Acceleration in AI Solving Erdős Problems

What if AI started solving mathematical problems that humans could not solve? This is not a future idea, this is happening already now. In mathematics, there are so-called open problems. These are math problems that no human has ever solved. One of the most important people connected to open problems was Paul Erdős. He was born in Hungary in 1913 and worked around the world during the 20th century. Erdős was famous for many things, but he was especially famous for the fact that he was collecting and sharing open mathematical problems.

His problems were usually easy to understand, but very, very hard to solve. Today, these questions are called Erdős problems. There are more than 1,000 of them listed online. Some of them are solved, many are still open. Each problem is like a test of how well we really understand mathematics. One of the most respected mathematicians alive today is Terence Tao. He has made major contributions to modern mathematics. When Terence Tao is speaking, the community listens. In the last month, something new has happened. AI tools have started solving Erdős problems, and very quickly.

Not just checking answers, but finding proofs, finding counter-examples, and writing formal mathematics, formal proofs. This work is tracked publicly so anyone can see the progress. In December 2025 and January 2026, AI systems worked on many of Erdős problems. Some of the problems were fully solved and formally verified with the most amount of progress in the last month, so in January 2026. This includes the work done by such tools as ChatGPT, Aristotle, AlphaProof, and others. One important example is Erdős Problem 728. According to Terence Tao, on January 6, 2026, this problem was solved almost autonomously by AI, after some feedback.

The result was not previously known in the literature, which basically means that AI has found a completely new proof. Shortly after that, on January 10th and then on January 11th, Problems 729 and 397 have been solved by ChatGPT 5.2 Pro. The proof was then later accepted by Terence Tao as well. This was shared publicly by Neil Somany. This is another clear signal that something is changing. This is not about AI replacing mathematicians. They will, of course, stay. This is about the speed of the progress. Mathematics is the foundation of science and technology, and when difficult problems are solved or are solved faster, everything built on top can move faster as well.

This is what people mean when they talk about acceleration. If you want to explore this yourself, it's actually very easy to do. There is a website, www.erdosproblems.com, and you can see all the Erdős problems, including those already solved and those open on this website. There is also a public GitHub page where people are tracking how AI are solving these problems. I will show all these links on the screen now. So as a result of all of this, I think we're entering a completely new phase, a phase of faster discovery, and I think it's only the beginning.

This was a thought on AI for today, and I'll see you in the next one.