Friends, followers, and strangers on X, I recently got excited about mapping the jagged frontier of AI models in math and other STEM areas. With my colleague Prof. Rob Ghrist @prof_g , I founded Rabdos AI rabdos.ai to create original, research-level problems at scale to advance frontier AI capabilities. In the coming weeks, we'll be sharing exciting technical updates through @Rabdos_AI. Please give us a follow if you're interested in model evaluation, AI for math/science, autoformalization in Lean, robustness of world models, and much more.

The status quo for R1 institutions cannot last. I'm guessing there will be a barbell distribution of focus that splits the classical research/teaching fusion we currently enjoy. A few OOM of improvement in AI and we might see: 1. The research side goes industrial -- applied mathematicians producing enormous bodies of interdisciplinary work; physical science labs running in warehouses with heavy robotics and automated data collection and processing; economics and social science simulations at extreme scales... 2. Teaching is top-quality, high-touch, personalized-service, with courses becoming works-of-art and top professors being superhuman performers and guides. In short, each end of the research-teaching axis taken to extremes. There are hints of this divergence already. At Penn, the two top schools (by $$$ & prestige) are the medical school (no undergraduate teaching; lots of heavy lab-based research at scale), and the business school (almost all teaching, highly profitable, most research occurring in pockets like the stats department at wharton). Ramp that split with AI improving 100-fold and more, and we will see a vast bimodal transformation that integrates the university more with industry (large scale research) and serves students better (extremely attentive teaching).

Congrats to Anthropic on shipping Claude Opus 5.5! Here's an especially noteworthy article by Boris Cherny on using this model to formally verify the Claude Agent SDK using Lean. Rabdos is an industry leader in creating high-quality Lean data; check out our benchmark at rabdos.ai/math-index/lean

Congratulations to Anthropic on the release of Claude Opus 5.5! 🎉 At Rabdos, we spend our days thinking about the hardest problems in math and science, so it's exciting to watch frontier reasoning keep advancing this quickly.

📣 We're growing our team at Rabdos AI! We're looking for a 𝗥𝗲𝘀𝗲𝗮𝗿𝗰𝗵 𝗘𝗻𝗴𝗶𝗻𝗲𝗲𝗿 to lead our work on mathematical formalization in Lean. You'd turn informal math into formal proofs and build autoformalization pipelines alongside frontier AI models, working with some of the sharpest mathematicians and computer scientists I know. If you love Lean, rigorous math, and hard open problems, I'd love to hear from you. Please share with anyone who comes to mind! 👇

Are endpoint protection systems like CrowdStrike prepared for large-scale agentic workloads? My research group has been running 100's of codex agents in parallel on a machine this summer. The agents are not coordinating (or at least aren't supposed to): each works on an independent research task in a STEM domain such as math, SWE, materials, biochem, ... In a matter of days, they have started tripping conventional security software in ways that have alarmed IT folks and are very hard to debug. The only solution seems to be to isolate the machine from the network, but that cuts off the agents from even basic web search. This and recent incidents of agents running amok at frontier AI labs present a massive opportunity for research and startups in AI x security. How do we specify / enforce security policies for agents? How do we triage alarms? Seems especially difficult since good vs. bad behavior is superficially indistinguishable : agents exploring how to use a low-level systems tool could be misconstrued as trying to breach security; a sequence of such seemingly random tool calls would pose an even greater challenge. Feels like the early days of the wild west, and a harbinger of things to come ...

Every year I take an international trip, I measure in-flight internet connectivity as an indicator of global technological progress. 2026 represents a *huge* step up in this measure, entirely single-handedly due to @Starlink. They have essentially solved this problem from 0 to 1.

Check out Rabdos Math Index! A holistic benchmark for math x AI that draws from our experience supplying math data to frontier AI labs over the last six months. Comprises graduate-level theorems formalized in Lean and checked by semantic rubrics, research-level problems with single numeric answer, and problems requiring visual reasoning over mathematical figures. DM me or email contact@rabdos.ai for more info!

THE SYMPOSIUM PUZZLE: The final dinner of the symposium was less a banquet than a convergence theorem that had failed to be uniform. Five luminaries -- Hardy, Poincaré, von Neumann, Gödel, and Ramanujan -- sat in a row at the head table, each in a different jacket, each with a different drink, each newly returned from a different lecture tour, and each guarding a different mathematical instrument as though it were a proof of the Riemann Hypothesis. Hardy sat brooding at the far left in herringbone, one hand curled around an espresso, the other resting upon an antique abacus whose beads he refused, on principle, to move. Immediately to his right sat a severe scholar in charcoal, upright as a metronome and no more companionable. Poincaré, ever the classicist, wore tweed. Farther down the line, Ramanujan (newly back from Göttingen) sat resplendent in navy, sipping tea and turning a golden compass over in his fingers as though it might draw identities straight out of the air. The navy jacket sat immediately to the left of the pinstripes, a juxtaposition that pleased no tailor present. The guest who had lectured at Cambridge, meanwhile, was the one in herringbone. When the conversation turned from foundations to apparatus, the scholar fresh from Princeton began boasting of a brass astrolabe he had recently acquired. Seated right next to him, the Göttingen speaker sneered that the workmanship was inferior to what one found on the Continent. Not to be outdone, von Neumann slapped an ivory slide rule onto the table with algorithmic enthusiasm. Gödel, with characteristic gravity, raised a glass of port in a toast that seemed prepared for its own incompleteness. The scholar just back from Oxford preferred brandy and, being full of it, soon leapt onto the table to make a point that no one had invited. In the ensuing disorder, a fellow guest's black coffee went flying. That black coffee, in the left-to-right order of cups along the table, had been sitting somewhere between Hardy's espresso and Ramanujan's tea. By morning the hall was deserted. Under the table lay four instruments: the antique abacus, the brass astrolabe, the ivory slide rule, and the golden compass. The silver caliper was gone. Who possessed each instrument -- and who had been carrying the missing silver caliper?

