Perhaps reading https://www.math.toronto.edu/mccann/199/thurston.pdf will help.

The point of mathematics is not to prove results. It is to build conceptual thinking about mathematics. Important problems are important because in order to solve them we have to build concepts tying different things together.

We're not searching for answers. We're searching for insights. Trying to understand the problem causes us to draw the connections and find those insights.

AI gives us answers. But it doesn't help us build those insights. AI has a complete mastery of existing human insights. But doesn't build new ones from its own experience. In a real way, it does not find the opportunity to really learn.

So it tackles problems and either solves them or not. If solved, we now have an answer. If not, it's too hard for humans.

Not a mathematician.

The issue I see with a handed-over proof is tunnel-vision: you explore only the understanding of the proof.

Without a proof, your exploration branches out much further, in directions that could seem fruitless, but may uncover new understandings that are now "hidden" because the handed-over proof drastically lowered the incentives to find them.

I think you're misunderstanding the point of math problems. Mathematics is as much a process as it is a result. This is why even from early on, relatively rudimentary mathematics questions you are graded by your capacity to correctly achieve the desired process to the answer than getting the answer correct. The risk here is that AI generated proofs removes the process part of mathematics, where actually interesting concepts live (because then you can apply novel concepts to other unsolved problems and then thereby unlock new concepts that way...) Sure you can kind of try to reverse-engineer it but you lose the entire intuition and "we tried applying it in X, Y, Z ways and it didn't work" intuition, because even the non-working process can teach you about how not to apply the working process to novel problem spaces.

Basically: Tasting a delicious soup doesn't tell you how to layer the flavors, but if you want to be a good chef, you better be learning flavors more than you learn dishes!

- If you have only a fuzzy idea of how to get to your travel destination, wrong turns and alternate routes may reveal sights and places you'd never have encountered without that wandering.

- If your GPS directs you straight to your travel destination, you are now where you wanted to be but missed out on the exploration. This is the sort of consequences the AI math proofs have.

STEM research thrives on that side exploration and unearthing unexpected things along the way. James Burke's famous documentary Connections spends the middle episodes talking about the unexpected directions that exploration has taken science. It's very hard to credibly make the case that this sort of meandering exploration is not valuable.

He's saying that in such a scenario, almost all of the value is located in the analysis and just dumping the proof has "negligible or even negative value". (The negative value would occur in the cases where the proof doesn't contain enough information to reconstruct what insights would have led a person to it.)