From the article about the Erdos problem:
> “This one is a bit different because people did look at it, and the humans that looked at it just collectively made a slight wrong turn at move one,” says Terence Tao, a mathematician at the University of California, Los Angeles, who has become a prominent scorekeeper for AI’s push into his field. “What’s beginning to emerge is that the problem was maybe easier than expected, and it was like there was some kind of mental block.”
> “There was kind of a standard sequence of moves that everyone who worked on the problem previously started by doing,” Tao says. The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question.
> “The raw output of ChatGPT’s proof was actually quite poor. So it required an expert to kind of sift through and actually understand what it was trying to say,” Lichtman says. But now he and Tao have shortened the proof so that it better distills the LLM’s key insight.
> More importantly, they already see other potential applications of the AI’s cognitive leap. “We have discovered a new way to think about large numbers and their anatomy,” Tao says. “It’s a nice achievement. I think the jury is still out on the long-term significance.”
You can debate whether the LLM used logic or not. I don't think you can debate that the LLM has in this case elevated human thinking, by leading us to a solution that had eluded world-class mathematicians for 60 years. And a new way to think "about large numbers and their anatomy".
And if it works for Terrence Tao and Erdos problems, then I'm certainly not above using AI to help brainstorm solutions for my little app at work.