My friend and mentor Peter M. Neumann died on 18 December 2020. There have already been many tributes to him and fond memories recalled. Some of these are reported through the Queen's college memorial page to him. Here I recall some personal early memories that are maybe not so widely known.
I went up to Queen’s in October 1964 at the age of 18 and immediately met the 23 year old Peter Neumann. He became my mathematical mentor first as undergraduate tutor and then doctoral supervisor, and was easily the biggest influence on my development as a mathematician.
In the acknowledgements in my D. Phil. thesis (1970) I wrote “My chief debt is to my supervisor Dr. P. M. Neumann, whose interest and encouragement were unfailing. It is a pleasure to thank him for all his advice and to record my appreciation of his friendship.” I was to know this warm, courteous, witty and clever man for a further 50 years and we had many personal and mathematical interactions. Here I’d like to mention some earlier memories as his student which, looking back, were particularly formative for me..
It was common in the 1950’s and 1960’s for boys to be called by their surname so I was taken aback when Peter immediately addressed me as ‘Mike’ and invited me to call him ‘Peter’. It was also a surprise that he always greeted me (and my fellow tutees) warmly when we met going about Queen’s. But for all this familiarity he had high expectations of his students and spared no effort in his encouragement.
In my first long vacation he got all of us to write an essay on a topic chosen from a list of mathematical topics well beyond the standard curriculum. I remember one of these was ‘The art of M. C. Escher’ but the one I chose was on Hilbert’s problems. Peter gave me the background. David Hilbert, in a famous address to the 1900 International Congress of Mathematicians, had proposed 24 problems that, in his opinion, were the greatest mathematical challenges of the day. Some of these had been solved, some had faded into oblivion, and some were open. My essay was supposed to summarise the present status of these problems. Peter appreciated that my mathematical knowledge would be inadequate to even understand some of these problems and offered help on request. I did indeed require help and the Oxford-Leeds correspondence that ensued gave me my first insights into the research mathematical literature and such tools as Mathematical Reviews. It also impressed on me how widely knowledgable Peter was.
I became increasingly aware of the formative role that Peter’s parents, Bernhard and Hanna, had played in Peter’s early life. He once told me, as a very young child, he had watched Bernhard prepare breakfast for the family, counting out the slices of toast in the mysterious sequence 1, 4, 9, 16, 25, …. He realised eventually that the rule must be that the differences increased as 3, 5, 7, 9, …. and was delighted when Bernhard revealed the sequence of squares rule.
While his parents were obviously key influences in Peter’s early mathematical life he became an independent mathematical thinker well before I met him, publishing his first single-authored paper while still an undergraduate. However he never forgot his debt to his parents and always spoke fondly of them. In 1969 he dedicated his splendid paper on BFC groups ‘to my father on his 60th birthday, with love’.
By the time I became his graduate student Peter had become the most versatile of a generation of young Oxford researchers in algebra. But he never talked down to his students or his colleagues and was willing to engage with them almost on demand. I remember in about 1969, when I had learnt the rudiments of the theory of group characters, hyperbolically proclaiming to him that this must be the neatest little topic in the whole of mathematics. I had some reason to hope that he might agree with this proposition since I had heard him lecture on William Burnside, one of the originators of character theory. It would have been easy for Peter to prick this pompous little bubble but, after some some careful thought, he offered an alternative opinion that the theory of complex variables was even neater. Since this theory is not even part of algebra it made me realise that taking an interest in areas outside my own would be a good habit to cultivate and that has stood me in good stead ever since.
I knew Peter in another role too. He and I were both members of the University folk-dancing society. Peter’s contribution to the dancing was in providing music on his violin. I do not know very much about Peter’s other musical activities but he was a superb asset to our folk-dancing many times being the only accompanist and (so it seemed) effortlessly sight-reading whatever we asked of him. Dancing and directing dancing has been an occasional activity of mine throughout my life and, on those occasions, I always think of Peter. His face would display a mixture of concentration and enjoyment, a combination which accompanied also so many of his mathematical activities.
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