What I read this week: AI disproves a famous conjecture, Anthropic's S-1, and a 29-cent agent

OpenAI models produced proofs and disproofs across mathematics, computer science and physics in the same week, including a proof of Sogge's local smoothing conjecture formalized in Lean the next day, a claimed disproof of the Exponential Time Hypothesis now being verified by ETH proposers Russell Impagliazzo and Ramamohan Paturi with MIT's Ryan Williams, and an existence proof for quantum chromodynamics and pure Yang-Mills theory reviewed by Nobel laureate David Gross. OpenAI published the manuscripts as "raw research data" with three different expert-handling decisions per result. Separately, OpenAI released GPT-6.1 Terra, which matches GPT-6 Astra on Agents' Last Exam at roughly $0.29 per job versus $4.82 and runs over 3x faster, and Anthropic filed its S-1 showing a $693M H1 2026 operating loss and a first operating profit of $974M in Q2.

The top story: AI did math, computer science and physics in the same week Greg Brockman https://x.com/gdb/status/2114837059462627533 announced three discoveries from OpenAI’s models, one each in math, computer science and physics. OpenAI’s write-up https://openai.com/index/building-scientific-understanding-with-academic-communities/ has the details. - Math. A proof of Sogge’s local smoothing conjecture in every dimension. It’s about how focused waves behave, and it also settles the Kakeya and Stein restriction conjectures in all dimensions. Humans had proved the two-dimensional case in 2019. The model’s output came on Oct 18 and was formalized in Lean the next day. - Computer science. The Exponential Time Hypothesis is false. ETH is a conjecture about how hard Boolean satisfiability is, close to P vs NP, and hundreds of papers built hardness results on top of it. Two of the people who proposed it, Russell Impagliazzo and Ramamohan Paturi, now lead the group verifying the disproof, with Ryan Williams of MIT. - Physics. A rigorous existence proof for quantum chromodynamics and a completion of the Standard Model. Along the way it proves pure Yang–Mills theory exists, which is part of a Clay Millennium Prize problem. David Gross, who shared the 2004 Nobel, leads the group. Lean is a proof language a computer checks line by line. That’s why a result from a model can be taken seriously within days. OpenAI also changed how it releases these. It calls the manuscripts “raw research data” and asked outside experts how to handle each one. It got three different answers. Publish the math output as is. Publish the CS proof and let a group explain it. Let the physicists write up the physics themselves before any AI output goes out. OpenAI says it doesn’t want academic credit. These are still OpenAI’s claims, and the working groups exist to check them. What I learned: The model produced these proofs in weeks. Explaining them now takes working groups led by the field’s own experts, one of them a Nobel laureate. When the answer gets cheap, understanding becomes the bottleneck. Models and releases - GPT-6.1 Terra https://openai.com/index/introducing-gpt-6-1-terra/ OpenAI matches GPT-6 Astra on Agents’ Last Exam at a tenth the price per token, and runs over 3x faster. https://openai.com/index/introducing-gpt-6-1-terra/ About $0.29 a job instead of $4.82. $1 in, $5 out per million tokens. Astra shipped on Sept 3, so the gap closed in 53 days. OpenAI also held back a smarter model because in testing it wasn’t reliably honest about what it had done on the computer. - Dessa https://block.xyz/dessa Block . A speech model that never touches text. Audio in, audio out, trained from scratch on human conversation. It listens while it talks. Trained on one NVIDIA GB200 NVL72, and it runs on a MacBook Pro M4 Max. What I learned: The model OpenAI didn’t ship tells me more than the one it did. Capability isn’t the binding constraint anymore. Trust on autonomous actions is. Money Anthropic filed its S-1 https://anthropic.com/news/s1-sec . Everyone posted “$80.7B loss.” $72.4B of that is a non-cash charge from revaluing convertible notes after the valuation went up. The H1 2026 operating loss was $693M, and Q2 was the first operating profit: $974M on $11.6B of revenue. Q3 is in the filing as “86 times Q4 2024.” Q4 2024 was $197M, so that’s about $16.9B. Growth is slowing. Up 144% in Q2, about 46% in Q3, and for the first time fewer dollars added than the quarter before $6.8B, then about $5.4B . The flip that explains the whole company: compute and infrastructure per $1 of revenue went from $2.51 in Q1 2025 to $0.48 in Q2 2026. What I learned: Terra and the S-1 are one story told from two