A prize

Time for a little blast on my own trumpet.

At the meeting of the London Mathematical Society today, it was announced that I am the winner of the Senior Whitehead Prize this year.

The rules for the prize state, in part,

The SENIOR WHITEHEAD PRIZE is awarded, in memory of Professor J. H. C. Whitehead, a former President of the Society. It is awarded in odd-numbered years. […] The grounds for the award may include work in, influence on or service to mathematics, or recognition of lecturing gifts in the field of mathematics […]

The citation says,

PROFESSOR PETER CAMERON of the UNIVERSITY OF ST ANDREWS is awarded a SENIOR WHITEHEAD PRIZE for his exceptional research contributions across combinatorics and group theory. His fertile imagination and encouragement of others have sparked activity in many fields.

Cameron has long been a leading figure in combinatorics and permutation group theory, frequently impacting on other areas and, through beautiful insights and questions, initiating a stream of research. As an example, starting in 1976 (with the first result in a now rich literature on reducts of homogeneous structures), he has led research on infinite permutation groups. He identified oligomorphic permutation groups, which link to model theory, making connections to combinatorial enumeration and notions of randomness, and led to `Cameron’s constant’ for sum-free sets. Another 1976 paper, with Goethals, Seidel and Shult, makes links between finite graphs with least eigenvalue −2, root systems, and systems of lines at 60 and 90 degrees. His 1981 article on the implications of the classification of finite simple groups made explicit the new methods emerging for finite permutation groups, and he and many others have continued to reap rewards; examples include his proof with Praeger, Saxl and Seitz of the Sims Conjecture. He has papers on many topics in coding theory, design theory, finite geometry, and graph theory, often spotting key interconnections. In a current collaboration with Araújo and others stemming from the Černý conjecture in automata theory, he has opened up links between permutation groups, semigroups, and graphs.

As a lecturer, Cameron’s enthusiasm and lucidity make tricky arguments easy. He draws people to his subject, encouraging problem-solving for starting undergraduates, giving advanced ones a taste of research, and giving sparkling conference lectures. His list of around 40 PhD students includes, among many with academic careers, Eric Lander, the founding Director of the Broad Institute of MIT and Harvard.

Whoever wrote that knows, apart from much else, what I consider to be valuable in my work!

I feel immensely proud of this. Among other things, let me just note that I am only the third person to win both a Junior and Senior Whitehead Prize, the other two being Robert Mackay and Frances Kirwan. (Henry Whitehead, incidentally, was my mathematical great-grandfather; my father Peter Neumann also won the Senior Whitehead Prize in 2003, and though my grandfather Graham Higman did not, he won the Senior Berwick Prize in 1962 and was awarded the De Morgan Medal in 1974.)