how your email, in fact, finds me

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Very useful technical lemmata for fellow sheaf nerds: arxiv.org/abs/2506.14007

I often rant about how 99% of attention is about to be LLM attention instead of human attention. What does a research paper look like for an LLM instead of a human? It’s definitely not a pdf. There is huge space for an extremely valuable “research app” that figures this out.

We have constructed Turing complete Navier-Stokes steady states via cosymplectic geometry. You can read it here: arxiv.org/abs/2507.07696

We live in a wonderful world to make & see such beautiful things

🌀 Universality in Computable Dynamical Systems: Old and New Can dynamical systems compute? From Turing-complete fluids to Topological Kleene Field Theories, we explore how dynamics encodes computation—past, present, and future. arxiv.org/abs/2507.10725

this is something i've not seen from GPT (4o) before: offering me an A/B choice with those circle-letter typewriter font icons. kinda charming.

working on my biggest usage of openai deep-research yet. had a prompt suggest 13 deep research topics to support a thesis. made a prompt to write out *long* *precise* deep-research requests. running each one takes 10-15 minutes apiece, each creating a ~30 page pdf. (!)

"[video game] as a community theater production" may be one of the most delightful Veo 3 Fast prompts Please enjoy, in order: GTA, Pokemon, Mario Kart, The Witcher 3, Stardew Valley, Tetris, Mortal Kombat, The Sims, & Death Stranding(!) Yes, the whole prompt was the one above.

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which areas of research will AI impact most/first? math? [theorems are hard but validate-able] natsci? [experiments take time & $$$ to check] econ? [theory is like math; sims are possible...] humanities? [but they hate AI?!] humanities is where the AI comet hits first & hardest.

prof-g (prof-g) is teaching the Artificial Intelligence course at the Engineering Summer Academy at Penn. Students are now hard at work on their final projects. Penn Engineering Penn Electrical and Systems Engineering #AIClass #SummerAcademy

Big day for Lean! Alex Gerko of XTX Markets is donating $10M to the Lean FRO and the new Mathlib Initiative to support the future of formal mathematics and machine-checked proofs. Thank you, Alex Gerko and Convergent Research, for believing in the mission. Read the full