I was thinking, for example of ergodic theory, as it appears to different kinds of views. The molecules in the air in my room are not all going to rush into one corner (physics), but in mathematical terms they might, and indeed are expected to for some tiny proportion of "all time". In units of a billion years, it's probably not something for me to worry about.

How serious would it be, if the idea that Goldbach is unprovable in normal mathematics gained currency? That would mean it is true, as has been said, so that it could be a new axiom. In other words number theorists could go on proving conditional results, but call them something else (results of plus-mathematics, say). This wouldn't be so interesting, because the axiom isn't ambitious, and the conditional results presumably wouldn't be very numerous. It would be better to select a very general form of conjecture on primes, such as the Bateman-Horn conjecture. And hope for a plus-contradiction!

The factor of the "group determinant" have degree equal to the degrees of the irreducible representations of the group over a given field. So the linear factors are in number at most the order of the group abelianised.

Theorem E there does seem to say something interesting about the "equilateral locus" in T, when each circle overlaps another. Then there is a simple closed boundary curve, made up of arcs, and in the "Venn diagram" configuration there will be inscribed equilateral triangles in most places. For small arcs (< 2\pi /3) those have vertices on at least two circles.

Strange to ignore totally the area of cryptography. The emphasis is obviously on "scientific computing".