Axis of Ordinary

Cryptography is now under attack from both mathematical superintelligence and quantum computing research. It is probably worth thinking about transferring a modest amount of assets into physical valuables that cannot be hacked.

Mistral Large 4 delivers performance within just 2 points of Claude Opus 4.8 (High) at a nearly 6× lower blended price: $3.47/M vs. $20/M tokens: https://arena.ai/leaderboard/code/webdev The cool thing here is that they achieved this with merely 4,000 Nvidia Grace Blackwell GPUs. For comparison, GPT-6 Astra was trained on 100,000 of them. --- I really hope Mistral doesn't give up. Even if European AI stays uncompetitive, it's very important to at least have a fallback option to ease exposure to foreign blackmail based on withholding access.

OpenAI is releasing a broad range of new mathematical results produced by an internal frontier model. The current catalogue contains 722 manuscripts organized into 372 families. On average, each result used three hours of ChatGPT Pro thinking compute with that model. Over the course of the evaluation, the model was posed approximately 4,000 problems. Read more: https://github.com/openai/math

I knew that I had come across the name John Urschel earlier today. He doesn't look exactly as I would have pictured him.

More links: 1. The experimental research taste of frontier models has doubled every ~3 months since December 2025. The best model, Opus 5.5, now exceeds the expert human baseline. https://www.lesswrong.com/posts/bAGagjZAPgXEHmkAH/tasteval-measuring-the-experimental-research-taste-of-ai 2. Current AIs out-persuade professionals in lab settings but (probably) not in the world https://www.lesswrong.com/posts/CzmMvnPy7YdSRucDH/current-ais-out-persuade-professionals-in-lab-settings-but 3. Amazon AGI presents Adaptively Looped Diffusion Language Models https://alo-dlm.github.io/ 4. Hackers Use Chinese AI Tool to Hit South Korean Banks, Exposing New Risk https://www.wsj.com/world/asia/hackers-use-chinese-ai-tool-to-hit-south-korean-banks-exposing-new-risk-5d4d3885 [no paywall: https://archive.is/mcL8S] 5. Formalizing Hironaka’s Resolution of Singularities https://resolution.org/post/formalizing-resolution-of-singularities 6. Eleven-square packing in Lean https://github.com/Queuingtheorydotcom/11SquaresFormalized 7. The human brain is approaching its ChatGPT moment. A manifesto on how brain computer interfaces can help align AI and preserve human agency. https://phaselock.satpugnet.com/

I wouldn't be surprised if Zelensky got a call from some European capital that they have permission to do this as retaliation for the Russian attack against Bulgarian ships. The timing here is just too suspicious.

