Jon Turow

@CarinaLHong and @byroncook had so much wisdom to share here. Most of the industry agrees there’s a ceiling “somewhere” in how sophisticated reasoning models can become with our current technical approach. Byron and Carina are pushing hard on one of the best vectors around to crash through that ceiling.

What a great evening of technical conversations about the future of AI reasoning with @axiommathai @BCapitalGroup and @MadronaVentures. To anyone who thinks formal verification is a far away sci fi tale, it’s happening right now.

AxiomProver keeps getting stronger. And @axiommathai keeps growing. I'm excited to share that Prof. Ken Ono @KenOno691 has joined Axiom as Founding Mathematician and FTE #15. He left his tenured position as STEM Advisor to Provost at UVA to build an AI mathematician with us. Here's Ken's story. (1)

@CarinaLHong and Axiom have a bold, fresh and exciting approach to AI reasoning. Plus one of the most talent dense early teams I have seen. And now we’re thrilled to welcome @KenOno691, UVA’s Marvin Rosenblum Professor of Mathematics and one of the most cited number theorists globally, to Axiom. wsj.com/tech/ai/math-k…

I had the pleasure of chatting with @TheTuringPost about all things Axiom and AI4Math! Tune in: - How I define AGI vs domain specific ASI, the plate metaphor, can a chatty or poetic model prove the Riemann Hypothesis, and math’s incredible transfer learning power to coding and engineering - Why an AI mathematician needs both proofs and constructions capability, mapping to the two branches of Axiom: formal proving, and specialized discoveries - Data scarcity compared to code, the chicken-and-egg problem of autoformalization, Axiom’s bold synthetic data bets, and how we think about new knowledge generation - Problem-Solving vs Theory-Building, why "Theory Building" is harder to benchmark than the International Math Olympiad (IMO), and why literature search / retrieval, so emphasized by LLMs today, is unsatisfying turingpost.com/p/carina

There are roughly 1,100 problems in the Erdos canon, compiled from decades of papers. They've guided serious research in combinatorics and number theory for generations. Of those 1,100, only 266 have ever been proved. And only 10 have proofs fully formalized in Lean. Axiom just added two more to that list of 10. Problem #124 is an additive number theory question about representing integers as sums of powers across multiple bases. It stayed open for ~30 years. Problem #481 is even older, from 1980. It asks whether a certain iterated arithmetic process must eventually produce a repeated element. Deceptively simple to state, but Erdos and Graham themselves wrote that it was "surprising" how difficult it turned out to be. Open for 45 years. A few weeks ago, OpenAI claimed GPT-5 solved Erdos problems, only for the community to point out it had just retrieved existing literature. Axiom actually solved it, with Lean that checks proofs down to foundational axioms. Every step must type-check. There's no hand-waving. Axiom is late to the game, with a fraction of the resources, and they're producing proofs that major labs aren't able to solve.

If you care about the next frontier of reasoning — not just faster LLMs, but systems that formalize, prove, and conjecture — Axiom is building it. An invitation to work on the hard, beautiful problems. A key piece is construction-driven discovery: the examples that seed conjectures, guide proof strategies, and surface structure we don’t yet understand. Axiom’s new post describes their tools for this — PatternBoost, Int2Int, and early mathematical world models.

@art_of_philo @CarinaLHong @axiommathai Cool story bro.

I literally don't care enough about your budding fails in itself; it's just another of many. What I'm saying is philosophically sound (and you have no response to it), regardless of how you move the goal-posts. All AI is massively hyped at this point, with fluffy claims that are demonstrably not true. It often takes time, but the truth does come out. This is a big game of musical chairs, and people like you will probably have your chair locked up by the time the music stops, but countless others are going to get screwed. I post only to try to keep some others from following people like you off the cliff.

Today, I am launching @axiommathai At Axiom, we are building a self-improving superintelligent reasoner, starting with an AI mathematician.

@art_of_philo @CarinaLHong @axiommathai Will leave this here for posterity, for when you claim you didn’t say it. Cheers.

