> Some years ago I suggested it might be interesting to have a kind of blockchain of formally verifiable mathematical proofs,

How does a blockchain help here?

> but was quickly shutdown by people telling me it was a useless endeavor due to Goedels incompleteness theorems.

I'm curious about those arguments ... what does incompleteness have to do with this?

> But I think the method of proving things will soon go out style as an endeavor to devote perhaps years of your life to.

I'm not in that camp. With the new tools available, it might change how this endeavor exactly works, but there will always be claims at the edge of our understanding for which we seek explanations and proofs are just that. The ones that can be easily and autonomously discovered by a machine will not be subject to human attention for that purpose, but there will still be a frontier that needs (and will get) attention.

Mind you that not all math activity happens at that frontier. Generations of aspirarional young math fans have re-proven countless foundational results just for fun, because it's a satisfying and eye-opening activity, and that's how you learn. That will not change fundamentally even though maybe the tools they use will.

It's also not new that the setting for frontier research changes. Not too many generations ago, proofs were written with literal pen on paper and communicated by letter to dear math colleagues in distant countries. That's very different today, but has not killed math as a profession. To the contrary. There are far more mathematicians today than there were 300 years ago.