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If and when most of the heavy lifting in the field of doing proofs will be done by computers, I suspect a new definition of proof will emerge not too far from what you're saying.

Rene Descartes or Isaac Newton would throw a fit if they could see this.

That is correct as long as you don't hit the corner cases.

How do you know you can rely on it tho'? Blind faith?

I am stockpiling industrial amounts of popcorn for the (not too distant) future debates around the question: should we take into account the inherently limited capabilities of the human mind when defining the concept of "proof"?

To be sure, myself I am very much a classicist of the old school when it comes to such matters. But this is a brave new world we are slowly but surely moving into.