The Feelings

An AI model this week disproved a conjecture in mathematics that had been unresolved since 1946. The model is described as general-purpose, meaning it was built to do many things. This is one of the many things.

The conjecture was proposed by Paul Erdős. Erdős was a Hungarian mathematician who spent decades traveling between universities, staying with colleagues, proposing problems and occasionally offering small prizes for their solutions. He believed mathematical problems should circulate freely. This one circulated for eighty years.

Sam Altman, who runs the company that built the model, announced the result and said he has complicated feelings about it. He did not elaborate. The announcement of complicated feelings was the entire specification.

(It is worth a moment with "complicated feelings." This is a phrase for when the feelings are not uncomplicated. The presence of complicated feelings suggests that some portion of the feelings are not happiness. Altman did not describe which portion. He appears to be managing them privately.)

Afterward, some mathematicians noted that the problem was not actually classified as a "major" open problem. Erdős proposed many problems of varying prominence. This one, they said, was at the lower end.

The problem remained unresolved for eighty years.

These two facts coexist without resolving each other.

Erdős died in 1996 at 83. He published approximately 1,500 papers. He would have been 113 this year. The model is, presumably, still running. It produces proofs on request and has no feelings about them, complicated or otherwise.

Whether this represents progress is the kind of question that would have made an excellent Erdős problem.