I recommend Terrence Tao's commentary on such a proof : https://mathstodon.xyz/@tao/117219101339291693
Key quote : "Solving the problem by purely AI-powered methods [would be a] net negative for the progress of mathematics."
I recommend Terrence Tao's commentary on such a proof : https://mathstodon.xyz/@tao/117219101339291693
Key quote : "Solving the problem by purely AI-powered methods [would be a] net negative for the progress of mathematics."
The for-case for this type of method is that this is economies of scale for mathematics.
We are basically mass manufacturing math. Just like you have just 100 designers for a product selling millions of units, you will now need 100 mathematicians to make millions of advancement. Yes you have factory workers, but if we are being realistic they have negative leverage in the world and the analogue of that is not something most of today's mathematicians would want to do. They would want to be in the 100.
Like Tao says, each advancement is now significantly less useful since it yields fewer usable objects. However, we will get many many advancements. Is the tower made with many worse bricks better or worse than the tower made with a few amazing bricks? Depends on the tower. And time will tell.
For some fields of math and some of it's usecases, economies of scale will be positive ROI overall. In others it won't. But we will know which is which only after it's been fully scaled up, which will take 10-15y in my estimate.
Some feel that in the majority of usecases it is negative ROI, some feel the other way, but that opinion is for practicing mathematicians like Tao to hold. Also, some opinions on either side are held in the context of a particular field or practice, and should not be interpreted generally.