The most important part of math is advancing human understanding. A correct answer by itself is not as important as understanding why it is correct.

Probably one of the funniest things to read on a site like this, when you consider that eg. Boolean algebra was entirely abstract and had little practical purpose for almost 100 years until Shannon picked it up for use in circuits

For most engineers a mathemetician is a machine for producing correct algorithms, like a chef is a machine for producing tasty food. In both cases that overlooks the human element, but that's a critical skill for a limited mind with finite resources to grok infinite complexity. You can read that as permission to be an asshole or a neccesary compromise.

No, it's not the most important part. It can be argued that most important part is asking the right questions

> The authors warn the consequences are already becoming visible. AI-generated papers could overwhelm peer-review systems with low-quality work …

It seems like a key problem here is that peer-review is expected but not explicitly funded/rewarded while it is probably one of the aspects where humans still add a lot of value. Academia’s incentives are hugely misaligned (… as usual unfortunately).

The wording in the declaration may be a bit romanticized. But the points are valid:

Is an 80 year old unsolved problem maybe unsolved because it was never prioritized? Some problems stay unsolved because few people consider them worth working on.

Who is going to validate the results? Or do we skip that, with the risk of flooding the literature and collective understanding with unverified proofs?

This reminded me of my 11 yr old who, when I give her math problems to solve, is too focused on “getting the right answer”. I’ve told her plainly, I don’t care if you get the right answer right now, I want to see your reasoning. She has yet to understand this.

Even from the most purely instrumental perspective, what we care about is our ability to make use of correct answers, which is quite distinct from the possession of correct answers.

There are many theorems that aren't directly interesting, but whose proof requires techniques that are of substantial further interest, that lead to new domains, and/or new practical applications. Simply being handed a proof for those theorems isn't enough--we require the ability to apply those techniques in the real world, or discover further areas of mathematical research that build on that proof or its techniques.

It may be that AI can build on its own work for the long-term, but so far, AI does best at exploration in areas that have precisely specified and measurable goals. Actually creating understanding, and making use of mathemtical results outside of pure mathematics is more challenging than simply creating proofs.

I think the field will figure out how to make use of AI, and it will be better off for it. But that is not the same as just saying "answers good, grog want more answers."

People need jobs. What's wrong with nerds having jobs via a program?

well put.