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In Today’s Issue:
🧮 Axiom and OpenAI make math breakthroughs a daily event
📈 Anthropic opens its books for a Nasdaq IPO
🖥️ OpenAI's GPT-6.1 Terra brings cheap, fast computer use
🌍 Google's Genie 4 builds practice worlds for robots
✨ And more AI goodness…
⚡ The Signal
AI spent Monday and Tuesday showing its work.
Axiom's agents turned the longest proof humans have ever written into one a computer can check line by line, and OpenAI and Anthropic each published a Lean-checked refutation of the Exponential Time Hypothesis, found independently on the same day. A machine-checked proof settles whether the logic holds; explaining what a result means still takes people, which is why OpenAI handed its claims to outside experts, including a Nobel laureate. On the business side, Anthropic opened its books for its IPO and OpenAI launched GPT-6.1 Terra. In mathematics, the slow part is now the reading.
All the best,
Kim Isenberg
(REUTERS/Dado Ruvic/Illustration)
📈 Anthropic Opens Its Books for a Nasdaq IPO
Anthropic has publicly filed its S-1 to list on the Nasdaq under the ticker "ANT", and its prospectus shows soaring sales and a core business that has swung to an adjusted profit. Revenue rose 1,368% year over year in the quarter to June 30, and adjusted operating income swung to $1.62 billion in the first half from a $1.85 billion loss a year earlier. The headline net loss of $80.7 billion stems mostly from a non-operating item tied to convertible bonds, while the real long-term bill is more than $600 billion in compute commitments with partners such as Amazon and Google. Some investors now value the company at about $1.5 trillion, according to Reuters, and the listing is expected before Thanksgiving.
👉 tl;dr: Anthropic is about to go public, and its filing shows booming sales and a core business now profitable on an adjusted basis, alongside enormous bills for computing power.
(OpenAI)
🖥️ OpenAI's GPT-6.1 Terra Brings Cheap, Fast Computer Use
OpenAI has released GPT-6.1 Terra, a fast, low-cost model built to operate software on screen, from filling out forms to editing videos. On Agents' Last Exam, a benchmark of professional computer tasks, it scores 15 percentage points higher than GPT-5.6 Terra at medium effort for about a third of the cost, and performs on par with the flagship GPT-6 Astra at a tenth of its price per token. Claude Opus 5.5 still scores higher on OpenAI's own chart, but at max effort OpenAI puts Terra's cost per task about nine times lower. API pricing is $1 per million input tokens and $5 per million output tokens, and the model is rolling out to Plus, Pro, Enterprise and Edu users in ChatGPT Work and Codex.
👉 tl;dr: OpenAI's new lower-cost model can handle everyday computer work, such as forms and invoices, about as well as its flagship at a fraction of the price.
(The Irish Times)
💸 Meta Plans a $95 Billion Stock Sale to Fund AI
Meta plans to raise $95 billion by selling new shares to pay for its AI infrastructure, with Nvidia, AMD and Broadcom signing on as cornerstone investors. It started on Monday with $35 billion in underwritten public offerings and plans another $60 billion through an "at the market" program that sells shares gradually. The raise follows a quarter with 26% sales growth and a forecast of up to $145 billion in capital spending this year, after Meta warned it would need "hundreds of billions of dollars" over several years for its AI bet.
👉 tl;dr: Meta will sell up to $95 billion of new stock, partly to the chipmakers it buys from, to keep building AI data centers.
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🎬 Watch This
Ken Ono, the number theorist who works as Axiom's founding mathematician and contributed to today's classification proof, explains how being outpaced by AI changed what he thinks intelligence is. In this EO interview he recalls struggling to write math questions ChatGPT would get wrong, then argues that knowledge has become cheap while knowing how to use and verify it has become expensive. He tells the story through his father, Ramanujan and the student who later became his boss, Axiom CEO Carina Hong.
"The core algorithm was found on October 16 by an internal Claude research model with 14M output tokens and no human input."
– Anthropic's paper refuting the Exponential Time Hypothesis, shared on X by Anthropic researcher Levent Alpöge
OpenAI's model found its own disproof of the same hypothesis on the same day, October 16. Two labs, working separately, reached the same surprising result, and both published Lean proofs for experts to check.
John Carmack poured cold water on robot-apocalypse fears with a Halloween test: no robot in the world, he wrote, can change the batteries in a jack-o'-lantern. Opening the battery pack and turning four tiny screws is still beyond general-purpose machines, so he suggests near-term doomer scenarios stop at "secretly controlling humanity".
Axiom Checks Math's Longest Proof as OpenAI Claims Three Breakthroughs
The Takeaway
👉 Axiom's AI agent swarms produced the first complete computer-checked proof of the Classification of Finite Simple Groups, a theorem whose proof runs roughly 15,000 pages, in 24 days.
👉 The check surfaced 34 noteworthy deviations from the published proof and produced a new theorem in group theory.
👉 OpenAI says its models proved the local smoothing conjecture in every dimension, refuted the Exponential Time Hypothesis and built rigorous existence proofs for theories including QCD; Anthropic says Claude refuted ETH independently on the same day.
👉 Independent expert groups, not OpenAI, will examine and explain the claims, and the math and computer science proofs are already public in Lean.
Within a day of each other, AI labs delivered some of the most ambitious results mathematics has seen in years, backed by proofs a computer can check line by line. OpenAI announced three new results in mathematics, computer science and physics, and Axiom Math released the first complete computer-checked proof of the Classification of Finite Simple Groups (CFSG), a theorem so long that mathematicians nicknamed it "the enormous theorem". Breakthroughs that once defined a decade now arrive between two news cycles.
