Well, I only know how to define computability in terms of Turing machines.
For math I don't have a fix definition, but it's surely a bit more specific than that (e.g. I wouldn't consider the computation that prints a 0 at the same place for infinity math) - but of course I do see the circularity in my argument: a Turing machine is a mathematical object in and of itself. Though being able to talk about something doesn't necessarily change which is "bigger".
As for the other direction, this gets a bit more into the philosophy behind math itself. Constructive math's territory is "easy" - but I am on the opinion that if humans (or any intelligent physical entity) are at most Turing-complete [1], then any non-constructive math "steps" or thoughts must also be at most computable. Well, unfortunately I can't prove whether math done by transcendent entities are also computable, though.
In any case, I am no mathematician, so whatever I think regarding this topic may not have much relevance to anyone, only done CS course with quite a bit of math, but that's obviously not the same.
[1] I believe religion is an escape hatch here from an argument perspective
For math I don't have a fix definition, but it's surely a bit more specific than that (e.g. I wouldn't consider the computation that prints a 0 at the same place for infinity math) - but of course I do see the circularity in my argument: a Turing machine is a mathematical object in and of itself. Though being able to talk about something doesn't necessarily change which is "bigger".
As for the other direction, this gets a bit more into the philosophy behind math itself. Constructive math's territory is "easy" - but I am on the opinion that if humans (or any intelligent physical entity) are at most Turing-complete [1], then any non-constructive math "steps" or thoughts must also be at most computable. Well, unfortunately I can't prove whether math done by transcendent entities are also computable, though.
In any case, I am no mathematician, so whatever I think regarding this topic may not have much relevance to anyone, only done CS course with quite a bit of math, but that's obviously not the same.
[1] I believe religion is an escape hatch here from an argument perspective