OpenAI will publish a set of new mathematical results produced by its internal cutting‑edge models. It says it has consulted and remained in contact with the Institute for Advanced Study, Princeton’s independent advisory panel on mathematics and AI, and used that panel’s input and public recommendations as the basis for the release.

On the sixth day of China’s National Day holiday, cross‑regional population mobility is expected to exceed 300 mln trips. Rail: nationwide railways forecast to carry 22.10 mln passengers today, with 2,199 additional passenger trains scheduled. Road: return traffic is dispersing; 44 highway sections are flagged as congestion‑prone, concentrated in Jiangsu, Guangdong, Hunan and Anhui. Air: civil aviation passenger throughput is expected at 2.471 mln today; popular routes include Shenzhen–Shanghai, Shenzhen–Beijing, Shenzhen–Hangzhou, and Shanghai–Guangzhou and Shanghai–Beijing. Water: waterborne passenger traffic is expected at 1.39 mln, up 25.3% YoY.

Von der Leyen said the EU must address structural issues that leave it exposed to volatility in foreign fossil-fuel markets.