Coxeter Once Nerd Sniped Conway

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Conway was once "Nerd-Sniped" by Coxeter ...

I wrote earlier about John Conway's passing and some of my memories of him: See Remembering Conway

If you don't know what "nerd-sniping" is then you can read on to get a particular example, or you can visit the XKCD page to learn about it, and then come back here:
I also mentioned there how he was once nerd-sniped by Coxeter. John didn't call it "nerd sniping" - he didn't know the term - but when I explained it, he was delighted, as it exactly matched his experience.

So here is the story, as told to me by Conway at MathFest, 2015 ...

Coxeter gave a seminar - he had a proof of a theorem, but it covered all the cases separately, and he was interested in having a more general proof that proved all the cases in some sort of over-arching theory.

Later that day, Conway was crossing the road when he realised how to make the proof work. He stopped in his tracks, and got hit by a garbage truck! He wasn't badly injured, but limped back to the department to share his result.

Much later Conway had the opportunity to announce to everyone that Coxeter had tried to murder him, at which Coxeter looked rather alarmed. As the story progressed, though, he realised where it was going and relaxed somewhat.

So that's the story as told to me in person. Later, when I talked about this a little, I wondered how accurate my memory was. But a little noodling around on the interwebs, and here it is. Quoting from "Candid Science V: Conversations with Famous Scientists" by Balazs Hargittai, Istv n Hargittai, the same story, with a little more detail.

Coxeter is my hero. I remember a story at one of the conferences in Coxeter's honor and people were telling how this wonderful man had turned them into mathematicians. I thought I must say something different. So when I got up, I said, "Lots of people have come here to thank Coxeter; I've come here to forgive him." I told them that Coxeter once very nearly succeeded in murdering me. His murder weapon was something that even Agatha Christie would never have thought of: a mathematical problem. Then I told the story, which is actually true.

Coxeter came to Cambridge and gave a lecture. Then he had this problem for which he gave proofs for selected examples, and he asked for a unified proof. I left the lecture room thinking. As I was walking through Cambridge, suddenly the idea hit me, but it hit me while I was in the middle of the road. When the idea hit me I stopped and a large truck ran into me and bruised me considerably and the man considerably swore at me. So I pretended that Coxeter had calculated the difficulty of this problem so precisely that he knew that I would get the solution just in the middle of the road. In fact I limped back after the accident to the meeting. Coxeter was still there, and I said, "You nearly killed me." Then I told him the solution. It eventually became a joint paper. Ever since, I've called that theorem "the murder weapon". One consequence of it is that in a group if $a^2 = b^3 = c^5 = (abc)^{-1},$ then $c^{610} = 1.$

So the details differ slightly, but it was a treat to be told it by Conway in person.

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