Comment by eric-hu

It depends on the kind of mathematician. Can you use a computer to demonstrate Russel's paradox? Clipped from Wikipedia:

> Let us call a set "abnormal" if it is a member of itself, and "normal" otherwise.

> Now we consider the set of all normal sets, R. Determining whether R is normal or abnormal is impossible: If R were a normal set, it would be contained in the set of normal sets (itself), and therefore be abnormal; and if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.

Russel's paradox "broke" set theory. In the century since he discovered it, category theory was introduced as a mathematical way to capture groupings in a way that set theory failed to do.

I don't see how computers can assist in this kind of mathematical research. I do believe there's lots of research of this kind too, pushing the limits of our current mathematical structures.