The wave of AI science/math collaborations is rising: 1. In 3 days, 90+ Opus 5.5 agents helped uncover two room-temperature magnetic semiconductor candidates in simulations: YBaMnFeO₅ and KV[Cr(CN)₆]. https://www.vals.ai/blogs/room-temperature-magnetic-semiconductors 2. Faster algorithms for 3SUM and shortest paths. Josh Alman and Virginia Vassilevska Williams report breaking longstanding theoretical running-time barriers. Their paper says Claude discovered the core algorithm; the researchers then simplified and extended it. https://arxiv.org/abs/2610.06783v1 Computer-checkable proofs for those algorithms via Anthropic’s public Lean formalization cover the main integer-input results. Its documentation explains which additional claims are covered and which remain outside the formalization. https://github.com/anthropics/formal-math/tree/main/3sum-apsp 3. A decades-old conjecture about Gaussian elimination. John Urschel reports resolving a conjecture explaining the stability of a widely used method for solving equations on Gaussian random matrices. AI helped extend his initial proof sketch; he wrote the manuscript. https://arxiv.org/abs/2610.06785 4. KLS conjecture: Song and Zhang. A claimed solution to a major problem in high-dimensional geometry and probability. The authors describe exploring more than 100 approaches through collaboration with OpenAI and Anthropic models. https://arxiv.org/abs/2610.01447v2 5. KLS conjecture: Bizeul, Klartag and Lehec. Another claimed proof, building on Song and Zhang’s criterion. The authors credit ChatGPT with most proofs and mathematical ideas, while identifying a key idea they supplied themselves. https://arxiv.org/abs/2610.05474 6. KLS conjecture: Balasubramanian and Kasiviswanathan. A further manuscript claiming a dimension-independent bound that would establish KLS. The authors describe substantial AI assistance in developing the argument. https://github.com/kriznakumar/paper/blob/main/KLS.pdf 7. Infinite towers of arithmetic surfaces. Timo Keller and Carlo Pagano report answering several questions in number theory and geometry. AI collaboration helped complete a strategy they had developed since 2022. https://arxiv.org/abs/2610.06461 8. An independent arithmetic-surface construction. Pablo Chenal gives a related, shorter existence proof and discloses that the example emerged through discussion with ChatGPT Astra. https://arxiv.org/abs/2610.05972 9. Planar Mumford–Shah conjecture. Francesco Deangelis claims a solution to a problem concerning boundaries in a mathematical model for image segmentation. He says ChatGPT Astra generated the initial strategy and draft through exchanges using background material he supplied. https://arxiv.org/abs/2609.26732v2 10. A counterexample to the Griffiths conjecture. Yun-Heng Du and Song-Yan Xie report a counterexample concerning positivity and curvature in complex geometry. They developed the initial framework and used AI to explore, test and refine the construction and proof. https://arxiv.org/abs/2609.26504 P.S. OpenAI is rumored to release hundreds of results soon.

French Mistral releases Mistral Large 4, aka Le Chonk. • 1T parameters, natively multimodal. 49B active. It is the best open weights model from US or Europe on aggregated benchmarks. • State-of-the-art on critical workloads, including cyber defense, manufacturing and finance and it surpasses closed frontier models on visual grounding. • Forged in Europe end-to-end and is deployable from Europe via our own Mistral Cloud infrastructure. • Available to all via API today. Working with cybersecurity partners privately. Open weights release end of October.

France just tested its newest M51.3 ballistic missile. One missile carries multiple independently targetable warheads. 10,000 km reach. Over 2,000 km altitude. 20,000 km/h on re-entry. A single French submarine can carry the explosive yield equal to 640 Hiroshima bombs.

Kind of tough for Russian propaganda to deal with. Do you let it stand that Ukraine is hurting Russia badly or do you defend Zelensky by calling out Trump's bullshit?

What's interesting about Brazil is that it shows that a white minority country can still elect a right-wing populist leader.

I had Claude scroll TikTok, then I gave it 200 bucks and asked for a music video 9 hours later it came back with this...

https://x.com/pleometric/status/2106515430529548579

During the Iraq war under Bush, a major argument was that Westerners did not care about those affected because they were not white Christians. Firstly, the anti-war rallies of 2003 were the largest protests in history, with over 15 million people attending, the vast majority of whom were American allies. And the war is now widely regarded as a huge misstep based on lies throughout the Western world. How many Russian allies protested against the invasion of Ukraine? Close to zero. And I strongly doubt they would care at all if Putin officially announced he was going to genocide every single Ukrainian tomorrow. Secondly, have you actually checked how much the majority of the Western political right and a big chunk of the left care about Ukraine? Not a single day goes by when I don't come across a comment by some German AfD voter demanding Russia to nuke Ukraine. Meanwhile, the political left is obsessed with Palestine. Despite dozens of Ukrainian cities and towns being reduced to ashes, they don't demand resistance but surrender. Ukrainian being white Christians didn't make them care more. In fact, it made them care even less than they cared about Iraqi Muslims. The only factions half-heartedly supporting Ukraine are some unpopular centrist politicians.

Tucker Carlson on Russia controlling its neighbors: "The state of play for all great powers." Tucker Carlson on US troops being stationed in Britain by invitation: It cost your country "your sovereignty and your self-respect." Jacob Rees-Mogg: "They're allies, we're in NATO together… they're very welcome here." Invading Ukraine: normal. Invited allies: occupation.

Imagine a Ukrainian biolab tech died of plague and 200 people were put in quarantine in a major Ukrainian city: https://www.axios.com/2026/10/04/russia-plague-outbreak-white-house-us Imagine a Ukrainian warlord and his mercenaries had marched on Kyiv, capturing a major Ukrainian city on their way: https://en.wikipedia.org/wiki/Wagner_Group_rebellion Imagine Ukraine had effectively banned major Western social networks: https://www.hrw.org/report/2025/07/30/disrupted-throttled-and-blocked/state-censorship-control-and-increasing-isolation Imagine Kyiv had a major Islamist terror attack with 151 deaths: https://en.wikipedia.org/wiki/Crocus_City_Hall_attack Imagine Zelensky had kissed the quran in front of a Muslim warlord: https://en.mehrnews.com/news/219987/VIDEO-Putin-kisses-holy-Quran-in-Chechen-mosque Imagine a mob had stormed a Ukrainian airport looking for Jewish passengers arriving from Israel: https://apnews.com/article/russia-dagestan-tel-aviv-flight-airport-makhachkala-fa06b16131ed41c0c789981cdcaac84f Imagine a Ukrainian warlord had publicly released footage of his son beating a 19-year-old detainee accused of burning the quran: https://www.reuters.com/world/europe/court-russias-chechnya-sentences-man-3-12-years-koran-burning-tass-2024-02-27/ Imagine operatives linked to a Ukrainian warlord had abducted a blogger from a central Kyiv railway station and beaten him, and, according to investigative reporting, walked away without charges while the blogger himself was prosecuted: https://novayagazeta.eu/amp/en/articles/2025/06/10/chechen-operatives-who-abducted-blogger-at-moscow-train-station-avoid-criminal-charges-en-news Imagine Ukraine had pardoned a man convicted of involvement in murdering a leading opposition politician in exchange for joining the war: https://www.reuters.com/world/europe/convict-kremlin-critic-murder-released-jail-fight-ukraine-agencies-2024-08-10/ Imagine Ukraine had sentenced three lawyers for a leading opposition figure to years in prison for helping transmit his messages from jail: https://www.reuters.com/world/europe/three-navalny-lawyers-jailed-belonging-extremist-organisation-mediazona-news-2025-01-17/

More links: 1. Agentic Meta-Reasoning: Let the model decide what to explore, what to build on, what to verify, and where to spend its next unit of compute: effectively constructing its own computational graph as it reasons. https://arxiv.org/abs/2609.38147 2. Combining the power of the “universal grammar” workspace (text summarization of feedback) with the standard activation space utilized by backprop. RLTL;DR: Self-improvement by Internalizing Self-generated Feedback https://arxiv.org/abs/2609.37633 3. Learning from Research: Toward Lifelong Agent Harness Evolution https://arxiv.org/abs/2609.40169 4. VeriHarness: Scaling Agentic Verification for Long-Horizon Tasks https://arxiv.org/abs/2610.00972 5. Timothy Gowers: "Another interesting perspective, from someone whose predictions about maths and AI have aged better than pretty well everyone else's." https://docs.google.com/document/d/e/2PACX-1vTSh-pyNP3Gi99WMmsinnLmE9V5CDI0HEm6WGbIPMNt3V5SGlClHF8-BetotKHOImrvQDSXmFdiOw8D/pub 6. Germany's Aleph Alpha releases open weights model Kolibri https://aleph-alpha.com/downloads/tech-report.pdf 7. ANY DAY NOW- The robots are coming (SLOPCORE) https://www.youtube.com/watch?v=-wS4lHfqsbc 8. Deep time art: 40,000-year-old mammoth ivory lion-human sculpture https://en.wikipedia.org/wiki/Lion-man_of_Hohlenstein-Stadel 9. “Russia and Ukraine are inventing the future of war”: former Google CEO Eric Schmidt https://www.youtube.com/watch?v=KgJI4Wxqqik