Apologies, I didn't mean to make that implication. I was referring to the history of the original computability paper. There was an era in math where we believed it may be possible to determine the rest of mathematics via algorithm, that the game was up. Turing showed that this was not possible, and in doing so invented the general purpose computer.

Computers may be able to keep up, but the title was invoking "magic algorithm" suggestions to me. At the moment it may be unclear, but you are correct that it appears that computation can mimic the brain. For computers to be used as more than just tools in humans exploration of mathematics, to "redefine the rules" I think it would have to look quite different than the computers we have today.