Surely something like $f_A(A)=0$ trumps that visually.

Have you looked at the other questions with the career tag? There's at least three on that tag's front page which seem germane.

Very nice answer!

Funny, I don't think this was a duplicate at all. There are many bizarre/amazing properties of 2 which do not relate (at least immediately) to 2 being the characteristic of a field, which is what Qiaochu's question addressed.

Added more description to the title.

Sorry, giving a downvote. I think projects like these on MO need to be extremely well thought out, and contain significant mathematical content and motivation.

Great, I'll take a look. Thanks for the references.

Incidentally, the chapter also mentions the distinction between $\mathbb{R}((x,y))$ and the fraction field of $\mathbb{R}[[x,y]]$, as in Pete's excellent response in the "fallacies" thread. Here an important distinction arises -- the former field is Pythagorean, and the latter field is formally real but not Pythagorean. Interesting!

I looked through the chapter -- very interesting, but I don't think it addresses the question at hand. The unique reference to "ring of integers" is to $\mathbb{Z}$ itself.

Nope, definitely not. I debated on that tag...pretty sure I've seen some authors refer to infinite (algebraic) extensions still as number fields, but this is probably less standard. No opposition if someone feels strongly that it should be deleted.

"Fermat's First Theorem"? Roughly as historically accurate as "Fermat's Last Theorem"...

Kind of like a wiki hatchery, but on land.