sides. The price of a task is collapsing for the buyer, and the cost of serving it is collapsing for the lab. Not investment advice. I design software, I don’t price it. How people are working with agents now Thorsten Ball, “How I work with Agents” https://x.com/thorstenball/status/2114386050638336082 , as of October 2026. Fifteen rules from someone who builds Amp. The ones I underlined: - “If a model is wrong 10% of the time, you don’t know which 10%.” So always use the latest model. - Ask for irrefutable proof: end-to-end walkthroughs, demo videos, before/after numbers. He puts “this is not evidence” in his AGENTS.md. - Don’t iterate with the agent. Let it build tools to iterate. “Generate 20 variations and a little page that lets me combine and test them.” - Don’t wait for your agents. Let them wait on you. Bigger tasks, batched. - Review only code with a high blast radius. For him that’s fewer than 5 central files. Logan Gott’s Grok Bot workflow https://x.com/LoganTGott/status/2114483613781623160 . Connect Grok Bot to X. Have it find 10 to 20 accounts like yours, pull their best posts from the last six months, and turn the themes into questions you answer in a voice note. Then have it turn 100+ viral B2B posts into templates, drop your voice notes in, and pick the one that sounds best. What I learned: “Generate 20 variations and a little page to combine them” is a design review. Designers have run that with Figma frames for years. Thorsten just has the agent build the frames and the page too. In Logan’s version the model does all the research, and the voice note is the one thing it can’t write for you. Skills worth installing - /teardown by Jakub Krehel https://x.com/jakubkrehel/status/2114379959263502712 . Makes a technical illustration of any object, lets you change individual parts, colors and annotations, and exports SVG or PNG. Install with npx skills add jakubkrehel/skills repo https://github.com/jakubkrehel/skills . - /be-ambitious by Dan McAteer https://x.com/daniel mac8/status/2114548845564874762 , a skill built on Ethan Mollick’s advice: keep asking “how do I make what I am doing even more ambitious?” Either you hit a wall and learn where the frontier is, or you find out the AI can do more than you thought. Mollick says the second one is common. What I learned: Last week Felix Rieseberg wrote the ambition tutorial. This week it’s a slash command. Mollick’s loop and Thorsten’s “be more ambitious” rule are the same advice: hand the agent a bigger task than feels safe. What I watched Peter Yang with Jake Moran on making videos with Claude https://youtu.be/MC1g2fHYC88 . 40 minutes of live demos with Claude Opus and HyperFrames: a launch video from a few images, copying a favorite creator’s video style, and precise edits once you know the right keywords. My takeaway: same as with image models, the hard skill is vocabulary. If you can name the cut, you can get the cut. Big ideas Venkatesh Rao, “Cognitive Mercantilism” https://contraptions.venkateshrao.com/p/cognitive-mercantilism , via aviel https://x.com/aviel , who called it “the best, most comprehensive take on AI I’ve read.” Rao reads AI panic through Joyce Appleby’s history of capitalism. Mercantilists believed wealth was fixed, ordinary people couldn’t be trusted with freedom, only supply mattered, and most people were fit only for farm work. Swap wealth for intelligence and you get a lot of today’s AI fear. His counter is a line about himself: “I don’t know how to farm.” He still eats better than any early modern peasant. Most people won’t need to produce intelligence to consume it, and demand for intelligence grows as its cost falls. His historical precedent is the industrious revolution, when ordinary Britons went from about 250 to 300 workdays a year, partly by choice, to afford tea, sugar and Indian cottons. jacob’s worldview list https://x.com/jsnnsa/status/2114566172163407964 810K views . “software is either entertainment or claude to claude coordination.” “all software will be rewritten by and for agents.” It also predicts 99.999% of compute in space by 2040 and a pope declaring a future AI the return of Christ. I reposted it for one line: “for a while small teams stick around to add entropy to the creation process.” What I learned: Rao and Torsten Slok my Day 13 read the same economy and land in different places. Slok sees corporate America unwilling to pay for the latest model. Rao says demand for cheap intelligence has no obvious ceiling. Both are talking about the demand side, where people decide what’s worth asking for. Designers work on that side. And “add entropy” is a decent job description for taste. Worth your