OpenAI Posts Two Kakeya Conjecture Manuscripts, Extending Work to Four Dimensions
On October 7, OpenAI released 722 mathematics manuscripts, including two on the Kakeya conjecture: a 97-page paper claiming a three-dimensional maximal-function result stronger than Wang and Zahl's, and a 175-page paper claiming the four-dimensional Hausdorff dimension case. Both are attributed to OpenAI, are not Lean-formalized or peer-reviewed, and OpenAI's README says some unformalized results may be flawed.
Model releases and updates
Google releases Nano Banana 2.1 image model with 4K output
Google released Nano Banana 2.1, an upgraded image generation model with 4K output, mask-based editing and improved subject consistency. According to Arena, it gained about 61.7 points on average across text-to-image, multi-image editing and single-image editing, and Google halved API prices for 1K and 2K images while cutting 4K by about 25%. It is available in the Gemini app and Google AI Studio, with 50 free credits daily.