A reasoning model cracked the Erdős unit distance conjecture with a verified 125-page proof that bridges algebraic number theory and combinatorics. Mathematicians applied its technique to other open problems within days. Plus: Anthropic and OpenAI on recursive self-improvement.

Source episodes:

- How a reasoning model cracked an 80-year-old math problem - Episode 20 (Open AI podcast) https://sphinx.acast.com/p/open/s/68470ba8d911dedd6501609c/e/6a20dd9301be5cffcd5fa141/media.mp3

- What OpenAI and Anthropic Think Happens Next With AI (The AI Daily Brief) https://anchor.fm/s/f7cac464/podcast/play/121063959/https%3A%2F%2Fd3ctxlq1ktw2nl.cloudfront.net%2Fstaging%2F2026-5-5%2F425587851-44100-2-014cc22bdebc9.mp3

- How Companies Are Becoming AI Token Efficient (The AI Daily Brief) https://anchor.fm/s/f7cac464/podcast/play/121018053/https%3A%2F%2Fd3ctxlq1ktw2nl.cloudfront.net%2Fstaging%2F2026-5-4%2F425526383-44100-2-33562354187ed.mp3

- Codex is Coming for Everything, Spotify's Disco Ball Disaster and Microsoft's Addictive new Agent (Department of Product) https://www.youtube.com/watch?v=FMtKI2YavZ4