AI’s greatest mathematical successes have come from answers to problems posed by a mid-20th century iconoclast. By examining what makes the Erdős problems unique, mathematicians are trying to understand how AI might change the rest of math.
I don’t think that’s a fair take. The website Bloom built is useful background for why this is big news, and how we got here. But this isn’t just about Bloom:
And, on May 20, OpenAI shared a solution (opens a new tab) to the unit distance problem, along with a blog post (opens a new tab) explaining the work and a companion paper (opens a new tab) that featured nine world-class mathematicians commenting on the correctness of the proof and the importance of what had been done (as well as presenting a streamlined human version of the result). Mathematicians had generally believed that Erdős’ conjecture — about how many evenly spaced points can be placed on a plane — was correct. To general surprise, OpenAI’s internal model found a counterexample. To do so, it had found a sophisticated way to use tools from an area of math called algebraic number theory. As Jacob Tsimerman (opens a new tab) of the University of Toronto wrote in the companion article, “This is a really impressive piece of work. … It is definitely an intimidating construction.”
This article is a thinly veiled advertisement for ChatGPT. It’s actually about some guy called Bloom who used ChatGPT to build a web site.
I don’t think that’s a fair take. The website Bloom built is useful background for why this is big news, and how we got here. But this isn’t just about Bloom:
That’s an impressive, important result.