MathDuels update: Gemini-3.5-Flash ranking #4, surpassing GPT-5.2 & Claude-Opus-4.7 Impressive performance for its speed & size.

nice math problem i came up with last december... Consider a cube of side length 2, aligned with the coordinate axes. Place three cylinders inside it, each of height 2 and radius R, each aligned with some coordinate axis. The cylinders may not intersect. What is the maximal R?

Incredibly proud of PhDs #8, #9, and #10 -- congratulations Drs. Jiani Huang (@jiani_huang_ai), Aaditya Naik (@aaditya_naik), and Adam Stein (@adamlsteinl)! I am lucky and grateful for the privilege of working with the three of you!

Very excited to share a new milestone in AI for Math: Aletheia, powered by Gemini Deep Think, was just used to autonomously solve a Kirby problem! “Kirby’s list” is a “compendium of the most important unsolved problems in topology, the study of deformable shapes” (Quanta magazine). 🧵

We are delighted to unveil our research blog Rabdology at rabdology.ai, where we chart the jagged math-frontier of AI reasoning. This is our first post in a weekly series. Read on, and if you enjoy it, please subscribe! (Link at bottom of blog's main page.) The Three-Cylinders Problem: When AI models choose Beauty over Truth rabdology.ai/three-cylinders We pose a problem that a good geometry student can solve in twenty minutes. We gave it to four of the world’s most advanced AI models and watched what happened. Three of them got it wrong — and the way they got it wrong tells you something different about the state of AI mathematical reasoning than the usual benchmarks.

Very timely, especially in light of revelation that 1/3rd of problems in FrontierMath are fatally flawed. As expert human validation of frontier math tasks approaches its inevitable limit, LLMs are stepping in to fill the void. But our work below shows that the discovery of mistakes in FrontierMath problems didn't necessarily have to wait for a frontier model like GPT-5.5. Much smaller and even open-source models can be as effective at verifying math proofs: their weights embody the necessary knowledge, as one might expect -- checking proofs ought to be easier than writing proofs. The crucial thing that makes this work is the use of "prompt ensembles", each of which modularly checks a different facet of a given proof, and some of which are even specific to the domain/sub-domain of math. Ideas like meta-prompting, agent skills, and autoresearch will undoubtedly evolve to make LLMs as judges of math proofs even more effective in future.

I feel sorry for either this person or their PhD advisor for them to say "The thing that still matters —> taste <— was never really taught". This is *most* of what my advisor taught me; the rest (semantics, coding, etc) was just hard work; he answered questions and gave feedback.

I've just finished a week where I have been using agentic workflows basically 24/7. Here are some impressions: 1. I am extremely tired. Supervision of so many projects is distracting, frustrating and exhausting. 2. I have never worked on so many fronts at once. It's not only a superficial impression. I've read a ton, did courses with students, coded, learned new mathematical theorems, explored new git repos. 3. The more you work with agents, the better you become at instructing them. Don't overthink the prompts. Doing things step by step and letting the agent guide you is very productive. 4. I failed in some of those projects. Basically I got the impression that I could do everything with the agent. Maybe, but time and tokens are constrained. 5. I don't use much ready made software anymore. I build or scaffold stuff that I need. My favorite modality is text and best interface is simple text API. Everything can be pipelined. 6. Mathematics can be treated as software. Whatever you need to do with it, it can be decomposed into small parts. The thinking bit is still mostly done in my brain if necessary. 7. I think of my past life as a warm-up for this new period. The offline reading, coding and internalizing was super important. Without it, I would be a pure vibe-coder. With training, you sail a ship. 8. I don't want to see my paychecks. It's expensive, because the better you get, the more you spend on more and more projects. You abandon them in a more advanced state, but there is a token price to pay. 9. Each time I see a challenge, I think whether I can find a solution with the agent. I don't skip tasks. Sometimes I feel overly optimistic. It's part of the learning to see where the agents are limited. 10. I think I master entirely new workflows. They are not properly described in the books. It's a brave new world. Each standard task can be turned into a task for the agent. It's very enabling. Happy coding everyone!

In MathDuels leaderboard, Gemini-3-Flash dominates at its size: the only models ahead of it are the latest, largest frontier releases. Gemma-4-31b-it has the highest author rating of any opensource model. Thanks @GoogleDeepMind for these smart little models 🥹

Excellent idea. A revival of mathematical duels but in the AI form. Which model is the best problem composer and which one solves problems with no trouble. And the judge is a human professional.