Apple (AAPL.O) announced pricing for the iPhone 18 Pro series: iPhone 18 Pro starts at $1,199 and iPhone 18 Pro Max starts at $1,299. For comparison, iPhone 17 Pro launched at $1,099 (8,999 yuan) and iPhone 17 Pro Max at $1,199 (9,999 yuan).

KYODO: JAPAN DEFENCE MINISTER KOIZUMI cancelled a planned visit to Indonesia.

Quanta reports OpenAI’s recent math advance built on prior academic work rather than arising from a blank slate. Mathematicians Diego Córdoba and Luis Martínez‑Zoroa had earlier proposed an “infinite cascade” approach and in 2023 proved singularities under relatively coarse forcing; the remaining technical hurdle was maintaining mathematical smoothness of the forcing. Princeton mathematician Charles Fefferman acknowledged the new result but identified Córdoba and Martínez‑Zoroa as the key contributors. Observers characterise the development as AI industrialising the research “last mile”: humans supply directions, many agents run parallel trial-and-error, and models fill in and formalise critical proofs. Terence Tao warns this could shift mathematics from “proof scarcity” to “proof abundance,” with future scarcities being high‑value questions, viable solution paths and independent verification capacity. The piece concludes compute is accelerating research pace but does not yet imply fully autonomous original research capability.