The authors of the declaration agree with you that this is how the field works today. They think that fact causes AI use to produce bad results, and they want to reformulate how the field works so that AI use will produce good results instead.
I understand the perspective: The journey of a PhD thesis is a learning experience greatly beneficial to the student. Yet that journey is funded by society (esp. for domestic students) and society benefits from the results. The average person benefits when progress is made.
Most math textbooks have solutions in the back. That didn't wreck peoples ability to learn math, did it?
So we are left to speculate about why solutions in appendix are fine, but LLM solving open problems is not fine.
The idea that when LLMs produce solutions, people won’t try to understand them and won’t learn from it, is obviously not true. Terry Tao himself spent time digesting and simplifying LLM proofs.
So again we’re left to speculate what the actual problem is.
Math understanding will increase with LLMs. Not just professional mathematicians but amateurs.
I think you’re struggling to understand what Tao and his cosignatories are saying because you’ve acquired a very specific kind of “AI-pilled” mindset from social media, where taking AI seriously implies accepting LLMs should be used at any time for any purpose. They’re saying in great detail that LLM solutions are unhelpful when presented in a particular way, but you can’t help but hear them saying that LLM solutions aren’t helpful at all, even as you rightly point out that this makes no sense and is inconsistent with their observed behavior.
Society doesn't benefit from results in research mathematics because it mostly consists of pure mathematics, which is completely useless for society.