He was N. M. Rothschild and Sons Professor of Mathematical Sciences and Director of the Isaac Newton Institute at the University of Cambridge from 2001 until 2006, when he was succeeded by Sir David Wallace. He is famous for developing the mathematics of the coalescent, a theoretical model of inheritance, which is fundamental to modern population genetics.
The grandson of a coal miner and son of a government scientist with a PhD in chemistry, Kingman was born in Beckenham, Kent, and grew up in the outskirts of London, where he attended Christ's College, Finchley, which was then a state grammar school. He was awarded a scholarship to read mathematics at Pembroke College, Cambridge, in 1956. On graduating in 1960, he began work on his PhD under the supervision of Peter Whittle, studying queueing theory, Markov chains and regenerative phenomena. A year later, Whittle left Cambridge for the University of Manchester, and, rather than follow him there, Kingman moved instead to Oxford, where he resumed his work under David Kendall. After another year, Kendall was appointed to a professorship at Cambridge and so Kingman returned to the University. He returned, however, as a member of the teaching staff (and a Fellow of Pembroke College) and never completed his PhD.
He married Valerie Cromwell in 1964. They have two children, including John Oliver Frank Kingman. In 1965 he took up the post of Reader at the University of Sussex where she was teaching, and was elected Professor of Mathematics and Statistics the next year. He held this post until 1969, when he moved to Oxford as Professor of Mathematics, a position he held until 1985. He has said of this appointment:
Statistics in Oxford in 1969 was frankly a mess. There was no professor of statistics, the only chair having been abolished some years before...[Maurice Bartlett and] I conspired to persuade Oxford to take statistics seriously.
The London Mathematical Society awarded Kingman its Berwick Prize in 1967. Kingman was elected a Fellow of the Royal Society (FRS) in 1971, later receiving its Royal Medal in 1983 "[i]n recognition of his distinguished researches on queuing theory, on regenerative phenomena, and on mathematical genetics". He was also awarded the Guy Medal in silver by the Royal Statistical Society in 1981. During his time at Oxford, as well as holding a Fellowship at St Anne's College from 1978 to 1985, Kingman also chaired the Science and Engineering Research Council (now the EPSRC) from 1981 to 1985, was vice-president of the Institute of Statisticians from 1978 until 1992 and held visiting appointments at the University of Western Australia (1974) and the Australian National University (1978).
In 1985 Kingman was knighted by Queen Elizabeth II for his work with the Science and Engineering Research Council. From October that year, Sir John was elected Vice-Chancellor of the University of Bristol. He remained in Bristol until 2001 when he took up his post at the Isaac Newton Institute in Cambridge. Shortly after making that move, Kingman drew some media attention for having the third-highest salary among British Vice-Chancellors and this having nearly doubled in his final year in the job, at a time when most academics received pay-rises of about 3%. Whilst at Bristol, he also served in a number of other capacities. In the academic field, he was president of the Royal Statistical Society from 1987 to 1989, and president of the London Mathematical Society from 1990 to 1992. In public service, he was a member of the board of the British Council between 1986 and 1991 and was on the Board of the British Technology Group from 1986 until after it was privatised in 1992. He also held directorships at a number of industrial companies, including IBM from 1985 to 1995 and SmithKline Beecham from 1986 to 1989. In 1987–88, Kingman chaired the Committee of Inquiry into the teaching of the English language. In 2000 the Chancellor of the Exchequer appointed Sir John the first chairman of the Statistics Commission, the body that oversees the work of the Office for National Statistics, the UK government's statistics agency. In 2002 Kingman attracted some media attention by telling the House of Commons Treasury Select Committee that the 2011 UK Census could be conducted using new technology rather than the traditional headcount, or even not conducted at all.
Kingman holds honorary degrees from the universities of Sussex, Southampton, Bristol, the West of England, and Queen's, Ontario.