🤖 Are mathematicians officially obsolete?
New Scientist: OpenAI announces 722 mathematical discoveries in one go:
OpenAI has dropped 722 mathematical papers proving and disproving a range of problems – a scale that academics say is as impressive as it is baffling.
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Having achieved impressive depth, OpenAI has seemingly now opted for breadth, releasing hundreds of mathematical discoveries in one fell swoop. The company didn’t name the AI made the discoveries, saying only that it was an “internal frontier model”.
Francis Johnson at University College London worked for many years on Wall’s D(2) problem – one of the hundreds of puzzles solved in OpenAI’s tranche of papers.
“I worked on this problem for 25 years. I produced two books on it. I, personally, gave up,” says Johnson. “I’m surprised that [AI] has done it quite so quickly, but I’m not surprised that it’s done it.”
Johnson recounts working with AI models in recent months and being “astonished with the sophistication and clarity of the analysis that they gave”.
“It puts us all in a very strange position,” says Johnson. “Let’s face it, the genie is out of the bottle now. We’re going to have to live with it. Human beings are supposed to be adaptable, so we’re going to have to adapt. I think for the moment, we just stand back and be astonished.”
But Kevin Buzzard at Imperial College London says we should exercise caution. He says the release included 30 papers that were relevant to his field of number theory, but only seven of those seemed impressive and only one was formally verified in Lean – a type of computer analysis that can prove mathematical results beyond reasonable doubt.
“Unfortunately, acceptance of these results by the community will take time, and journalists are going to have to wait while the mathematicians do their job,” says Buzzard. “The six unformalised results will have to wait until either an expert is motivated to read and check the text, or a Lean formalisation is produced.”
But while it is important not to get ahead of ourselves on the validity of the results, Buzzard says the general upwards trend in AI mathematics is astonishing. He says that, assuming the new results turn out to be mostly true, then we will get some kind of idea as to what the new normal is. “It has been a long time since there were humans who were experts in all of mathematics, but now we seem to have machines with this property,” he says.
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Unusually for mathematical research, the papers were published on GitHub, an online database more commonly used to share computer code.