Did AI Just “Solve” Math? (Let’s Take a Closer Look) | AI Reality Check

Last week, OpenAI published a press release titled, an OpenAI model has disproved a central conjecture in discrete geometry. They were talking specifically about the planar unit distance problem, which was first posed by Paul Erdos in 1946. Now this is actually a a pretty simple problem to state. It basically says, what is the maximum number of pairs of points in a set of endpoints in a flat plane that can be exactly one unit of distance apart? Now back in the nineteen forties, Airdos proposed an answer to this question. He couldn't prove it, but he thought he knew what the answer was. Last week, OpenAI essentially announced that they had used an LLM to prove that Airdos's proposed answer was, in fact, incorrect. The OpenAI press release was accompanied by a video that featured dramatic music and a group of researchers writing earnestly on a comically small blackboard as they explained why this was a big deal. Here, let's play a clip of that video. This is the first mathematical breakthrough due to an AI. It's it's been described as the most well known problem in combinatorial geometry. So for for a whole subfield of mathematics, it's like maybe the best known problem there is. The mainstream press soon picked up on this story with enthusiasm. Here's the new scientist headline. Mathematicians stunned by AI's biggest breakthrough in mathematics. People on x predictably went even more wild. Peter Diamonis tweeted the following, an OpenAI model just proved an eighty year old math conjecture from Paul Erdos, one of the most prolific mathematicians in history. We're going to solve everything. Alright. 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 air dose 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 gonna do. As always, I'm Cal Newport, and this is Deep Questions, the show for people seeking depth in a distracted world. Alright. 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. Alright. So we're looking at this this unit distance, planar unit distance conjecture. Erdos was convinced that he had identified the answer to the question. I I don't wanna get too mathy here, but just to say it quickly, Airdos thought that if you were placing end points into the plane, the maximum number of points that you could get to be a unit distance apart would be upper bounded by …