Harmonic
Harmonic brings formally verified mathematical reasoning to theorem proving and code verification.
Harmonic builds Aristotle, an AI-driven mathematical reasoning engine that uses formal verification via the Lean 4 proof assistant to solve complex mathematical problems with provable correctness. The platform translates natural-language math problems into formally verified proofs, eliminating the guesswork in mathematical reasoning. Harmonic serves mathematicians, quantitative researchers, software verification teams, and enterprises needing formally verified code generation. Unlike general-purpose AI models that can hallucinate intermediate steps, Aristotle guarantees each reasoning step is mathematically sound.
Problem solved
Mathematical and software verification currently relies on costly manual verification processes, and general AI models often fabricate intermediate reasoning steps without formal proof.
Target customer
Mathematicians, quantitative researchers, software verification teams, enterprises in safety-critical systems (aerospace, automotive, finance), and academic institutions seeking reliable proof automation.
Founders
T
Tudor Achim
CEO & Co-Founder
Former CTO of Helm.ai (autonomous driving), PhD candidate in Computer Science at Stanford, B.S. from Carnegie Mellon University, previously worked on ML at Quora.
V
Vlad Tenev
Co-Founder & Executive Chairman
Founder and CEO of Robinhood, accomplished mathematician, provides strategic guidance and mathematical expertise to Harmonic.
Funding history
Series A
$75M
September 2024
Led by Sequoia Capital
· Index Ventures, Era Funds, GreatPoint Ventures, DST Global, Nikesh Arora, Jared Leto
Series B
$100M
July 2025
Led by Kleiner Perkins
· Paradigm, Ribbit Capital, Sequoia Capital, Index Ventures, Charlie Cheever
Series C
$120M
November 2025
Led by Ribbit Capital
· Sequoia Capital, Index Ventures, Kleiner Perkins, Emerson Collective, NVentures (Nvidia)
Total raised:
$295M
Industries
Pricing
Pre-revenue beta model. Free API for developers currently available at aristotle.harmonic.fun. Waitlist for Aristotle iOS app beta announced. No public pricing disclosed; enterprise pricing expected upon commercialization.
Notable customers
Pre-revenue, beta stage. Early adopters include mathematicians and quantitative researchers using the API beta. No named enterprise customers publicly announced.
Integrations
Lean 4 proof assistant (core integration), API-based integration for developers, iOS app beta in development.
Tech stack
Google Analytics (Analytics)
Apache HTTP Server (Web servers)
Google Workspace (Email)
GoDaddy (Hosting)
Website
Competitors
OpenAI o1
Hides intermediate reasoning steps for IP protection, charges $15-60 per million tokens, leverages ChatGPT ecosystem but lacks formal verification guarantees.
Google DeepMind AlphaProof & AlphaGeometry
Specialized systems for math olympiad problems and geometry, achieved silver-level IMO performance, bundled into Google Cloud offerings but less focused on code verification.
Anthropic Claude
Positioned as safer reasoning model with strong enterprise compliance features, broader general-purpose reasoning but lacks formal mathematical verification capabilities.
Why this matters: Harmonic achieved unicorn status ($1.45B valuation) within two years by combining world-class founders (Robinhood CEO + Helm.ai CTO), $295M in elite VC backing (Sequoia, Kleiner Perkins, Ribbit Capital, Nvidia), and a genuinely novel approach to AI reasoning. The company is solving a critical gap in AI—formal verification—just as code generation becomes the dominant LLM use case, positioning it at the intersection of AI safety, software verification, and mathematical automation.
Best for: Research mathematicians and quantitative analysts needing to accelerate proofs and explore new mathematical directions; software verification teams in safety-critical domains requiring formally verified code; enterprises building AI systems that must guarantee correctness.
Use cases
Formal Code Verification
Engineering teams use Aristotle to automatically verify correctness of safety-critical code without manual proof-checking. Particularly valuable in aerospace, automotive, and financial systems where a single bug can be catastrophic. The formal verification approach eliminates costly human review cycles.
Accelerated Mathematical Research
Academic mathematicians leverage Aristotle to rapidly explore new theorem proofs and validate hypotheses. Rather than spending weeks on tedious verification, researchers can focus on novel insights and problem directions. Early users report the system contributing to breakthrough research directions.
Code Generation Verification
Development teams integrate Aristotle via API to verify AI-generated code before deployment. As LLM-based code generation becomes standard, Harmonic provides the missing verification layer to ensure generated functions are mathematically sound and won't fail in production.
Educational Theorem Proving
Computer science and mathematics programs use Aristotle to teach formal proof methods. The iOS app makes olympiad-level reasoning accessible to students, providing immediate feedback on proof attempts and helping educators scale proof-based learning.
Alternatives
OpenAI o1
Choose o1 if you need general-purpose advanced reasoning with massive ecosystem integration; choose Harmonic if you specifically need formal mathematical verification with guaranteed correctness.
Google DeepMind AlphaProof
DeepMind excels at olympiad-style problem-solving and is integrated into Google Cloud; Harmonic targets code verification and production systems requiring formal proofs.
Coq / Isabelle Theorem Provers
Traditional theorem provers require deep expertise and manual proof writing; Harmonic automates proof generation from natural language, making formal verification accessible to non-specialists.
FAQ
What does Harmonic do? +
Harmonic builds Aristotle, an AI engine that translates natural-language mathematical problems into formally verified proofs using the Lean 4 proof assistant. Unlike general-purpose AI models, Aristotle guarantees mathematical correctness by formally verifying each reasoning step before producing an answer. It's designed for mathematicians, researchers, and software verification teams.
How much does Harmonic cost? +
Harmonic is pre-revenue and currently in beta. The API is accessible to developers, and an iOS app beta is rolling out via waitlist at aristotle.harmonic.fun. No public pricing has been announced; enterprise pricing will be available at commercialization.
What are alternatives to Harmonic? +
OpenAI's o1 model offers advanced reasoning at scale but lacks formal verification. Google DeepMind's AlphaProof achieves olympiad-level performance but focuses on problem-solving. Traditional theorem provers like Coq and Isabelle provide formal verification but require manual proof writing and deep expertise.
Who uses Harmonic? +
Early adopters include mathematicians and quantitative researchers using the beta API. Target customers are software verification teams in safety-critical industries (aerospace, automotive, finance), academic institutions, enterprises building AI systems requiring formal correctness guarantees, and research organizations seeking to accelerate mathematical discovery.
How does Harmonic compare to OpenAI o1? +
OpenAI o1 offers broader general-purpose reasoning at higher token costs ($15-60 per million tokens) but hides intermediate steps and lacks formal correctness guarantees. Harmonic focuses specifically on mathematical and code verification, formally verifies each step, and offers API access to developers. Choose o1 for general reasoning; choose Harmonic when you need mathematically provable correctness.
Why is Harmonic backed by Vlad Tenev? +
Vlad Tenev, founder and CEO of Robinhood, is a talented mathematician who co-founded Harmonic with Tudor Achim. He serves as Executive Chairman and provides both strategic guidance and deep mathematical expertise to the company's development.
What is the Lean 4 proof assistant? +
Lean 4 is a formal verification language and proof assistant that Harmonic uses as its foundation. It allows mathematical claims to be formally verified with absolute certainty, ensuring that Aristotle's reasoning cannot contain hidden errors or fabricated steps.
Tags
mathematical reasoning
formal verification
theorem proving
AI safety
code verification
Lean 4
proof automation
software correctness
research mathematics
safety-critical systems