started off as a botanist, and then when she worked for Otto Frankel in the Division of Plant Industry at CSIRO she became a wheat geneticist. Later on, when we were in Kentucky, she studied for a masters degree in cytogenetics. While we were in Sheffield and also when we came back to Australia she worked on human genetics, and she ended up by being a human geneticist. In fact, her last job was as an honorary research fellow, or something of that nature, in the John Curtin School, working under Sue Serjeantson (who is now the Executive Secretary of the Academy).

Ruth kept talking to me about genetics, about biological models, and I got very interested in those. I had started being interested in epidemics because of Maurice Bartlett, but she got me even more interested. (I mentioned earlier the paper on the DNA cycle, of which she should have been the co-author.)

You have now found a way of commemorating your wife's memory.

Yes, indeed. We retired in 1994, and very sadly, Ruth died in January 1997. She had been diagnosed with breast cancer in 1992, and she had a mastectomy, she had chemotherapy et cetera. But it got worse and she died. I was devastated. I still miss her. But you can't argue with death.

I have now offered the Academy a medal for human genetics which is named the Ruth Stephens Gani Medal, and it is going to be awarded for the first time in May of this year. Sue Serjeantson and Faye Nicholas, at the Academy, have been extremely helpful, both in setting it up and in organising the design. It is minted by the local Government Mint, and they have done a great job. There is a difference this time, however. I helped with the Hannan Medal, which like the Moyal Medal and so on has an effigy of the person being commemorated. But you can't recognise them. So on this medal we just have a DNA strand. It's come up very nicely.

Did any of your children follow you in a life of science?

Well, two of my children are doctors. The eldest, Jonathan, who was born in Perth in 1957, is now a very well-

known abdominal surgeon in Newcastle, in Australia. And my last child, Sarah, who was born in East Lansing, Michigan, in 1964, is a GP in Sydney.

Miriam, who was born in 1959 in New York, is now a senior lecturer in law at the ANU, interested in criminal law, among other things. She writes quite a number of papers, most of which I can't understand. [laugh]

Matthew has inherited the mathematical gene, or part of it. He was born in 1961. He did a degree in electronic engineering and a joint degree in mathematics at the University of New South Wales, and he now works as an electronic engineer in Seattle, America. He is married to Jennie, a novelist. They don't have any children, whereas both Jonathan and Miriam do.

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Serious and humorous aspects of social activism

You've maintained a certain social activism in statistics in Australia. Could you talk a little bit about that?

I've long been interested in the social function of mathematics, the uses of mathematics in the society. I've written a fair bit about it, for example in the paper 'The role of mathematics in society', in The Mathematical Scientist, 1980, and 'Some comments on the social contributions of mathematics and statistics', which appeared in 1980 in a Portuguese publication, Boletim Informativo de Estatística [e Investigação Operacional].

Also, history is one of my very strong interests. One of my earliest writings on historical topics was the paper 'Newton on "a Question touching ye different odds upon certain given Chances upon Dice"', in The Mathematical Scientist, 1982. In 1982 also I edited a book, The Making of Statisticians, where I got individual statisticians to write about their life histories. I enjoyed doing that. And in 1981, with Chris Heyde, I wrote a pamphlet on statistics, published by the Australian Academy of Science in Mathematical Sciences in Australia.

Then I've got various other bits and pieces, like the paper 'Markov to Chebyshev: some useful inequalities', in Teaching Statistics, 1984. I wrote on Isaac Newton in the Encyclopedia of Statistical Science, 1985, and on statistics and history in Mathematical Spectrum, 2001–02. And for Statisticians of the Centuries, the book that you edited with Chris Heyde, I wrote articles on Daniel Bernoulli, Pyotr Dimitrievich En'ko and Anderson Gray McKendrick, all of whom worked in epidemic theory.

I talked earlier about being a failed artist [laugh]. I'm also a failed historian! I would have liked to be involved more in history, but unfortunately life is limited and you can only do so much. Anyway, what I have done has been really enjoyable.

