AI Breakthrough: OpenAI’s ChatGPT Solves Complex Math Problems
Over the weekend, Neel Somani, a software engineer, former quant researcher, and startup founder, stumbled upon a remarkable discovery while testing the math skills of OpenAI’s new model. After inputting a problem into ChatGPT and letting it ponder for 15 minutes, he returned to find a complete solution. Somani, intrigued by this breakthrough, sought to gauge the capabilities of large language models (LLMs) in solving open math problems.
Somani was astounded by the depth of ChatGPT’s mathematical prowess, effortlessly referencing complex theorems like Legendre’s formula, Bertrand’s postulate, and the Star of David theorem. The model even unearthed a solution from a Math Overflow post by Harvard mathematician Noam Elkies, offering a fresh perspective on a problem posed by the legendary mathematician Paul Erdős.
With the release of GPT 5.2, Somani noted a significant improvement in mathematical reasoning compared to earlier versions, sparking a wave of solved problems that challenged traditional notions of AI capabilities in mathematics.
The Erdős problems, a collection of over a thousand conjectures by the renowned mathematician, have become a prime target for AI-driven solutions. Recent advancements, including AlphaEvolve’s autonomous solutions and ChatGPT’s prowess with high-level math, have led to a surge in solved Erdős problems, with AI models playing a pivotal role in the process.
Renowned mathematician Terence Tao acknowledged the contribution of AI models in solving Erdős problems, highlighting the significant progress made in autonomous problem-solving. While AI systems are yet to operate independently in mathematical domains, their role in advancing mathematical frontiers is undeniable.
Tao emphasized the scalability of AI systems in tackling obscure Erdős problems, suggesting that AI-based methods may outperform human approaches in solving simpler mathematical challenges.
The shift towards formalization in mathematics has further propelled AI tools like Harmonic’s Aristotle, streamlining the process of verifying and extending mathematical reasoning. Tools like Lean, a proof assistant developed by Microsoft Research, have revolutionized formalization in mathematics, paving the way for automated tools to enhance the process.
For Tudor Achim, founder of Harmonic, the surge in solved Erdős problems signifies a shift towards embracing AI tools in mathematical research. The endorsement of AI tools by esteemed mathematicians and computer science professors reflects a growing acceptance of automation in mathematical exploration.
