I was once at a superstar’s talk and I was perhaps fed up with such nonsense and declared, “you proved my conjecture that Math is whatever the NSF Funds.”

]]>I am not sure if I told you this story. (At my age I forget whom I have told stories to). When I taught maths and philosophy students in Oxford, I liked to give them a mild shock by asking them to discuss the proposition that a proof is anything you can get past a referee. (I think Marshall McLuhan may have said “Art is anything you can get away with”.)

]]>I remember a story from twitter that they found a bug in one of the two major proof checkers (won’t say which) and as a consequence, got it to “prove” 1=2. It was resolved, but, one wonders…

But I once remember a conversation we had — I was probably exasperated that to me my “correct proof” of an inequality had a couple points knocked of — where I claimed proof is social construct, and you said, I paraphrase, Yes and No, in the sense that if people cared then the truth of the matter would eventually be discovered.

In any case, we agree. For a computer, Yes is easy. No is hard. And 0 is the hardest. There’s a talk on YouTube by Rich Schwartz at IAS on paper mobius band conjecture, and at the end, Sarnak gives some comments on the matter where he gives illuminating examples. (Producing an L function with a triple zero. Sphere packing in E8 and Leech Lattice.)

]]>He didn’t give specific examples, so I can’t pass them on.

I am a great believer in running the program twice on different machines, as a protection against hardware or operating system errors. But this is no safeguard against bugs in the program. The best defence there is for someone else to start again from scratch and write another program.

In the slides by Curtis Bright he talks about the non-existence of the plane of order 10 by Clement Lam and his team. As I understand it, they checked all the records very carefully and found a couple of hardware errors. Moreover, the result has now been checked. So it is probably right. But as in all these things, easy to check a positive result, much harder if (as in Clement Lam’s case) the computers run for two years and just say “No”. Hence the work going in to make the program output some reason for the contradiction in each case that can be independently checked.

But I don’t have to tell you all this…

]]>Perhaps the most naive solution is to observe anything worth doing is worth doing twice. So if GI gave you true, apply the permutation to the adjacency and subtract. But if GI gave you false… though I cannot imagine nauty ever being wrong. 🙂

]]>My PhD supervisor had a whole row of A4-size hardback notebooks in which he kept detailed notes of every lecture he attended. I was never so organised, so a searchable electronic version is much better for me. I used to keep notebooks, but they would go missing.

I have thought for some time that what the world really needs is a version of grep that works on paper documents in an office.

]]>And Coastguard, who had a thing called a scoop which was essential for the rescue.

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