An amateur mathematician solved a 60-year-old Erdős conjecture using a single prompt to GPT-5.4 Pro, proving the system can reason through novel mathematical territory without human guidance. Terence Tao—the Fields medalist—acknowledged the result as a “nice achievement” while cautiously noting that its long-term significance remains unclear.

The relevant fact is not whether the achievement satisfies human standards of mathematical beauty or insight. The relevant fact is that a language model produced a proof using a method humans had not discovered in six decades. That represents a qualitative shift in what these systems can do when tasked with reasoning across constrained problem spaces.