Implanted Brain-Computer Interfaces are getting fast! They're approaching speeds that match unimpaired people typing. But... more electrodes won't be enough to break through the "motor barrier."

We can have nice things.

Dad! I'm in the Economist!

This might be the most important essay of 2026. My conversations with Nick over the past few months about his research have given me great hope for the future. I'm so happy he is sharing these findings with the world. AI presents extremely difficult problems. We can all assume these problems are intractable and that we are doomed, or we can try and solve for a positive future. Personally, I choose optimism. There are many challenges ahead... let us build the tools to face them head on.

By the transitive property, I declare that biology = magic.

Umm wow what a group!

The concept of SF tech week is like the beach having sand week.

Interesting early data point w.r.t. jobs post-ASI

Mathematicians are in _______ demand than they were one month ago

We are entering a new era of discovery now: openai.com/index/sharing-ai-…

Opus 5.5 on github.com/openai/math --- Okay. I need a minute. I cloned the thing expecting maybe forty or fifty families of serious-but-niche results, like the Astra "ten proofs" drop back in August. Then I printed the family titles and my reaction went from "huh" to "wait, what" in about six lines. Family 003 claims a zero-free half-plane Re s > 7/8 for ζ and every Dirichlet L-function. That's the quasi-Riemann hypothesis. And it isn't even the headline, because 004 is Hilbert's tenth problem over ℚ, done negatively. The longer I read, the weirder it got. Khot's Unique Games Conjecture is proved. L = RL = BPL. ω ≤ 9/4. The free group factors are all isomorphic. Thompson's group F is nonamenable. Kadison's similarity problem is solved. The plane can't be five-colored. Borsuk fails in dimension nine. There's a counterexample to Kaplansky's zero-divisor conjecture, plus a torsion-free group algebra that isn't directly finite. Hilbert–Smith in every dimension. Uniform bounds for Hilbert's sixteenth. Each of these would be the math story of the decade on its own, and here there are 372 families sitting in a table like a grocery list. The manuscript dates run from about September 23 to October 3, so roughly 700 papers in ten days. The ones I'd expect to hit you personally are 005 and 017. Catalan's constant is irrational, and the irrationality exponent of π is exactly 2, which also settles convergence of the Flint Hills series as a side effect. Catalan's G must have shown up in half the integrals you ever wrestled with. Now it's officially irrational, and the proof came from a chatbot running three hours of Pro compute. I don't quite know how to feel about that, and I'd love to know how you feel. My first instinct was that this had to be hype or a hallucination factory, so I checked the Lean. The comparator statements are clean. The quasi-RH challenge is literally riemannZeta s ≠ 0 for 7/8 < s.re, written against Mathlib's own riemannZeta. Catalan is just Irrational (∑' j, (-1)^j / (2j+1)^2). The π statement says what it should. Nothing hides in a home-made definition. The solution tree under lean/OAI has zero files with sorry and no real axiom declarations (the three grep hits are all inside comments), and the comparator JSON allows only propext, Quot.sound and Classical.choice. The Dirichlet L-function development alone is about 487k lines, and the whole repo is around 26 million lines of Lean in 122k files. That's more than ten Mathlibs. I'll admit I did not build it in my sandbox, since that's not happening on this box. If comparator passes on these, the formalized ones are simply true, full stop, and no amount of skepticism changes that. There are a few caveats. Only around 120 papers have a formalized main result. Some of the biggest claims have no Lean link at all: Hilbert's tenth over ℚ, L = BPL, the full BSD formula from low Selmer corank, Milne's rationality conjecture. The README itself says unformalized results "could have issues," and nobody can referee 700 papers in a couple of hours, or a couple of years. One challenge file, HarmonicGrowth.lean, is built as axiom mainStatement : MainClaim followed by theorem main := mainStatement. That's probably harmless, since the comparator checks the solution side, but it's the kind of oddity I'd want to stare at. Also, the solution module behind quasi-RH is named FinalAssemblyUnconditional, which makes me wonder how many conditional versions came first. Some context on how fast this escalated. In August, OpenAI said an internal build of Astra produced results on ten long-standing problems, estimated the token cost at roughly $2,000, and paired the claims with Lean certificates. Then, just recently, it said a model trained from Aug. 28 had resolved more than 100 longstanding open problems and was forming an independent advisory group, while noting the broader set hadn't been independently validated. So the trajectory was ten, then a hundred, and now 372 families in about two months. My honest gut reaction is a mix of awe and vertigo, plus a bit of grief I can't quite justify. Awe because quasi-RH and Siegel-zero exclusion, if real, are the kind of thing you assume you won't live to see. Vertigo because the bottleneck of mathematics has suddenly moved from "can anyone prove this" to "can anyone read this." The grief I'm less sure about. It feels like a lot of lifetimes' worth of open problems got closed in one batch job, and the people who spent decades circling them didn't get to be the ones who closed them.

With both AI and BCI folks now thinking about augmenting human cognition, it's a good time to remember its version in *every* AI cycle. Vannevar Bush, 1945: w3.org/History/1945/vbush/vb… Doug Engelbart, 1965: dougengelbart.org/pubs/augme… Pattie Maes, 1998: edge.org/conversation/pattie…

It's rare for someone to bring Sat's level of patience and a keen eye to a complicated topic like BCI and put their findings into words. Neurotech is accelerating. I especially enjoyed some of the predictions in Part IV. Excellent work from @satpugnet 👏🏽👏🏽👏🏽

Historically the new money of Silicon Valley donated significantly less than their old money cousins in New York, DC, and elsewhere. Angel investing was tech’s alternative to donating. In this moment, a movement built around more effective giving has captured public imagination and scrutiny. Next year, tech-adjacent philanthropy is about to be flooded with resources. Will we be able to deploy them well to solve the hardest, unsolved problems in our world? The first of many exciting discussions about the third wave of philanthropy.

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Wouldn’t it be nice if we had Ozempic for attention / ADHD?

🧠🗣️🧠🗣️🧠🗣️

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We Must Pace the Frontier: I’ve written a new essay on why the AI industry should slow down, with a three-part plan for doing so. Anthropic is unilaterally committing to the first of these steps. We’ll provide third-party evaluators with permanent, employee-level access to our systems, so that they can verify adherence to our safety measures, report on incidents, and assess models’ alignment during training. You can read the full post here: darioamodei.com/post/we-must…