Mathematics

Terence Tao Warns AI-Driven Proof Abundance Risks Mathematical Comprehension Crisis

In a paper prepared for the 2026 International Congress of Mathematicians, mathematician Terence Tao argues that artificial intelligence will force a restructuring of mathematical research practices, publication criteria, and education. The essay, released on arXiv (2608.16753), outlines how the transition from proof scarcity to proof abundance creates operational and epistemological challenges distinct from earlier debates over automated theorem proving. Tao frames the incoming disruption agai

An AI system produced a machine-checked proof of the 246 prime-gaps theorem

Neurosurgery resident solves Crouzeix's conjecture with GPT-5.6

A neurosurgery resident with no formal advanced mathematics training has solved Crouzeix's conjecture, a 22-year-old open problem in numerical linear algebra, using a 16-hour autonomous run of GPT-5.6 Sol in ChatGPT Work mode. Dr. Shanmu Jin, a postdoctoral researcher and neurosurgery resident at Peking Union Medical College Hospital, prompted ChatGPT 5.6 on July 30, 2026 to work on the conjecture. The model ran autonomously for approximately 16 hours, exploring proof strategies through a branc

Claude Advances Riemann Zeta Function Research, Raising Zero Point Bound to 67.2%

Claude Advances Riemann Zeta Function Research, Raising Zero Point Bound to 67.2%

OpenAI says Astra solved ten open math problems for about $2,000

OpenAI has named its next major model, Astra, by publishing ten mathematical results it says were generated by an internal version of the system. The company released a technical paper, reasoning walkthroughs and Lean certificates that allow the formal proofs to be checked by software. The more important part of the announcement is not the count. AI-generated mathematics has produced enough false starts that a headline number alone is weak evidence. OpenAI's decision to publish machine-checkabl