Assuming, of course, that SAT isn’t [symbol]w/symbol. And there are problems which do have that property–that’s a basic result taught in introductory graduate classes, so you’re no doubt familiar with it.
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Ah. This is what I thought might be a disconnect. You’re talking about the math department vs. the CS department, and we’re talking about the discipline of math vs. the discipline of CS.
Now, I won’t deny that math and computer science are separate fields. Anyone can see that. But what I claim is that the theory of computability is a mathematical theory, and as such, it is a branch of mathematics. It deals with computations, so it is also a branch of computer science. Do you disagree with that?
And one of the millennial problems is a physics problem. Why has no one come to correct that?
Whoever solves it will, in my view, be acting as a mathematician, no matter what their actual job is. For the reasons ftg mentions, it will probably be a computer scientist.