The mathematician John Horton Conway died just over a week ago. (I recommend Siobhan Roberts's biography Genius at Play.) I' intend to write a post later about what his book On Numbers and Games meant to me, but in this post I will share a couple of memories of Conway. I emphasise - these are memories and their accuracy is not guaranteed.
First,a personal story of how I was caught out by his exam question. When I studied Part III of the Mathematical Tripos at Cambridge I took Conway's course on Sporadic Simple Groups (this at a time when the Classification of the Finite Simple Groups was not complete and indeed before it had been proved that the Monster group actually existed). In the exam we had to do any three questions out of six (or similar). The last question was something like "Write an essay on anything in the course you haven't covered in your previous answers." Now, I had three good topics I knew pretty well, and they all came up in other questions. So I thought to myself, "Well, I'll do the essay question first, while I think about which two of the other three questions to do." As a result I wrote the essay on my fourth-best topic, and didn't use in the exam one of my three strongest topics. Not good exam technique! (To be honest, I feel that's why it wasn't a very fair question to set in an exam!) I have sometimes wondered: if I had answered that question first, and written about my best topic, and then afterwards answered the question on that topic, since that wouldn't have been a previous answer, could I have got credit for the same material twice?)
My other memories are of an email mailing list for those interested in the history of mathematics, which ran for some years from the late 1990s before splitting and dissolving in acrimony as these things tended to do at the time. Anyone could discuss or ask any questions, and Conway was one of the regulars.
One one occasion two schoolboys posted an email saying they were in primary school and they wanted to know more about some mathematical topic. Conway sent a lovely long reply, at an appropriate mathematical level, saying probably how nice it was to hear from such enthusiastic students. The boys sent a thank-you letter, adding at the end that they weren't actually at all interested in mathematics, but their teacher had told them to ask a question.
On another occasion a university student (I think a PhD student) asked about a result of Lagrange (I think), noting that there were several proofs of the result and asking if anyone knew which was Lagrange's original proof. Conway wrote a long reply, saying that he didn't know, and going on to explain why he didn't think it mattered: there were several simple proofs and it would have been a matter of chance which one Lagrange came up with first, since the proof of the theorem was trivial. Immediately someone jumped in, accusing Conway of appalling rudeness in describing the question as "trivial" (he hadn't) and suggesting that such treatment from an established mathematician would likely deter the student from further mathematical studies. Others argued about this (not all members of the list were native English speakers and the word "trivial" did seem to have very negative connotations for some: which surprised me as I was very familiar with its use in this mathematical context and didn't think it at all offensive). Conway said he hadn't intended to be rude or to suggest the question was trivial - indeed, by writing a long and detailed answer, he had shown his respect for the questioner - and he apologised profusely. But the criticism continued until the student who had asked the original question replied. He said that far from feeling upset by Conway's response, not only did he not interpret it as critical, but he was absolutely thrilled that the great Conway himself had replied to his question: he had been walking on air ever since!
I admired Conway's willingness to engage with anybody on that mailing list, regardless of their age or experience. I hope I have learned from that.
Sorry for your loss.
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