Eric Brandon Berger

Donate in to the memory of my brother Shuby ⬇️⬇️⬇️

[Eric Brandon Berger @RationalRisk]

Never looking back 😀

[Eric Brandon Berger @RationalRisk]

NFL Sunday! I’ve missed you it’s been too long 🏈

[Eric Brandon Berger @RationalRisk]

From dust to dust 🎶

[Amelia hazel @ameliahazelai]

50 websites that feel like the internet’s hidden toolbox 🧰

1. https://t.co/Je5WodiBhe — Free research papers
2. https://t.co/xso5O6ypiD — Borrow books online
3. https://t.co/abjG7P1KYI — Free academic journals
4. https://t.co/tvx5D0nJrl — App alternatives
5. https://t.co/4L1fhKAevO — Find where to stream
6. https://t.co/sgyCsLUWnb — Internet archives
7. https://t.co/p7M01LZDUC — 70K+ free books
8. https://t.co/DBHcEPBaCz — Free textbooks
9. https://t.co/Vs1x36sPdA — Free courses
10. https://t.co/cnfk4o6crb — Solve complex problems
11. https://t.co/sRJEWiHkJR — Photoshop alternative
12. https://t.co/0mO2BmrgiS — Compress images
13. https://t.co/I9R1C7Fbs7 — Remove backgrounds
14. https://t.co/GPkIB2zITq — Remove objects
15. https://t.co/Yyx25932lu — Remove video backgrounds
16. https://t.co/2fRA8eScih — Beautiful code images
17. https://t.co/67rvkjTiXa — Code screenshots
18. https://t.co/rkvTB3TnBF — Product mockups
19. https://t.co/ulukLPCmR5 — Create mockups
20. https://t.co/rrWXP90Y6q — Check data breaches
21. https://t.co/lbCviBMKfm — Scan files & URLs
22. https://t.co/TbSGVMPbH7 — Self-destructing notes
23. https://t.co/NQFiqAWuDe — Temporary email
24. https://t.co/5tWQ2nONaG — Temporary file sharing
25. https://t.co/pz7eRmSowl — Save webpages
26. https://t.co/oL9FaYxRnp — Find similar websites
27. https://t.co/oyca5FBTgD — Explore global radio
28. https://t.co/DLz36rIwQf — Discover music genres
29. https://t.co/qcrnXWmPHw — Find songs from shows
30. https://t.co/Og2wEzcmKI — Focus music
31. https://t.co/Z3lgtSYlY8 — Custom background sounds
32. https://t.co/6F7nghFeZX — Café ambience
33. https://t.co/6zmgFmPloW — Research assistant
34. https://t.co/o4zSKhOYWd — Research-backed answers
35. https://t.co/8gd1PU1L56 — Research connections
36. https://t.co/yZ8C49vzbw — Academic search
37. https://t.co/pObdpd7WUe — Understand research papers
38. https://t.co/TRf64dOqw2 — YouTube summaries
39. https://t.co/DzX9x86uIj — AI for developers
40. https://t.co/IwSKKbtV64 — Test regex
41. https://t.co/pdl1SzaZd4 — Format code
42. https://t.co/gz36ylE53G — Format JSON
43. https://t.co/NG6yh38HSl — Understand terminal commands
44. https://t.co/jHqFuBQ2b3 — Bookmark manager
45. https://t.co/qBRbUTy6qe — Check outages
46. https://t.co/wJk9ey5zpS — Reverse image search
47. https://t.co/LzITdcrExn — Internet speed test
48. https://t.co/YGk4iO3tNw — PDF tools
49. https://t.co/kPdDhZYUPF — Merge/split PDFs
50. https://t.co/zA6025sC61 — Temporary email

Save this. You’ll definitely need some of these later. 🔖

Follow @ameliahazelai for more useful websites, AI tools & tech resources.

[Eric Brandon Berger @RationalRisk]

New Year started off right 👌

[Eric Brandon Berger @RationalRisk]

Finch mission + Chabad for Rosh Hashana 🤗

[Eric Brandon Berger @RationalRisk]

25 years ago my father lived 🙏

[Eric Brandon Berger @RationalRisk]

Thursday Night Football!

[Eric Brandon Berger @RationalRisk]

Shana Tova season

[Probability and Statistics @probnstat]

Navier–Stokes and OpenAI’s New Advance

The Navier–Stokes equations describe the motion of viscous fluids:

∂ₜu + (u·∇)u = −∇p + νΔu,  ∇·u = 0.

The famous Navier–Stokes existence and smoothness problem asks whether every smooth initial condition in 3D remains smooth for all time, or whether a finite-time singularity can develop.

OpenAI has now announced an AI-generated proof claiming that smooth solutions can indeed develop a singularity in finite time. Its system reportedly used around 10,000 AI agents working in parallel, with the resulting argument formally checked in Lean.

An important part of the mathematical story, however, predates this announcement. The blow-up programme of Diego Córdoba and Luis Martínez-Zoroa, including their work with Fan Zheng, established crucial finite-time blow-up results for related forced/hypodissipative Navier–Stokes models.

Thus, the recent development should be viewed in the context of this broader mathematical programme: Córdoba and Martínez-Zoroa developed key ideas underlying the route toward blow-up, while OpenAI claims to have pushed such ideas to the classical 3D Navier–Stokes problem.

If independently verified, this would be a historic advance—not only for fluid dynamics, but also for AI-assisted mathematical discovery.

Diego Córdoba and Luis Martínez-Zoroa, whose foundational blow-up programme is an important precursor to this line of work.

[Eric Brandon Berger @RationalRisk]

TIFF afternoon! 🎬

[Eric Brandon Berger @RationalRisk]

How our current system incentivizes how we navigate the AI frontier through the profit motive might be the actual danger, not the technology itself.

[Eric Brandon Berger @RationalRisk]

But the voices in my head go

[Eric Brandon Berger @RationalRisk]

Finally NFL season is back!

[Eric Brandon Berger @RationalRisk]

Rainy day poker @888poker 👌

[Eric Brandon Berger @RationalRisk]

🌭🌭

[Eric Brandon Berger @RationalRisk]

This Rosh Hashana is going to hit dif

[Eric Brandon Berger @RationalRisk]

New ink 💪

[Eric Brandon Berger @RationalRisk]

Rage against the dying of the light ✨