AI-human collaboration could possibly achieve superhuman greatness in mathematics
Mathematicians explore ideas by proposing conjectures and proving them with theorems. For centuries, they built these proofs line by careful line, and most math researchers still work like that today. But artificial intelligence is poised to fundamentally change this process. AI assistants nicknamed “co-pilots” are beginning to help mathematicians develop proofs—with a real possibility this will one day let humans answer some problems that are currently beyond our mind’s reach.
If you are writing a proof with the help of the Caltech co-pilot, you can click on a button to request new lines of Lean’s programming language to represent the mathematics you are working with. Several options, which Anandkumar calls “tactic suggestions,” will appear on the right-hand side of the screen; you then simply choose whichever option looks most appropriate.
But Hairer, who is not involved in the Caltech project, believes AI co-pilots will eventually take all that grunt work away. “Once you present a statement which is obvious to most mathematicians, an LLM should then be able to generate the code for it,” he says, adding that this faster process could “possibly lure a new generation of mathematicians to Lean.”
Yet “soon there will be systems which approach that level,” says David Silver, vice president of reinforcement learning at Google DeepMind. “I think this will essentially lift human mathematicians to a place where they are able to operate, and ponder ideas, at a much higher level.” Mathematics is beginning to transform, he says, just like it did when the electronic calculator was invented.
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