Aren’t there dozens of proofs of the Pythagorean theorem? The goal isn’t to just “prove” but create something well written and intuitive to the average practitioner. And by gaining a deeper understanding we can ask better questions.

Something that often comes out is "it is about the journey, not the destination".

Many math problems are practically useless if you only care about the answer, the millennium prize about the Navier-Stokes equation is such a problem. The solution makes no physical sense, real life fluids don't follow the Navier-Stokes equations in such extreme conditions. But in the process of finding the solution, we may get insight into what will end up being really useful. The big mess that OpenAI produced is the solution no one really cared about, but it didn't deliver much of what people actually wanted.

One reason it is sometimes seen negatively despite being at least something is that it broke the incentive. Without the million dollar prize and with only the privilege of being second, people are much less likely to go for the insightful solution.

But up until now, the mathematics community has valued the "prove" part much more highly than the "deliver an insight" part. Mostly because with a little work they went hand in hand.

And going from zero proofs to one proof (even a sloppy one) is a big deal regardless of whether it was written by AI or a human.

You are wrong if you consider academic incentives, funding, human nature(reproduction/survival) and capitalism.

It would be fantastic if university and science was like "here is 100M$, play around and develop some 'understanding'". However the reality is that human societies are hierarchical and currently capitalistic which implies value creation and status building.

1) the funding bodies/agencies need proof of value that you're using the resources meaningfully to be able to assign resources

2) Humans are status seeking, power seeking, resource seeking and sexual reproduction seeking. If you hold a lot of power and make decisions, you have more of all of the above.

No, haven’t you heard? Since the AI bubble began we’ve collectively decided that outcomes are all that matter. /s