(Axiom Math) Every finite simple group belongs to one of these families or is one of 26 sporadic groups, the largest being the Monster.
The classification is the periodic table of symmetry: it lists the building blocks from which every finite group is made. Its human proof sprawls across roughly 15,000 pages in more than 500 articles by about 100 mathematicians. Over 24 days, Axiom's team directed swarms of dozens of AI agents that rewrote it as about 43.1 million lines of Lean, a programming language in which a computer verifies every logical step, with Richard Lyons and Ronald Solomon, who worked on the original classification, advising on the hardest gaps. The machines found 34 noteworthy deviations from the published record, and repairing the largest, in the Unbalanced Group Theorem, yielded a new theorem in group theory.
(Axiom Math) Axiom's dependency graph of the formal proof, with the final classification theorem at its center.
At OpenAI, internal models produced a proof of the local smoothing conjecture, a 1991 question about how briefly waves can stay sharply focused, in every dimension, which would also settle the Kakeya and Stein restriction conjectures in all dimensions. A second result claims to refute the Exponential Time Hypothesis (ETH), the widely used assumption that the logic puzzle 3SAT needs exponential time to solve. Anthropic says an internal Claude model found its own refutation on the same day, October 16, and has published the paper and a Lean proof as well. The third is a rigorous existence proof for certain four-dimensional quantum field theories, including QCD, the theory of the strong force, and pure Yang-Mills theory, whose existence is one part of a Clay Millennium Prize problem. MIT's Ryan Williams, who is co-leading the independent review of the ETH claim, spelled out the stakes:
The results now go to outside experts. OpenAI says it seeks no academic credit and has picked shepherds for each: Williams and two of ETH's original proposers, Russell Impagliazzo and Ramamohan Paturi, for computer science, and a group led by Nobel laureate David Gross, which will write up the physics result itself. Lean checks the logic, but humans still have to confirm that each formal statement says what mathematicians mean, a step Axiom describes openly. Even so, in the space of a day, AI delivered a machine-checked version of the longest proof humans ever wrote and claimed answers to three long-open questions.
Why it matters: Mathematics has become the clearest test of whether AI can produce new knowledge that anyone can check. With machine-verified proofs attached, the bottleneck moves to the people who have to understand, explain and build on them.
Sources:
🔗 https://axiommath.ai/research/the-enormous-theorem-formalized/
🔗 https://t.co/9BX8HWQDTJ
🔗 https://openai.com/index/building-scientific-understanding-with-academic-communities/
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The chart: Artificial Analysis maps how far Microsoft AI's MAI-Image-2.7-Preview trails the best image editor in each of ten use cases on its AA-Image-Editing v2.1 leaderboard, in Elo points from its Image Arena preference votes (0 means it leads the category). The new model sits at the top in UI/UX Design, Consumer, Live-Action Film and the category AA calls Frontier, within 14 points in four more, and trails most in Marketing & Advertising (−62) and Retail & Ecommerce (−46). Its August predecessor, MAI-Image-2.6 (dotted line), sits well inside that outline almost everywhere.
The lesson: Microsoft's in-house image editor now ranks #2 overall, just behind OpenAI's GPT Image 2.5 Sunburst (max), and first on four of the seven editing actions AA measures, including text edits and restoration. For interface mockups, consumer photos and film frames, Microsoft now offers frontier quality; for ads and product shots, the best tool is still elsewhere. The biggest gains over 2.6 came in composition (+57 Elo) and text edits (+49).
The caveat: This is a preview, available only for editing in MAI Playground, with text-to-image announced as coming soon. Arena Elo reflects human preference votes as of October 25 and can still shift as more votes come in.
🌍 Google's Genie 4 Builds Practice Worlds for Robots
⚡ Bottom line
Google DeepMind unveiled Genie 4, a world model that generates photorealistic, interactive worlds with sound and speech in real time.
💡 Why it matters
Robots need far more practice than real labs can safely supply; Genie 4 can simulate those situations on demand.
🔎 What it means
Simulated worlds steered by Gemini could become the place where robots rehearse a task before touching anything real.
Google DeepMind's new Genie 4 turns a text prompt into a world you can move through in real time, and DeepMind wants robots to learn inside it. Announced today, the world model generates photorealistic scenes with believable physics, people who move and react naturally, and, for the first time in the Genie series, native audio, including dialogue. Users steer with keyboard controls and plain-language prompts: change the weather, move the camera, add a person or an object.
(Google DeepMind) Gemini 4 Argon breaks a checkers game into steps (left) while Genie 4 simulates Apptronik's Apollo humanoid playing it (right).
The robotics part is where Gemini comes in. While Genie renders the world, Gemini 3.8 Flash watches each frame, breaks a goal into steps and checks whether each step succeeded, changing the plan when the world or the user changes. In one demo, Gemini 4 Argon splits a game of checkers into steps that Genie renders as Apptronik's Apollo humanoid playing a person; in another, a simulated lab robot arm lowers a pipette into a sample plate.
(Google DeepMind) A simulated robot arm in Genie 4, with Gemini's reasoning steps tracking each stage of the task.
Robots learn from experience, and real experience is slow, costly and sometimes risky to collect. Fiddly physical work, the kind John Carmack mocks with his jack-o'-lantern test in today's Rumours, needs enormous amounts of practice. DeepMind pitches Genie 4 as a way to create "safe, infinitely variable simulations" for training robots and agents, so a machine could rehearse a thousand kitchens, labs and warehouses before entering one.
For now Genie 4 is an early research preview for trusted testers, with Google AI Ultra subscribers in Project Genie and early Gemini API partners next in line. DeepMind calls simulating the world "a crucial aspect of building AGI", and Genie 4 is its most realistic practice world yet.
