Over the weekend, software engineer and former quant researcher Neel Somani made a surprising discovery while testing OpenAI’s latest model, GPT 5.2. After pasting a complex math problem into ChatGPT and letting it process for 15 minutes, he returned to find a fully worked solution. Somani evaluated and formalized the proof using Harmonic, a tool for verifying mathematical reasoning—and it all checked out. “I wanted to see when LLMs could tackle open math problems versus where they fail,” he explained, noting that the model’s performance surpassed expectations.
The model’s reasoning stunned experts, demonstrating familiarity with advanced concepts like Legendre’s formula, Bertrand’s postulate, and even the Star of David theorem. While reviewing its process, ChatGPT referenced a 2013 Math Overflow post by Harvard mathematician Noam Elkies. Although it drew inspiration from Elkies’ elegant solution, GPT 5.2 produced a more complete proof for a variant of a problem posed by the legendary mathematician Paul Erdős—a collection of over 1,000 conjectures that have challenged human mathematicians for decades.
AI’s presence in mathematics has grown rapidly, from formalization tools like Harmonic’s Aristotle to literature review assistants such as OpenAI’s deep research features. Since the release of GPT 5.2, the number of AI-assisted solutions to complex problems has accelerated, with 15 Erdős problems recently marked “solved,” 11 of them credited to AI contributions. Even revered mathematician Terence Tao acknowledged that AI models are making measurable progress, particularly in systematically tackling the “long tail” of obscure problems that have straightforward solutions.
A key driver of this progress is formalization, the labor-intensive process of making proofs verifiable and extendable. Tools like Microsoft Research’s Lean and AI assistants like Aristotle have simplified formalization, allowing models to produce proofs more efficiently and reliably. Tudor Achim, founder of Harmonic, emphasized that the significance lies not just in solved problems but in the fact that top mathematicians are now using AI tools seriously. “These are people with reputations to protect,” he said. “When they use AI, that’s real evidence.”
While AI is far from replacing human mathematicians, its growing ability to solve high-level problems signals a new era for research and discovery. From autonomous solutions to guiding formalization, large language models are beginning to push the boundaries of knowledge, helping researchers explore problems that were once considered out of reach. As GPT 5.2 and its successors evolve, AI may become an indispensable partner in unraveling the most challenging puzzles of mathematics.
source: Techcrunch