A true act of AI creation

What happens when AI makes the 'leap'?

I am watching out for a moment in the development of AI when it makes an ‘intuitive leap’ and develops a new idea that is not like what has come before. This is vague, I know. Demis Hassabis talks about a superintelligent AI being able to invent a game like Go, something as physically beautiful and engaging and intellectually deep as that game. Can’t AI already do this, more or less, you might ask? Maybe not quite to the level of inventing Go yet, but certainly some acts of creativity? But I don’t think so, not yet. I don’t think AI can yet write a story that is truly original and captivating, or start and run a successful business, or give you advice as an individual that is as good as you would get from a wise human mentor who knows you. There is still a ‘leap’ that is missing.

This week there was a story that made me think perhaps the leap was here, and I am still not completely sure, but I don’t think so. On July 19 the mathematician and Anthropic employee Levent Alpöge posted on X that Fable had found a counterexample to the Jacobian Conjecture, first proposed in 1939, which asks whether a certain kind of polynomial transformation that is reversible locally must also be reversible globally. The counterexample means it is not true, even though mathematicians had mostly thought it was. Legit mathematicians have tried and failed to find such a counterexample over the years, including Yitang Zhang, who spent seven years on it during his PhD before becoming world-famous for his breakthrough on the twin prime conjecture in 2013. So finding one is a pretty big deal. Finding one with AI is a potentially huge deal, depending on how it was done.

So the question is: Is this the leap? Did Alpöge say, ‘Hey Fable, give me a counterexample to the Jacobian Conjecture’ and out it popped? Irritatingly, Alpöge has not released the conversation he had with Fable (my guess is there’s all sorts of other random stuff in there; he talked about doing this during the World Cup final, which, in his defense, was stultifyingly boring). But Alpöge is a heavyweight mathematician in his own right, and he did his PhD under an even more heavyweight mathematician, Manjul Bhargava, who won the Fields Medal for work on the geometry of numbers, including counting number fields and bounding the ranks of elliptic curves. I must admit I don’t know what that means, but according to Claude the counterexample is very much in Alpöge’s mathematical wheelhouse. So I think it’s likely that Alpöge had some kind of insight into where the counterexample might be found, gave it a rip on Fable while waiting for Argentina to consider venturing a shot at goal, and he just happened to strike gold. Claude agrees with this insights-from-human-mechanistic-work-from-AI hypothesis (with some hedging of course), and in Claude’s view the work has Alpöge’s ‘fingerprints’ on it. I would love to see evidence to the contrary, and hopefully Alpöge will tell his story in more detail at some point, but right now I don’t think AI has made the leap yet.

The counterexample was important enough that even mathematical mega-mind Terence Tao wrote about it, and he also posted the conversation he had with ChatGPT where he dug into its details. The nuances of that discussion are not accessible to anyone without a pretty significant mathematical background, but what is fascinating to me is how he just asked question after question, 53 turns in all, probing and interrogating and suggesting things to do until finally rebuilding the counterexample from scratch out of his own understanding by the end. I believe this is how AI will be used by master practitioners in every domain -- asking good questions and using the AI to carry out the work of answering them, until they arrive at some new insight or decision.

So then the question becomes: How do you ask good questions? And the answer is unsatisfying: understand the domain, understand other people, understand yourself, have a deep store of experience to pattern-match against, and use all of that to somehow make the ‘leap’ to the right question. Be the right kind of person, in other words. Fortune magazine in its coverage said: ‘Beyond calculating, beyond even logical reasoning, “understanding,” at the bottom, is knowing what to ask, what Silicon Valley has taken to calling “taste.”’ Then they quote mathematician Kevin Buzzard as saying: “People have tried to get machines to ask questions, and they’re abysmal … All the questions they ask are either boring or obviously true or obviously false.”

So clearly, he does not think AI has made the leap yet, either. I don’t want to tempt fate, but long may it last.