
Peter M. Neumann (19402020) (Photo by Bert Seghers, Wikimedia Commons, Public Domain) 
A very sad post  the mathematician Peter M. Neumann died on Friday 18 December of Covid19/ Peter was my moral tutor when I was a postgraduate student at The Queen's College, Oxford, and like many others I was enormously influenced by him. I was very lucky as a student to have wonderful support from several great mathematicians  Ray Lickorish and Michael VaughanLee in particular  but I feel myself especially privileged to have known Peter. Indeed, in many ways I consciously tried to model myself on him, and the best things I have done in my career in teaching owe much to Peter.
In this post I'm going to share some rather rambling and inconsequential memories of him (with the warning that my memory is fallible).
I first met him when I went for interview at Queen's  which turned out to be a conversation in the Fellow's Garden with Peter and Graham Higman. I had been reading my notes from my course on Combinatorial Group Theory on the train journey, which was probably a mistake because I confused myself and attributed to Higman what was actually the BaumslagSolitar Group. Peter questioned it and my heart sank as I realised my blunder, but before I could say anything Higman jumped in to say that in fact that group had been his original idea and Baumslag and Solitar acknowledged him in their paper.
Anyway, despite such blunders, I was accepted. I was very impressed that, when I turned up at Oxford six months later and knocked on Peter's door, he remembered who I was. But then when I introduced myself to my officemates in the Mathematical Institute the next day, one of them said, 'Yes, I know your name. When I knocked on Peter Neumann's door last week, he said, "Hello, you're Tony Mann, aren't you?"' So perhaps Peter's strategy was to guess one of the names of the new DPhil students so that he would be right at least once!
I attended Peter's famous Kinderseminar  a Wednesday morning gathering of doctoral students and visiting professors in Peter's rooms, with coffee and friendly conversation before a presentation on someone's research. I remember my first presentation. It was dreadful. (To be fair to myself, I had never given a presentation before  it wasn't part of the Cambridge mathematics curriculum  and so my experience of mathematics talks consisted entirely lectures which were primarily dictation of notes and research seminars which were generally over my head.) Knowing the expertise of the three visiting professors, I naively assumed they knew everything there was to know about my research topic, so I cased through the background material to avoid boring them. After five minutes of rushed, garbled talking, I looked at the audience and realised that none of them had followed at all. If I were in that position now, I would stop and restart the presentation at a sensible pace, but at the time I panicked and continued with the presentation for another hour, completely wasting everyone's time. When Peter gave feedback, he began by saying "That was terrible, wasn't it" (I guess it's to my credit that I was already aware of that) and, although that's all I remember of his feedback, it must have been very generous because I felt encouraged rather than dismayed.
I also remember that Peter particularly disliked the works of C.P.Snow, a favourite writer of my father's whose novels I had also liked. I recall Peter saying that good novelists "show" and leave readers to form their own judgments while bad ones like Snow tell the reader what they should think. (While there is a lot in this, I don't entirely agree with Peter: there are different but valid ways of storytelling.) Years later I discovered that Peter's antipathy to Snow may have been due to his strong feelings about Snow's introduction to G.H. Hardy's A Mathematician's Apology: a muchpraised account of Hardy which Peter felt misrepresented the great man by exaggerating his supposed unhappiness.
Peter himself should have written much more  but he always said "There are already too many books". While this is true, more books by Peter would have benefitted us all.
Other old memories of Peter  when he sent one a message it was always on an interesting picture postcard rather than just a scrap of paper. This is something I copied, building up a stock of postcards to use when I had to write a short note to somebody (and I have retained my postcardbuying habit even though electronic communication means I never send anybody any notes any more!)
I remember going to a barbecue at Peter's house at which several of us we watched the EnglandArgentina World Cup match, and regretting my enthusiastic response to Maradona's wonder goal when others were upset that it put England out of the tournament.
Peter had a cautionary tale for those of us who have to write many of references for students. A prospective student applied to Queen's and his teacher's reference said, "Without a doubt this student is by far the best mathematician this school has ever produced." Since the school in question was Peter's own school, this reference did not have the positive effect the teacher intended!
I remember Peter's stories about his house number  403. He used to go into schools to talk about maths and he would refer to prime numbers "like, 2, 3, 5 or 403, for example". Only once, a hand immediately went up in the audience, "But, sir, 403 isn't prime, it's 13 times 31". Peter told how, when the house was built, he went to the Post Office to be allotted a number for it, and was told, "There are no numbers left  you'll have to give it a name instead." After offering to find some more numbers for them, he and Sylvia called the house "Burnside" after the great mathematician. I remember him saying that he had thought of calling the house "Burnside Hall" after his two favourite mathematicians.
I was privileged to work with Peter on a couple of book projects: it was a joy particularly to collaborate with him and Julia Tompson (I was very much the junior partner) in producing Burnside's Collected Papers. One of Peter's qualities was that he had very high standards and I feel that his book reviews could be rather ruthless. So it was a rather good move on my part that both books I have edited involved working with Peter so he wouldn't be able to review either of them!
I was lucky enough to attend the conference celebrating Peter's 60th birthday, twenty years ago next month. Peter's birthday was at the end of December and so the birthday took place at the beginning of January 2001  giving Peter the possibly unique achievement that his 60th birthday was marked by a conference in a different millennium from the event it was celebrating!
I owe so much to Peter  and so do many many others. His contribution to mathematics goes far beyond his own mathematical discoveries, significant though these are, He taught, inspired and encouraged so many others, and was much loved as well as much admired.