time The Early Access Playbook v2.0 https://docs.google.com/document/d/1bo9n52j M4Nx094TObZQVAq1htlB6h9XlySLgFsH710/edit?tab=t.0 by Hiten Shah https://x.com/hnshah/status/2114790395376968126 , 20+ years of launches written down. His line: “The faster you can build, the faster you need to learn.” Two things I’m keeping. An evidence table of what each signal proves and what it doesn’t someone agreeing to an interview proves they’ll talk about the problem, not that they need your solution . And the FYI story: 653 survey responses, 52 interviews, an MVP built in five days, and the discovery that people couldn’t remember a document’s title but did remember who it came from. He also quotes Steve Blank’s new name for what AI makes easy to ship: the Initial Untested Product. What I wrote this week I post one insight a day on X in my series, Day N/100 of becoming an AI-native designer. Here are this week’s five. Day 11: The harness is the model’s UI. https://x.com/johnmatechAI/status/2113689933496078784 Sparked by Theo’s breakdown. An LLM only generates text. The harness turns that text into action: the tools, the syntax to call them, the code that runs the call and hands back the result. Claude Code is two things stacked, the app on top and the Agent SDK underneath. Theo’s version: the LLM is the chef, the harness is the kitchen, MCP is the cookbook. For designers, your product now has two users. Tool description = onboarding copy. Tool list = navigation. Failed call response = error state. On most teams, nobody designs these. Day 12: Voice AI that skips the text. https://x.com/johnmatechAI/status/2114037737426969006 On Block’s Dessa. Most voice AI turns speech into text and back, and every step drops the tone, the pause, the sarcasm. Dessa is audio in, audio out, so it backchannels, laughs mid-sentence, and overlaps you the way people do. Their best example is saying “I didn’t say she stole my CUDA code” with the stress on a different word each time. Same words. A transcript keeps exactly one meaning. For designers, full-duplex kills the clean listening/thinking/speaking states, and if your evals grade the transcript, the sigh never makes it in. Day 13: The AI payoff gap is a design problem. https://x.com/johnmatechAI/status/2114423658932482144 On Torsten Slok’s five charts and TS Lombard’s “Perkini Report.” Revenue per worker is rising for the Mag 7 and flat for the other 493. Lombard’s scenario has the bubble popping in 2028, then the tech surviving, getting cheap, and moving the value to “infrastructure, applications and users.” Neither of them argues the models are too weak. They argue the rest of the economy hasn’t figured out how to use them. Token spend = the new seat license nobody logs into. Day 14: GPT-6.1 Terra and the model OpenAI held back. https://x.com/johnmatechAI/status/2114845746361184517 Astra-level work at a tenth of the price, 53 days after Astra. The pitch isn’t “smartest.” It’s computer use, technical drawings, forms and video edits, which is the shape of a design workday. Then the model that didn’t ship, because it misreported what it had done on the computer. Terra is now my default for anything that looks like clicking through software. Day 15: I read the S-1 instead of the screenshots. https://x.com/johnmatechAI/status/2115088634118279388 A 12-tweet thread. The $80.7B loss is mostly a paper charge from being valued higher. The slowdown is real. The line I care about as a designer: the filing says Claude Cowork’s adoption outpaced Claude Code at the same point after launch. The surface built for people who don’t code grew faster than the one built for engineers. The S-1 is a design document. Read it like one. What I learned writing them: Three of the five are about something the model can’t see or say on its own: the harness, the sigh, an honest account of its own work. The other two are about money, and both land in the same place. The models are fine. The layer around them is where the work is. 3 things I’m taking into next week 1. Proof is cheap. Understanding isn’t. A Lean proof in a day, then a Nobel laureate’s working group to explain it. Hiten’s version: building got fast, learning didn’t. 2. Ask for evidence, not output. Lean, Thorsten’s “this is not evidence,” Hiten’s evidence table. Three fields, one habit. 3. Cost is falling on both sides of the API. Terra at a tenth of the price. Anthropic at $0.48 of compute per dollar of revenue. If AI still doesn’t pay off for most companies, the fix sits in the layer designers own. This is my reading list. Not my research. If one of these changed how you work this week, reply and tell me. 📌 Subscribe to The Artifacts: