Comment by jeremyjh
1 day ago
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/
I don't know, this just seems like gatekeeping of the term "research" simply because you don't like the way it's being done.
Many modern medicines do not have understood mechanisms of action, yet we know they work. Are the people who found them not conducting drug research?
Do we even have a different term for what the AI labs are conducting if it's not mathematical research?
Additionally, I would argue that any work that adds to the total corpus of known facts increases human understanding, even if the path to get to each fact isn't understood. It's hard to argue we'd be better off with less total information.
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