No claims? LOL. I'm not the one hyping yet another failed-in-principle AI. It's failed-in-principle because its founder presumes that "axioms" and algorithms can advance mathematics. You mention "logic," but you apparently don't know the relation between logic and mathematics, and you apparently haven't read Gödel with understanding. If all this AI is seeking is more decimal digits of Pi, well, more power to you. But that is NOT how this is being hyped. If you want a "claim" from me, it is simply this: Mathematics does not reduce to logic, and for sufficiently complex formal systems (such as frontier mathematics and polyadic predicate logic with identity) it has been deductively demonstrated that proofs cannot be algorithmically produced. For example, a proof (or disproof) of the Riemann Hypothesis cannot be developed algorithmically. Humans are doing something "intuitive" and non-algorithmic when producing proofs in complex systems. There are implications that go far beyond the scope of this post (or discussion), but there are deep weeds here that no AI is going to mow through. Of course, the word "advance" is malleable, so people with vested interests in this start-up will just keep moving the goalposts as necessary and keep the hype going. But this is just another failed-in-principle project. But, just tack the term "AI" onto anything, and investors fall all over themselves to pour money into it. The bubble will burst. This is like watching a slow-motion train wreck. I hope you can stay cool and take care.

@art_of_philo @CarinaLHong @axiommathai Your second post in a row with no claims. Same info density as the rest of your feed. Cool story bro. Take care.

@jturow @CarinaLHong @axiommathai You couldn't possibly have more missed the point! You're to be forgiven for your ignorance in your post, but since you've invested money, hopefully your ignorance didn't just sink other people's money.

@art_of_philo @CarinaLHong @axiommathai Math proofs are not remotely just algorithms! They contain rigorous logical thinking.

@jturow @CarinaLHong @axiommathai If you think that "mathematical reasoning" is reducible to algorithms, then you deserve to lose all your money.

Let's go!

98% error reduction. Built-in production backends. Frontier AI agents, zero CLI. Dental offices building patient portals. Sales teams spinning up custom CRMs. Domain experts creating tools that would've needed dev teams last year. Software creation, democratized. Congrats @stackblitz team

@oanaolt @oanaolt so great to have you there. Let’s go!!

Last night, I attended a founder dinner on e-commerce redefined by agents and AI. Thanks to @jturow and Darya Zakharova for hosting. Commerce is going through an interesting evolution: 1️⃣ Location‑driven retail – in this wave, foot traffic & real‑estate decided winners. 2️⃣ Frictionless e‑commerce – the second wave was won by Stripe, Shopify & Amazon, which made checkout disappear. 3️⃣ Agentic personalization – AI agents now crawl reviews, weigh prices, and hit “buy” for us. Whoever owns the agent owns the customer. Watching the founders in the room, you could literally see the stack for this third wave coming together: • @rye – a universal selling API that turns any pixel into a storefront. • @TryArcade – authenticated “tool‑calling” so agents can act, not just chat. • @PaymanAI – compliance rails that let agents move money safely. • @browserbase – headless browser infra so agents can click, scroll, purchase at web scale. • @GumshoeAI – “SEO for AI” helping brands rank in ChatGPT & Perplexity answers. • @sardine – real‑time fraud & risk intelligence to keep it all secure. Plus, builders like Astral built by @SavannahFeder (marketing agents), firmly ai (instant checkout), and @TollbitOfficial (monetizing AI scraping) are filling critical gaps. Why it matters: When an agent can fulfill a request as specific as “find me a non‑toxic espresso machine under $300 that fits a 10‑inch shelf,” loyalty shifts from storefronts to the agent that knows you best. Commerce changes overnight. If you are obsessed with agentic commerce infrastructure, agent first shopping experiences, and “Agent SEO” tools that keep brands visible when LLMs do the recommending, I'd love to meet you.

Huge congrats to @CoolestAK87, Idan, Barak. Thrilled to support you on this journey along with our friends at @AmexVentures, @VisaVentures, @pk_iv, @shyamalanadkat, and @theaievangelist More here → jonturow.substack.com/p/why-agents-n…

We believe agents must become trustworthy before they can become trusted. And when they are, they’ll stop being demos — and start contributing to GDP. Nekuda makes that future happen faster.

AI agents are already driving real economic activity — Visa reports a 1,200% YoY spike in retail traffic from agents. But agents aren’t like bots — they are bots. And payments infra isn’t ready. That’s why we backed @nekuda_ai: the trust layer for agentic commerce. 🧵👇