As part of your social activism, your morning coffee sessions at ANU are famous.

I tried to re-create the kind of atmosphere that we had in the early ANU, where everybody met everybody and talked about everything. After retirement I formed the so-called Coffee Club, consisting basically of people in the mathematical sciences. One of our favourite members is Ken Brewer, a delightful person and the best kind of British eccentric. The other day we had an immense discussion about the verb 'to wit'. I went to my dictionary and found, 'Past tense wot, wottest, wotteth', and Ken said to me, 'I disagree. It's not right!' [laugh]

Is it a good opportunity to exchange statistical gossip?

Well, we also exchange views about things in general – philosophy, politics, mathematics, the latest SBS television programs, whatever. Recently, with Dingcheng Wang, a Chinese visitor, we discussed an SBS program about sex in the new China. Dingchen said to us, 'It is very different from my time and my parents. The new Chinese are very different!' We solve some problems, many things which don't crop up more formally. For example, I very often ask questions about computers, and there's Mike Osborne who knows about these things and can give advice. And there's David Heath, who discusses financial mathematics. Chris Heyde was a very active member when he was alive. We really shall miss him.

I can understand that. I have had the good fortune of attending some of these sessions at the times when I have been in Canberra.

We tell lots of jokes!

You are famous for your jokes. I remember at the last ISI [International Statistical Institute] session, in Sydney, you were supposed to talk about statistics in state universities. After about 10 minutes you said, 'I'm going to put all that aside,' and you started on your statistical jokes.

[laugh] I'll tell you one of my favourite Jewish jokes. It's about a Jewish mother who is going to turn 80. She has three very successful sons, and one of them is a builder. Another one is a car dealer, and the third one is an academic. And the builder says to his mother, 'Mother, I'm going to build you a dream villa. It's going to have a sauna, it's going to have a swimming pool,' et cetera, et cetera. So he builds her this marvellous 20-room house. The second son says to his mother, 'I know you don't drive, but I'm going to give you a Mercedes, and because you don't drive I'll give you a chauffeur.' The third son is an academic and he doesn't have much money, but he hears that there is a Hasidic sect who train parrots to recite from the Psalms. His mother is fairly religious, so he'll go and buy one of these parrots.

The birthday comes and the mother, like all Jewish mothers, complains. She says to the oldest son, 'Ohh-ohh, you had to build me a house with 20 rooms. I have to clean 20 rooms and I live in two of them!' And the son is very crestfallen. She goes to the car dealer and she says, 'You had to give me a car. You know I don't go anywhere. And the chauffeur is always chasing my chambermaid and she can't get her work done.' And he goes away feeling pretty bad. To the third son she gives a big smile. 'Son,' she says, 'that chicken was very tasty.'

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Diversified interests, close friends, golden times

Do you remember some instances when you had a flash of inspiration or revelation?

Perhaps my first revelation was after reading the paper by Pitt. That's when I really latched on to what research was about. And since then many of my bright ideas come when I least expect them: while I am enjoying having hot showers or as I'm waking up in the morning, or when I go walking. But they'll come when they feel like it, and I've learnt now, I mustn't push. I mustn't get obsessed with something. I must just sit back and relax, and think about nothing, and something will pop into my head – very often after reading somebody else's paper.

It was said that as a graduate student you kept a notebook by your bed. Do you still do that?

[laugh] Not any more, no. I am very often surprised that my memory is still reasonably good – not as good as it used to be, but I can remember things and I have lots of sources to fall back on if I'm a bit doubtful about a date.

We haven't yet mentioned your 'academic hobby', the type-token matrix. It is another area in which you have been influential.

