Comment by atleastoptimal
1 day ago
>AI is solving mathematics problems (that nobody - including mathematicians - wanted it to solve)
Do people need permission from mathematicians to solve math problems? Is one of the Millennium problems not worth applying a new system to work on it?
I understand the despair people are feeling at AI automating their work, but we have to be serious about the fact that the frontier labs are just responding to natural incentives. Mathematics, coding, all are just applications of logic, and it makes sense that a system trained on inferring patterns from data would work well in that domain.
You are misunderstanding what mathematics research is. Its objective is the development of human understanding of mathematics. This requires open problems to research. AI are “solving” the open problems without creating any human understanding.
At the very least, the single bit of information of whether a conjecture is true or false advances human understanding. It allows researchers to abandon paths which would not have been fruitful.
I'm pretty sure OpenAI's proofs, while difficult to understand, have a net-zero impact on human understanding of mathematics. It took the first Millenium problem years to verify its accuracy. It's only been days since OpenAI released its problems, surely it would take years to evaluate whether the solutions meaningfully advanced human understanding.
It may provide that one bit of information but it could still be a net negative if it destroys current institutions (such as graduate studies) and no new institutions can be developed that provide a clear signal of who is doing meaningful work. That was a byproduct of solving open problems that are now lost. These are not my ideas, these are things that Terence Tao and others have written about that were recently on the front page of HN, e.g.:
https://mathstodon.xyz/@tao/117395269325940185
https://mathstodon.xyz/@tao/117394287977270632
Who determines the objective of mathematics research?
All mathematics researchers in the whole world have agreed upon that objective apparently?
This is basically the dictionary definition of the word "research". But yes, all the work they are doing is focused on this goal. They write papers for humans to read, give lectures for humans to listen to, have discussions with humans - all with the objective of improving human understanding of the subject.
Many of them - all but a couple of the living Fields Medalists - recently signed an open letter about this.
https://mathandai.org/
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OpenAI to this day is not aware if they solved or not Navier Stokes.
Mathematicians are not gate keepers but I understand the frustration. If someone claims they spent 30 million dollars to solve one of the most difficult problems yet there’s no new knowledge, understanding, nor certainty. Then what’s the point besides marketing?