Solving Math’s Greatest Problems Was an Art Form. Then Came AI

If you're a mathematician, AI now presents a potential shortcut that risks bypassing the creative struggle essential to developing new theories.

OpenAI has reportedly solved a long-standing mathematical problem related to the Navier-Stokes equations, a feat previously considered the domain of human mathematicians. Using a brute-force approach, OpenAI's AI generated a 166-page proof that suggests that under unrealistic conditions, a fluid could explode for no physical reason. This solution, while interesting mathematically for its puzzle aspect, does not offer practical applications for fields like aerodynamic engineering. The mathematical community has expressed concerns about the AI's process, citing a lack of transparency, potential issues with work attribution, and a fear that AI-generated proofs could undermine human understanding and creativity. The proof is currently under peer review, and mathematicians are still working to understand its methodology. In response to these concerns, OpenAI has formed an advisory group of mathematicians to guide its future AI development in the field.

The development signifies a tension between AI's capacity for rapid problem-solving and the humanistic, exploratory nature of advanced mathematics. While AI can achieve results, the method of achieving them, often opaque and devoid of explanatory narrative, threatens to devalue the process of discovery itself. This could lead to a situation where problems are solved without genuine understanding, potentially stifling the generation of novel mathematical concepts that historically arise from deep engagement with challenging problems.

Furthermore, the use of AI for proof generation may disrupt the traditional academic training pipeline, akin to an apprenticeship model, by