Been discussing this with a pal.

Me: “Either the Basis Theorem or the Nullstellensatz ought to be in there

– I’d have put both. It’s disgraceful to leave Hilbert out of ANY list of mathematical achievements.

“‘Sylow’s Theorem’? Which one?

“If Brouwer’s fixed point theorem (known affectionately to my generation of undergrads as the Cat’s A**hole Theorem, viz.: ‘Every cat has an a**hole’) makes the cut, why not Hopf’s more general form?

“And the Fundamental Theorem of Algebra is, as any algebraist could have told them, neither fundamental, not a theorem, nor much to do with algebra.

It merely states a property of the complex number system.”

He: “Yeah, although the ‘fundamental theorem’ one at least has some justification in that it’s used by most anything past 8th grade arithmetic.

I’d have put Goedel higher, with Cantor’s denumerability, Cohen’s nondecidability, Turing undeciability(s), and the noncomputability of Diophantine equations in there. — Or maybe mashed them all together by putting Greg Chaitin’s algorithmic information theory unification in.

“I’d also probably put the Central Limit Theorem up higher, just because of the number of times I’ve had otherwise educated people simply refuse to believe it. (My old chemistry professor girlfriend, for one. She was doing lengthy experiments that produced a result that was easily predicted using the Central Limit Theorem, but when I explained it to her she’d not only never heard of it, but didn’t believe it could apply…)”

[Me again] I just noticed they missed the Jordan Curve Theorem, which I would have put in. Picard’s Theorem, too… no, this won’t do.