A couple of years ago I got interested in an old paper of his, "Continuous Functions Defined on Spheres", where he proves that for any continuous function defin

A couple of years ago I got interested in an old paper of his, "Continuous Functions Defined on Spheres", where he proves that for any continuous function defined on the sphere, there are four points forming an equatorial square (ie four points equally spaced along some great circle) on which the function takes equal values. Interestingly, this theorem can be used to prove the Wobbly Table theorem, that any square table can be rotated on a (possibly bumpy) floor so that all four legs touch the ground simultaneously. I found the theorem interesting, and it has the flavor of the Borsuk-Ulam Theorem (commonly explained as "there are always a pair of antipodal points on the Earth that have the same temperature and pressure"), but it bugged me that the proof was not at all similar to the standard proofs of the Borsuk-Ulam Theorem. So I found my own proof of Dyson's theorem, in the spirit of the Borsuk-Ulam Theorem. Wrote it up but didn't publish traditionally — it's at https://haggainuchi.com/wobblytable2.html https://haggainuchi.com/wobblytable2.html — but it never occurred to me to send it to Dyson or that he might be interested. Too late now, sadly.