It might as well happen, similar to how AlphaGo was superseded by AlphaZero, at some point a model might produce better math if it's trained through self-play where it poses its own problems, instead of looking for open problems in literature.
What's the objective function or RL environment for "interesting conjecture"? Not saying it can't be done - I no longer have any specific task that I'm confident AI won't be able to do - but I don't see how. It feels to me like something that would require a qualitatively new approach.
LLM's are trained on human knowledge and taste. They are actually pretty good at deciding if a conjecture would be found "interesting" by the mathematical community or not.
Note that I am saying LLM, and not chatbot or agent. But even a chatbot can often still reasonably rank a list of mathematical statements by vague properties like "interestingness".
How to RL this is a bit of an open question, but there are interesting conjectures of how to do it.
It might as well happen, similar to how AlphaGo was superseded by AlphaZero, at some point a model might produce better math if it's trained through self-play where it poses its own problems, instead of looking for open problems in literature.
What's the objective function or RL environment for "interesting conjecture"? Not saying it can't be done - I no longer have any specific task that I'm confident AI won't be able to do - but I don't see how. It feels to me like something that would require a qualitatively new approach.
> but I don't see how
LLM's are trained on human knowledge and taste. They are actually pretty good at deciding if a conjecture would be found "interesting" by the mathematical community or not.
Note that I am saying LLM, and not chatbot or agent. But even a chatbot can often still reasonably rank a list of mathematical statements by vague properties like "interestingness".
How to RL this is a bit of an open question, but there are interesting conjectures of how to do it.
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> It feels to me like something that would require a qualitatively new approach
This sentiment has been a recurring theme throughout the history of the field.
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