Sad news indeed
Conway was my supervisor at Sidney Sussex, Cambridge, 1968-70.
I can still clearly recall our first supervision (there were, IIRC, three students) in his rooms in college. An incredible mess of stick-and-string models of polyhedra and other things.
"You know those dolls, that always stand upright no matter how you knock them down, I think they're called Kelly dolls?" he said.
"Yeeees" we replied.
"Well, I have discovered a polyhedron made from uniformly dense material that has the same property: it will always come to rest on the same surface. I'd like you to work out its shape by next time".
I think that was probably when I realised that I was unlikely to become a professional mathematician.
A few weeks later I was walking down Sidney Street when this extremely hirsute chap (long hair and beard) coming the other way smiled and waved at me. I did the same and only after he'd passed did I realise that it was not a fellow student but one of my teachers...
I think the date of 1970 for the Game of Life is not quite accurate; 1970 was the year I dropped out of Cambridge, but I can recall sitting in his office in the Maths Faculty building while he told me about it and that "apparently a million dollars of computer time was wasted last year in the USA playing it".
He also showed me the printout of the multiplication table of his group, which was arrayed around all four walls of the office. Given that I knew that the order of the group was something massive, like 4.8x10**18, I must have looked a little dubious.
"Oh, each symbol represents a hundred-square matrix". Well, obviously.
A fellow Sidney student the year above me told me that he'd had a supervision with JC in the afternoon after he'd discovered the group in the morning. He couldn't talk about anything else and they hardly saw him for the next term, as he was gadding about round the world lecturing on the group.
I'm afraid I never found him a good teacher (although, for various reasons, at this point in my life I was hardly a good student), mainly because he could never seem to understand that you found anything difficult .
"Just think of a determinant as a volume transform of two vector spaces." Right...
Fast forward thirty or so years and I arrive home around midnight one Saturday evening after rehearsing with my band. Flicking TV channels with the remote I came upon a PBS showing of the documentary on Andrew Wiles' proving Fermat's "Last" theorem.
"Hang on!" I think, "isn't that John Conway?"
And so it proved, cutting to the chase as ever. The question arose as to whether Wiles's proof was the same as Fermat's. Wiles himself, IIRC, said no, his proof was based upon a lot of 20th century mathematics and could not have been constructed in the 17th.
Conway: "Fermat said he couldn't fit his proof into the margin of this book [holds book up]. Andrew's is 250 pages long. It's NOT the same proof".
I still maintain that JC was the only bona-fide genius I have ever known, however briefly and tangentially.