Harmonic
@HarmonicMath
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Building Mathematical Superintelligence
Joined January 2024
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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Aristotle is ready
Nice guest post on Buzzard’s blog by Boris Alexeev on his and others’ use of AI systems to attack Erdos-type problems (thanks to Bloom’s @thomasfbloom website collating them): https://t.co/XBgHLly41H In particular, with systems like Harmonic’s @HarmonicMath Aristotle,
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Cool
I have completed a full auto-formalization with @HarmonicMath Aristotle of the following general group theory problem Fix three positive integers n, k, m. Prove that a group subgroup H of S_{6+(n+k+m)} generated by g1:=G!(1,6,4,3,a_1,...a_n); g2:=G!(1,2,4,5,b_1,...,b_k);
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BREAKING: “Aristotle has now written the majority of the public formalized solutions on https://t.co/IkaHak8lfY.” — Boris Alexeev, mathematician
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Beyond math: Aristotle achieves SOTA 96.8% proof generation on VERINA: Benchmarking Verifiable Code Generation. You can read more about this performance on our engineering blog linked in bio
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This is just the beginning 🚀
One after another, math problems open for decades are being solved by AI! Congrats to @HarmonicMath !
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Let’s go
We are currently at the beginning of the Erdős Rush phase of the Proof Boom😅 @HarmonicMath
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A new golden age of mathematics
We are entering an era of abundance in mathematics, and it feels absolutely fantastic. Mathematicians are becoming like orchestra conductors-coordinating, guiding, and shaping the vision. What a time to be alive.
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Aristotle proved another Erdos problem autonomously last night, concurrently with @AcerFur, and at @AcerFur's request. As far as we are aware, this is not an easier version of another problem Erdos intended. Before @AcerFur published his proof, he made two requests to Aristotle:
gist.github.com
Aristotle's generated proofs for Erdos Problem 481, from Kevin Barreto's submission through the free app: https://aristotle.harmonic.fun/. Despite saying "Sorry, Aristotle ...
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BREAKING: Math world is stunned! Aristotle AI by @HarmonicMath just independently cracked a 30-year-old Erdős problem (#124). ✅ Solved in 6 hrs ✅ Lean-verified in 1 min ✅ Zero human help Terence Tao is impressed. This is the "vibe proving" era. A true mathematical moonshot!
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🦾
The age of AI discovered mathematics has officially begun This is AI completing proofs humans couldn’t touch. Boris Alexeev just cracked Problem #124 (Erdos problems), a puzzle that’s been unsolved for 30 years. And the insane part? The solution was 100% AI generated 👀
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At Harmonic, one of our core values is humanity: We believe that humans must direct the progress of mathematics and science, and we build our tools accordingly. If you'd like to help us on the journey, check out our Careers page. We're hiring! https://t.co/rfVg7reg8m
jobs.ashbyhq.com
Harmonic Jobs
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Hypothesis #3. Humans will remain at the center of mathematics research. This is the big one. If we look back throughout history -- we have always changed the definition of mathematics to be what machines cannot automate. A big part of a mathematician's work in the early 1800s
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Hypothesis #2. There will be dramatically more mathematicians in 10 years than there are today. By automating the drudgery of verification and proving simple lemmas, Aristotle can not only speed up the work of highly sophisticated professional mathematicians, but also lower the
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Hypothesis #1: The number of mathematical proofs and the aggregate amount of mathematical data will expand exponentially. This one is perhaps uncontroversial. AI models, under the direction of humans, are already creating voluminous amounts of math. Now the bottleneck has gone
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✅
Aristotle by @Harmonic is acing group-theory puzzles. Here is a complete formal proof of the popular Yu Tsumura 554 puzzle. What's nice is that the proof is very transparent, with easy-to-follow steps. It was generated in less than an hour without any hints. I am attaching the
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Our goal is to unleash the mathematician’s full potential
I think our definition of mathematics will fundamentally change. Mathematicians used to spend their time solving complex equations, and automation freed them up to do more abstract creative work. But despite all the advances in computers, communications, and AI, math is still
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Mathematical superintelligence is coming, faster than you imagined
We are on the cusp of a profound change in the field of mathematics. Vibe proving is here. Aristotle from @HarmonicMath just proved Erdos Problem #124 in @leanprover, all by itself. This problem has been open for nearly 30 years since conjectured in the paper “Complete sequences
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We’re excited to announce our $120M Series C as we accelerate the development and commercialization of Mathematical Superintelligence. We’re grateful to our investors, including @ribbitcapital and @EmCollective, for their continued partnership.
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