AI models are beginning to solve complex Erdős conjectures

Software engineer, former quant researcher, and startup founder Neel Somani recently tested OpenAI’s GPT 5.2 model to establish a baseline for when large language models can solve open math problems compared to where they struggle. During his testing, Somani let the model think for 15 minutes before it returned a full solution. He found the model to be anecdotally more skilled at mathematical reasoning than previous iterations. This testing focused on the Erdős problems, a set of over 1,000 unsolved mathematical conjectures maintained online. While the first batch of autonomous solutions to these conjectures emerged in November from a model called AlphaEvolve, progress has continued. Since Christmas, 15 problems have been moved from open to solved on the Erdős website, with 11 of the solutions specifically crediting AI models.

This progress is supported by a growing focus on formalization, which is the process of translating mathematical reasoning into a format verifiable by computers. Mathematicians are increasingly adopting tools like Lean, an open-source proof assistant software developed at Microsoft Research in 2013, to verify and extend proofs. Startups are also building automated tools for this task, such as Harmonic, which developed an AI tool for formalization called Aristotle. Tudor Achim, the founder of Harmonic, explained that he cares more about the fact that math and computer science professors are using these AI tools than the sudden jump in solved problems. Achim noted that the adoption of these tools by respected academics serves as real evidence of their utility. “These people have reputations to protect, so when they’re saying they use Aristotle or they use ChatGPT, that’s real evidence,” Achim said.

Mathematician Terence Tao has offered a nuanced view of this development. Tao suggested that the scalable nature of AI systems makes them better suited to be systematically applied to the long tail of obscure Erdős problems, many of which actually have straightforward solutions. According to Tao’s tracking, AI models have made meaningful autonomous progress on eight different problems, with six other cases where progress was made by locating and building on previous research. Tao added that many of these easier Erdős problems are now more likely to be solved by purely AI-based methods than by human or hybrid means.

Why it matters

The recent surge in AI-solved Erdős problems, particularly with GPT 5.2, suggests that large language models are starting to crack high-level math problems and are increasingly capable of pushing the frontiers of human knowledge.