AI Assistance in Proving the Spherical Hadwiger Theorem

A recent paper by Wang & Wu from Hunan University claims to prove the Spherical Hadwiger Conjecture, which has been open since 1974, with the assistance of AI technology. The authors disclosed that OpenAI Codex was utilized for developing proof details, identifying gaps, organizing the manuscript, and editing. They affirmed that they reviewed and verified all AI-assisted content and made all final decisions regarding the manuscript. The paper is noted for its polished presentation, suitable for research mathematicians. The author reflects on the implications of AI in mathematics, noting that the potential impact of large language models (LLMs) on mathematicians' work is significant, as indicated by a report from OpenAI. The report suggested that 100% of a mathematician's job is exposed to LLMs, a higher percentage than for writers or artists. The author draws a parallel between the support for classical musicians and the potential need for a 'mathematical conservatory' to sustain the field of pure mathematics in the face of AI advancements. The piece emphasizes the importance of continuing support for research mathematics, which is seen as a cultural endeavor that deepens understanding of reality. However, it also raises concerns about the changing incentive structures in light of AI's capabilities, questioning how society will value human contributions in mathematics as AI becomes more prevalent.