# A probabilist's journey in mathematics: an interview with Sir John Kingman

Beginning his career at Cambridge in the 1960s, John has spent time at the Universities of Oxford, Sussex and Bristol. Before his academic career eventually came full circle when in 2001 he returned to Cambridge to become Director of the elite maths research centre, the Isaac Newton Institute.

John has also played a notable part in the advancement of statistics outside of the academic sphere. His involvement in the Royal Statistical Society, and his role as President of the Society, preceded his appointment as the first chairman of the Statistics Commission in 2000.

But before our discussion about his later experiences with official statistics, we started a few decades back and talked about the path that led him from an early interest in mathematics to his eventual destination in probability theory.

John Kingman was born just days before the outbreak of the Second World War. His father was a scientist, which kept him from the frontlines of the war but also meant a firm belief in education became an important element in John’s childhood. This influence, and that of a school maths teacher he credited in his autobiography, led him to study Mathematics at Pembroke College, Cambridge.

His autobiography contains an intriguing story of how he first became interested in the theory of probability at Cambridge. As a summer job during this time, he went to work at the Post Office Engineering Research Station at Dollis Hill. He was put to work doing simple probability calculations to model the demand for telephone cables, back when the phone network was still limited in its capacity. Did witnessing this practical application first hand provide the catalyst he required for his interest in probability to be sparked?

‘I don’t think I needed it, but the way I saw probability being applied in the telephone engineering world made that branch of mathematics that bit more interesting. When you do a maths course at Cambridge for example, the so called applied maths courses are actually very theoretical. You don’t get a feel for how it is being used. So I think seeing how people applied these theories, didn’t make me want to become a telephone engineer, but it did make me more interested in probability.’

John always stresses that the theory is what has always interested him about mathematics, but in this context he admitted. ‘A lot of my friends in the subject are highly theoretical, and I think that’s a pity because you don’t get such a broad view of the subject if you are out of touch with some applications of the theory.’

Following his summer at Dollis Hill, John returned to Cambridge ready learn more about probability theory. The lecturer teaching the course that year turned out to be Dennis Lindley, who John described as ‘an absolutely brilliant lecturer, one the best I’ve come across.’ In his autobiography, John makes the eloquent point that at the time of his exposure to Dennis’ teaching he ‘had not yet met Bayes on the road to Damascus’.

This laid the foundations for what John would devote his faculties to over the next few decades of his life. His third year involved lectures from Peter Whittle on stochastic processes and further teaching from Dennis Lindley on statistics. As he says himself, ‘when I came to the end of my third year it was natural progression to stay on and do research on probability.’

At this time, Cambridge was going through a period of immense change. When he arrived, the university didn’t have a Mathematics Department, instead there were lecturers, readers and a faculty that set the syllabus. He explained what prompted a change in the status quo.

‘The applied mathematicians, found they were losing out on research funding, so they set up a Department of Applied Mathematics and Theoretical Physics. Then the pure mathematicians found they were losing out to the applied mathematicians, so they formed another department.’

Also involved in this story is the fascinating account of what happened to the Statistical Laboratory in this reorganisation. ‘Before all this there had been a Statistical Laboratory set up by John Wishart in a terrible slum, a sort of prefabricated single storey building. But when the pure mathematicians set up their department, the Statistical Laboratory thought it had better join as they felt more affinity with them. But at that time the statistical laboratory was dying, everybody was leaving. And then eventually the university realised the problem was there was no Professor of Statistics, largely under pressure from the RSS.’

At the time these developments were taking place, John had moved to Oxford to work under the tutelage of David Kendall. However, the fate of the Statistical Laboratory would bring him back to Cambridge and he only learned exactly how this came about when he was writing the biography of his old mentor Kendall.

‘The RSS had raised some money towards creating a Professor of Statistics and put pressure on the university, so they were given two places on the appointments committee. These were filled by Egon Pearson and Maurice Kendall and they pushed for David Kendall (no relation) because he was the statistician who the pure mathematicians really respected. They tended to be scathing of many statisticians and regarded themselves as superior, but David could match them, on their own terms. He then revived the statistical laboratory and it has gone from strength to strength.’

Following a couple of years back at Cambridge as an Assistant Lecturer, his career took a surprising turn when he left the world of the old established universities and accepted a position at the newly created University of Sussex. The 1960s saw the creation of a host of new universities as higher education went through a major revolution of its principles and organisation. This gave John the opportunity to mould a mathematics working group himself, ‘It was my job to build up the statistics group and we got some very good people.’

One of major new departures that began in Sussex and the other new universities was the introduction of a course in elementary statistics into the social sciences. John was one of the first to teach a course to social science students who had never previously been required to learn statistics. The legacy of this development was that, ‘the social sciences and even the humanities have become much more mathematical and statistical. You can’t be a serious economist, sociologist or social psychologist now unless you have a good understanding of mathematics and statistics.’

In 1969, he returned to Oxford to become the Professor of Mathematics. In a previous interview, he explained that statistics at Oxford ‘was frankly a mess. There was no Professor of Statistics, the only chair having been abolished some years before. I conspired to persuade Oxford to take statistics seriously, and now there is a proper statistics department teaching mathematicians and non-mathematicians.’

John stayed in Oxford for many years and while he was there he published some of his most important research. At this point, our discussion turned towards his most celebrated theoretical discoveries, and his view of them gives an intriguing insight. ‘You work away and try and make a few discoveries, write papers and books and so on. And then you find that the things you thought were rather good are ignored, and the things you thought were fairly trivial seem to achieve a life of their own.’

Some of his most famous work was on coalescent theory in the early 1980s, he reflects on the influence it has subsequently had. ‘It made very little impact after I published it, but now you have whole International Conferences on it in genetics and genomics. Some of the work done by Peter Donnelly for example, is absolutely first class, far beyond anything I could have done.’

He further explains his own personal view of his body of work in this way, ‘I think I know what is important on my criteria, but what the world thinks is a very different matter. The world thinks that the coalescent, sub additive ergodic theorem and the work I did on queues are the things that will be mentioned in my obituary. And the theory of regenerative phenomena for instance, which I think is rather important, will probably not be mentioned at all. I don’t mind that, I’m quite happy that I have done some things that people find interesting.’

The best insight into his view of mathematics and statistics came when he discussed what his options were at the time he completed his final year at Cambridge back in 1960. He stayed on to research probability but as he explains. ‘The alternative would have been to take the Diploma in Mathematical Statistics, but what put me off that was the amount of data analysis, I have always been interested in the theory of statistics. The idea of sitting down with a great pile of numerical data and a primitive calculator was frankly not very appealing. This was before the days when you fed it all in to the computer and it did all the work for you.’

‘If I had become a real statistician, as oppose to a pure and applied probabilist, I would probably have become a Bayesian, but that’s because my instincts are those of a mathematician who wants something cut and dried,’ he observed. ‘Whereas the great statisticians, people like David Cox, don’t mind that the data is messy. And that is much healthier in a statistician. But mathematicians are different, they never really grow up - statisticians have to. Mathematicians are better if they stay a bit childish and play the game as a game.’

In this illustration, John succinctly sums up how he views the beauty of mathematics. ‘This is the key to teaching mathematics, it’s not to flood people with practical problems, rather it’s to say that this is the best game that has ever been invented. It beats Monopoly, it beats chess and it happens that it can enable you to land rockets on the moon. The real mathematical advances have been made by people who just loved it.’

*Part two of our interview looks at John's time as President of the RSS and then Chair of the Statistics Commission. Image used is ©Godfrey Argent Studio*