The Unreasonable Effectiveness of LLMs in Mathematics (www.chrishayduk.com)

In July 2025, OpenAI’s raw LLM achieved a groundbreaking gold medal at the International Math Olympiad (IMO), outperforming DeepMind's AlphaProof, a specialized model designed to construct mathematical arguments in Lean, a formal proof language. This achievement poses critical questions about the effectiveness of general-purpose models versus custom-built systems in mathematical reasoning. Despite AlphaProof's innovative approach utilizing reinforcement learning and tree search algorithms, it needed extensive computational resources and refinement to reach its potential, highlighting the complexities of theorem proving in formal environments. OpenAI’s success with a standard LLM suggests a paradigm shift in mathematical problem-solving, emphasizing the importance of a less rigid reasoning process that mimics the subconscious thinking of mathematicians, as articulated by psychologist Jacques Hadamard. This model simulates the fluidity of human thought, engaging in higher-level reasoning rather than strictly sequential proof construction, allowing it to explore various conceptual paths. The findings signal a significant departure from traditional application-specific systems, indicating that the inherent flexibility and intuitive capabilities of general LLMs may redefine benchmarks in AI-driven mathematics and other creative fields.