Cal Newport

People on X predictably went even more wild.

Peter Diamandis tweeted the following.

An open AI model just proved an 80-year-old math conjecture from Paul Erdos, one of the most prolific mathematicians in history.

We're going to solve everything.

All right, so what's actually going on here?

Did AI just reach genius level?

Has math as a discipline just been automated?

As a theoretical computer scientist myself who has published a lot of applied mathematics research in my days and someone who proudly boasts an Erdos number of three, which you can look up if you don't know what that means, I am, for obvious reasons, particularly interested in these questions.

Well, it's Thursday, which means it's time for an AI Reality Check episode of this show, which is the perfect opportunity to seek some answers.

So that's exactly what we're going to do.

As always, I'm Cal Newport, and this is Deep Questions, the show for people seeking depth in a distracted world.

All right, so we need to start by getting more specific about what exactly OpenAI actually did, and then we can get into the implications of what that means for the rest of us.

All right, so we're looking at this unit distance, planar unit distance conjecture.

Erdos was convinced that he had identified the answer to the question.

I don't want to get too mathy here, but just to say it quickly, Erdos thought that if you were placing endpoints into the plane,

the maximum number of points that you could get to be a unit distance apart would be upper bounded by n raised to the power of 1 plus some constant c divided by the double log of n. Now, as you're probably noticing as you listen to me, that second term in the sum is going to tend towards 0 as n increases, asymptotically speaking.

So this result, the answer...

asymptotically is going to approach plain linear as the point set increases.

That's a really elegant answer.

Erdos was convinced that was right.