Perhaps several sources, but most notably Wikipedia, list the open question of whether Beggar-my-neighbor (a game introduced to me in the UK as "Draw the Well Dry") terminates as an example of John Conway's "anti-Hilbert problems", but nowhere seems to have a list or even a single example of these other problems. Wikipedia's citation also only refers to this problem, speaking of the full list as having been suggested "about 40 years ago" (in 2002). A slightly older mention is in an article from 1999 (https://www.jstor.org/stable/2589054), which quotes Conway also only mentioning this problem (and not even citing the source), but I cannot find what it could have possibly originally appeared in, and I even skimmed through Conway's publications of around that time period and didn't uncover anything. It occurs to me that it's possible that it was never published, and that this was simply something referenced among friends (which Guy and Conway were), but I am very interested in the rest of this list. Can anyone provide me with the list or at the very least a more specific pointer of what to search for in Conway's work? He was very prolific so I did not conduct an exhaustive search, and I would not be surprised if it is relatively accessible but I overlooked it.
2026-04-03 09:28:13.1775208493
Full list of Conway's anti-Hilbert questions?
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I heard Conway specifically identify the thrackle problem as one of these.
This was sometime in the 1990s, at a post-talk tea or something like that. He offered a cash prize for solving the thrackle problem, because he had been thinking about it since he was a child.
And he said that, as Hilbert had given an address in 1901 on the problems that mathematicians should be working on in the coming century, he wanted to give an address in 2001 on the problems that mathematicians should not be working on in the coming century, and the thrackle problem would be one of the problems he would discuss.
I don't remember him mentioning any other examples, and I don't remember him mentioning Beggar-my-neighbor.
Sometime after 2001 I dropped by his office at Princeton to find out whether he had actually given the talk (he had not) and to ask what other problems he had planned to talk about. I think he didn't give me any more examples. It seemed like something he had forgotten about, but maybe he just wanted me to go away.
Sorry I couldn't be more help, but at least you now have another example, and you know you are not alone in wondering about this.