Well, I've always been interested in literature, and I remember starting to write on models for type-token structure. When you write or say anything, the total number of words you say are referred to as 'tokens', and 'types' are individual words. For example, suppose I say to you, 'Eugene, please would you kindly open the door?' Every time I reach a new word that hasn't occurred before, that's a type. A matrix has cropped up in certain genetic problems that also characterises the structure of the type-token model, and I got interested in that and started writing about it. Quite a long time ago I wrote a paper with Daryl Daley and David Ratkowsky on type-token models, and it's been a continuing interest. Whenever I get bored with epidemics or queuing or dams I go back to that.

Technically it's connected with your old interest in Markov chains, in a sense. What about the matrix you spoke about?

The model basically is one of a Markov chain where you move up one every time you get a new word. You have the total number of words, but the matrix incorporates the move up by one if you have a new word.

It's good to have a continuing academic hobby like that.

It is indeed, yes. It has also diversified my interests. In that regard, I always feel rather badly about the narrow training of our modern graduate students.

Let's talk a little, then, about how you perceive the interest and direction of young researchers, graduate students today, as compared with maybe 30 or 40 years ago.

My impression is that they are not as well prepared. This may have something to do with the change in the structure of bachelors degrees. In the old days, if you got an honours degree in maths you were extremely well prepared. Nowadays honours degrees are on the wane. But on the whole the students do catch up.

I think the American system, whereby they do a very general degree and then a masters degree, after which they do coursework and a thesis, is a good one. The American PhDs are a bit short on the research side, and I think the Australian degrees are a bit short on the breadth of knowledge. Some combination of the two would be ideal.

In the 'good old days' of a PhD in statistics, a student produced something like four or five papers while the thesis was being written.

That's right. The American PhD is basically one paper, but I think that the Australian degree still involves about three or four papers. That's a good idea.

But I am more concerned that students should have a broad scientific background. Certainly in our area, the broader your interests, the more the problems that you will be able to tackle and solve. If your interest is very narrow, if you learn only about one thing – say, the bootstrap – you have a very narrow viewpoint. I would consider myself a general scientist with a particular interest in this or that, and I think it's an impoverishment if you're only interested in one thing. In contrast, Chris Heyde collaborated with his wife on biochemical and other problems, and later with David Heath and others on financial problems. It's good to have a broad background.

What are you most proud of creating in your life?

Well, if I were absolutely honest: my children! Following that, I'm very pleased that the Applied Probability Trust has done as well as it has. I never, in my wildest dreams, expected it. It has now been going on for 44 years and has done well financially, it's done well in terms of kudos. It is really a very good organisation, and I am pleased to have been its founder.

Which part of your life generally has been the happiest, the one you remember as a golden period?

I would probably say the period in Sheffield, basically because of the stability. I thought I was going to be there forever. My return to CSIRO was in a sense rather accidental and it caused a lot of heartache – leaving was really quite a wrench. The CSIRO time was wonderful while it lasted, but I got a severe shock with the way it ended. And then while I certainly enjoyed my years in America, it's not a country I would like to live in permanently.

I would say that although I've had a rather broken-up life, looking back I don't regret it. I consider myself to have been extremely lucky, not least in my marriage and in my children, but also professionally. I've had a lot of hurdles to overcome, but fortunately I haven't been left with a nasty taste.

And you had two very important friends in your life, Ted Hannan and Chris Heyde.

Indeed. Ted was very much like a brother. We used to exchange views, we used to talk about everything – Ted was a person of very wide interests, extremely well read. I still have a copy of the poems of WB Yeats which he gave me on one occasion, and which he used to quote. I can never remember poetry, but he used to be very good at quotation from Yeats and other poets.

'An elderly man is like a stick with an esophagus'...

That's right! [laugh] Ted was a wonderful man. I am still very good friends with his widow, whom I visit regularly.

Chris was more like a son (there was a 15-year difference between us) and he was a very clever, very loyal colleague. Now it's our turn to support Beth Heyde, who has lost her very dear husband.

Ted and Chris were family. As, I might add, you are too.

Well, thank you for that, Joe. I think this interview will be a fitting tribute to your role.

And thank you very much. I really appreciate it.

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