The amount and accuracy of passing in the game of soccer—called football across much of the world—has climbed in recent years, according to new research. The average passing volume, pass accuracy, and ...

A Mathematician with early access to XAI Grok 4.20, found a new Bellman function for one of the problems he had been working on with my student N. Alpay. Not an Erdős problem, but original research.

The public release improves audio, speech, debugging, and developer experience. Additionally, a more cost-effective mini ...