True, but that's not what's going on here. One can define 0! by extending the rule n!=n*(n-1)! with n=1, or by computing that \Gamma(1) in its integral form is indeed 1. And it's only very mildly a convention that we choose \Gamma as the interpolating function for the factorial function.

I think the people who ascribe to this formula excessive mystery might not find matrix exponentials particularly less mysterious.

Both of Mariano's references are good. Also, there's plenty of lectures notes and unofficial write-ups of this material all over the web. For example, try googling "mcgill seminar on cohomology" (no quotes).

Ah. Then my comment is particularly ironic. :)

This would be a fairly significant result. I think it's safe to say that if a proof of either is found, this will become public knowledge rather quickly and trickle down to the Wikipedia page (regardless of the $100 payout).

Yes. Of particular interest is Maire's paper "On Infinite Unramified Extensions", in which he explicitly constructs infinite unramified extensions over fields with trivial (or near-trivial) Hilbert class field. Such extensions are necessarily nonb-abelian.

Interesting -- I had not seen the trivial Massey product calculation via $d(f^3)$. My interests in this problem as well lie in the construction of certain Massey products, hence the focus on explicit cohains from cup products. Am I right in understanding that the hierarchy of products you mention all involve operations beyond cup products?

There's a difference?

I can't help but wonder what makes a person non-commutative. Were you born like that?