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I had a great-uncle who was a “human calculator”. It’s an odd, rare ability that allows people to multiply large numbers quickly in their heads. I remember using a hand calculator and seeing if my uncle could get it right without a tool faster than I could; more often than not, he could.
Human calculators used to be very valuable as employees, back when calculation was done by hand. Today they’re just a curiosity. Technology came along and superseded that particular human ability, as it has so many others. The story of John Henry being superseded by the steam drill, or Paul Bunyan by the chainsaw, is a metaphor for the march of progress. In some cases, like Garry Kasparov or Lee Sedol losing to computers at chess and Go, the moment really happened.
This week marked another important such moment in the history of man versus machine. OpenAI announced that its new model, Astra, managed to solve ten major outstanding problems in math and theoretical computer science. Here’s a simple explanation of the problems. The general consensus seems to be that these are extremely important, stunning breakthroughs.
This does not mean that computers are now capable of doing every kind of math better than humans can. Some people have argued that AI is good at results where the solution can be found by reading the entire literature and combining existing insights — exactly the kind of thing you might expect a computer to be superhuman at — but still not as good as humans at making truly novel leaps of insight. This may represent a real, general limitation of LLMs’ capabilities — as Tom Zahavy of Google DeepMind put it, it may still be the case that “LLMs can’t jump.”
But the trend line is becoming clearer. The University of Toronto’s Daniel Litt, one of the most prominent skeptics of AI’s potential for frontier math research, recently conceded a major bet about what AI could do:
Litt appears to no longer believe that there is any important type of math that AI won’t soon be able to do, writing: “The models don’t yet seem able to do certain kinds of high quality research, but I also expect this is a matter of (not too much) time.”
Some mathematicians have reacted to this development with despair. Kirwin Hampshire’s post is probably the most evocative and the most well-read:
