Building Mathematical Superintelligence
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Many of us intuitively feel that the field of mathematics is going to change, so let's unpack the likely outcomes, without resorting to hyperbole or doomerism.
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Harmonic retweeted
@HarmonicMath is hiring a Formal Verification Engineer to develop Aristotle and apply it to formally verify production hardware and software!
The work spans formal methods research, product development and customer deployments.
Join our team in Palo Alto or London!
🔗 jobs.ashbyhq.com/Harmonic/5e…
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Today we're launching Miles v0.1, an open-source RL framework for LLMs and multimodal models.
RL training is easy to start and hard to debug. Miles helps you ensure your run is correct, use hardware efficiently, and keep RL running at scale.
Over the past 9 months, 72 contributors have landed 1,326 commits, 85 GPU E2E CI tests, battle-testing Miles on frontier open models like Kimi K3, DeepSeek V4, Qwen 3.8, GLM 5.2, Inkling, MiniMax H3, etc.
Miles powers frontier-model development and production RL workloads at @humansand, @periodiclabs, @modal, @DecagonAI, @Eigent_AI, @nebiusai, @IBM and more, on both @NVIDIAAI and @AIatAMD hardware.
Here is what we built, and why teams picked Miles🧵
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Aristotle
I am absolutely stunned by how effective @HarmonicMath is at lean 4 formalization of mathematics. It's able to fill in gaps and understand intent as well as intelligently leave out of scope work axiomatized when automatically formalising math.
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🔥Sir Timothy Gowers shares how he used Aristotle to effortlessly autoformalize a complex paper into Lean—without needing to know a single line of Lean himself.
The future of mathematical research is changing fast.
Read more:
gowers.wordpress.com/2026/07…
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Harmonic retweeted
Luckily, I had recently been contacted by @PietroMonticone from harmonic.fun, who asked whether I had any formalization projects I would be interested in undertaking using their Aristotle system. I'm happy to say that it has just successfully formalized our paper.
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Harmonic retweeted
A pleasure to help @wtgowers and his colleagues get their preprint formalised with Aristotle (@HarmonicMath).
The long case analysis that a referee would understandably prefer not to check by hand is now formally verified in @LeanProver.
The code should be available on @GitHub before long. After some further cleanup, parts of the supporting API may also be suitable for upstreaming to Mathlib.
Leonardo Franchi, Fredy Yip and I recently solved a problem of Ben Green by showing that if A is an open product-free subset of the open interval (0,1), then A has measure less than 1/3, a bound that it is not too hard to prove is sharp. 🧵
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AI is accelerating mathematical research in increasingly deep problems
We’re partnering with the @AIMathematics to develop open, human-centric benchmarks for AI in mathematical research
The benchmark is built around 50+ hard problems selected by mathematicians to measure how AI can accelerate discovery, from generating new ideas to tackling some of the field’s most challenging questions
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List: aimath.org/pastworkshops/ain…
Article: axios.com/2026/07/20/harmoni…
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verified codegen is inevitable
it's the only solution to ubiquitous, cheap, and ever-improving offensive cybersecurity capabilities
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From @emilyriehl on the #aboutlogic podcast (w/ @DenizPhiMa):
"I much prefer to interact with an autoformalisation agent than a large language model in discussing mathematics, because the large language models will feed you a lot of bullshit ..."
"I came up with my own counterexample, and then I asked Harmonic's agent Aristotle to verify it for me in Lean as a kind of extra check that my counterexample was correct. I did not ask a large language model for this, because if they tell me it's correct, that gives me no assurance ..."
"Aristotle was able to confirm that it is a valid counterexample."
We are very happy that Emily Riehl @emilyriehl joined or little podcast #aboutlogic and talked about higher categories, synthetic mathematics, formalization and much more.
piped.video/4MQbd5wTlI8?si=0QL_…
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🪄🧙Aristotle is the mathematician's super-assistant
Check out how @LorenzoLuccioli uses Aristotle to develop new results in algebraic combinatorics
Happy to share that our paper
“Mapping Uncharted Symmetries: Machine Discovery in Combinatorics”
has been accepted to the ICML 2026 AI4Math Workshop.
We study AI for discovery in algebraic combinatorics, with verification in @leanprover using @HarmonicMath’s Aristotle.
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The negation of Erdos unit distance conjecture, now formalized by Aristotle
You can try it for free at aristotle.harmonic.fun
Oh and Kim Morrison used Claude + Aristotle + Codex to formalize the negation of the Erdos unit distance conjecture: github.com/kim-em/erdos-unit…
It's nice to see that this was built on top of PNT+; so despite the fact that we haven't been able to upstream it to Mathlib (the Residue Theorem we have in PNT+ is just for rectangles, and Mathlib will want a much more general version...), it's still useful in other applications!...
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JUST IN: Aristotle claims the top spot in lean-eval, the Lean AI formalization leaderboard!
Aristotle is getting stronger and more capable by the day, try it out for your formalization needs.
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Harmonic retweeted
Happy to share that our paper
“Mapping Uncharted Symmetries: Machine Discovery in Combinatorics”
has been accepted to the ICML 2026 AI4Math Workshop.
We study AI for discovery in algebraic combinatorics, with verification in @leanprover using @HarmonicMath’s Aristotle.
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NOW LIVE: Ask Mode for Aristotle Agent
Get real-time insights into your agent's work without interrupting its execution with Ask Mode.
If you need to change direction rather than just ask questions, Instruct Mode is still active to let you steer mid-run. Try it out and let us know what you think!
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Formal verification is the future of crypto
We at Protocol Snarkification - me and @alexanderlhicks, plus about 30 or so external collaborators - are working hard with formal verification to ship the highest-assurance zkVMs possible. (see end of thread for collaborators) (1/n)
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🔥
Fantastic to have Rustan Leino join us at @HarmonicMath to help advance AI ✕ mathematics ✕ verification.
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In the future, all critical software will be formally verified.
As we discussed with @VitalikButerin on our Fireside, formal verification is a big positive outcome from AI that will more than counterbalance the effects of AI finding new bugs.
I am strongly supportive of math AI tools like Aristotle from @HarmonicMath driving this forward.
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