What Harmonic does

Harmonic is a privately held AI research lab founded in 2023 and headquartered in Palo Alto, California, that is building what it calls Mathematical Superintelligence (MSI) — AI systems capable of producing formally verified mathematical and software proofs. Its flagship product is Aristotle, an automated theorem prover that combines reinforcement learning with the Lean 4 proof assistant to generate machine-checkable proofs verified down to foundational axioms. Aristotle is distributed via a public API at aristotle.harmonic.fun and a beta iOS mobile app, and has set or matched state-of-the-art results across three independent benchmarks: 90% on MiniF2F, gold-medal-level performance on the 2025 International Mathematical Olympiad (formally verified solutions to five of six problems), and 96.8% on the VERINA code verification benchmark.

The lab operates a vertically integrated technology stack that includes a custom automated RL training system, a proprietary Lean execution framework (the REPL service) that scales to nearly 500,000 concurrent CPUs at 95–100% utilization on preemptible cloud instances, and specialized geometric solvers (Yuclid and Newclid 3.0) that run up to 500x faster than AlphaGeometry 1. Harmonic has open-sourced supporting infrastructure tools (pbcc, python-memtools, Yuclid/Newclid 3.0, IMO 2025 proofs) and invests in the broader formal-verification ecosystem through a $1 million mathematician sponsorship program and a $300,000 donation to the Lean Focused Research Organization. Co-founders Tudor Achim (former Helm.ai CTO, Stanford CS PhD candidate) and Vlad Tenev (Robinhood CEO) lead a team of 11–50 employees with engineering presence in Palo Alto and London.

Harmonic's current commercial model centers on free public API access with pricing not publicly disclosed, complemented by a beta iOS app and a stated but not yet launched enterprise commercialization motion targeting safety-critical industries (aerospace, chip design, industrial systems, healthcare). The company has raised $295 million in venture capital across three rounds (Series A $75M led by Sequoia in September 2024 at a $325M post-money, Series B $100M led by Kleiner Perkins in July 2025 at ~$900M, Series C $120M led by Ribbit Capital in November 2025 at a $1.45B post-money), with additional participation from Index Ventures, Paradigm, Emerson Collective, and Nvidia. As of the source data, Harmonic discloses no revenue, ARR, paying enterprise customers, or published pricing.

Name

Harmonic

Legal name

Harmonic

Website

https://harmonic.fun

Company type

Private

Founded year

2023

Operating status

Operating

Headcount range

11–50 employees

Short description

Harmonic is a Palo Alto AI lab founded in 2023 that builds Aristotle, a reinforcement-learning formal-reasoning engine producing Lean 4-verified mathematical and software proofs. It distributes Aristotle via a public API and beta iOS app to mathematicians, developers, students, and researchers.

Ownership category

akta.pro rank

Product category

Automated Theorem Proving Software

NAICS

Computer Systems Design and Related Services (54151), Computer Systems Design Services (541512)

SIC

Services-Computer Programming Services (7371), Services-Prepackaged Software (7372)

akta.pro primary industry

Fine-Tuning, Adaptation & Custom Model Training (PEFT/LoRA/RLHF) (HDAAACAC)

akta.pro secondary industry

Model Testing, Validation & Quality Assurance (HDAAABAH)

Keywords

• Automated theorem proving
• Formal verification
• Mathematical reasoning AI
• Proof assistant
• Reinforcement learning

Headquarters

HQ city

Palo Alto

HQ country

United States

HQ region

North America

Offices2 records

Markets served

GTM type

B2B and B2C

Offering type

Software

Cost components

Technology or R&D, Personnel, Infrastructure, Marketing or Sales, Operations

Revenue model

1. Aristotle API access: Public API for the Aristotle mathematical reasoning engine; users sign up via the website. Pricing/terms not publicly disclosed; the company states it is exploring commercialization of Mathematical Superintelligence.
2. Aristotle for iOS (Beta): Mobile consumer/utility app for verified AI reasoning with photo-based problem solving; rollout underway via a waitlist, suggesting potential future consumer or freemium revenue.
3. Commercialization of Mathematical Superintelligence: Stated future commercial direction to integrate MSI into 'useful and delightful real-world applications' across safety-critical industries (aerospace, chip design, industrial systems, healthcare) — implying upcoming enterprise/usage-based contracts.

Pricing tiers

Go-to-market motion4 records

Distribution channels4 records

Marketing channels9 records

Core offering

Harmonic develops and operates Aristotle, an AI foundation model that generates formally verified mathematical proofs and code verifications using the Lean 4 proof assistant combined with reinforcement learning. The product is delivered to mathematicians, researchers, developers, students, and the general public through a self-serve public API and a beta iOS mobile application, with stated plans to commercialize the underlying Mathematical Superintelligence technology into enterprise applications in safety-critical industries.

Product overview

Harmonic offers a unified Mathematical Superintelligence (MSI) platform built around its flagship AI model Aristotle, which generates formally verified mathematical and code proofs using the Lean 4 proof assistant. The core Aristotle model is exposed through multiple interfaces including the Aristotle API (publicly accessible at aristotle.harmonic.fun) and the Aristotle for iOS Beta mobile app. Underlying the model are specialized solver systems including Yuclid and Newclid 3.0 for geometric problems, and supporting infrastructure tools including the REPL service for Lean execution at scale, pbcc for high-performance Protobuf serialization, and python-memtools for Python process debugging. All of these components together form Harmonic's portfolio aimed at producing reliable, verified AI reasoning for safety-critical applications in mathematics, software engineering, and science.

Differentiator

Problem solved

Functional benefit

Brands

• Aristotle: Harmonic's flagship AI reasoning engine / mathematical superintelligence model, used for formal theorem proving, code verification, and solving open mathematical problems. Made available via the Aristotle API and an iOS Beta app.

Products and services

• Aristotle Aristotle is Harmonic's flagship AI foundation model that generates formally verified mathematical proofs using the Lean 4 proof assistant combined with reinforcement learning. It achieves gold-medal-level performance on the 2025 International Mathematical Olympiad and state-of-the-art results on the MiniF2F (90%) and VERINA (96.8%) benchmarks, producing both natural-language solutions and machine-checkable Lean 4 code that verifies correctness down to foundational axioms.
• Aristotle API The Aristotle API is the public self-serve programmatic interface to Harmonic's Aristotle model, hosted at aristotle.harmonic.fun. It enables developers and researchers to integrate verified mathematical reasoning and Lean 4 proof verification into their own applications and workflows.
• Aristotle for iOS (Beta) Aristotle for iOS is Harmonic's beta mobile application that lets users capture math problems as photos and receive verified solutions, with parallel question support and visible Lean 4 code that verifies each answer. It targets students, self-learners, and individual consumers.

Quantifiable outcome

• 96.8% on the VERINA Code Verification Benchmark (160 of 189 specifications; new SOTA)
• +5 more outcomes

Segments5 records

Ideal customer profiles5 records

Technology focussed Yes

API detail

Has API

Yes

API docs

API detail

Core technology

AI maturity

App detail

AI capability11 records

Feature7 records

Partnerships

One partnership is on record.

• Kleiner Perkins25 November 2025

Scale indicators10 records

Recent moves7 records

Expansion highlights7 records

Direct peers

• Google DeepMind: DeepMind develops AlphaProof and AlphaGeometry 2, which are the most directly comparable AI systems for automated formal theorem proving and geometric reasoning. It operates in the same research category (AI for mathematics/formal reasoning) and is the closest competitor to Harmonic's Aristotle on benchmarks like MiniF2F and IMO-style problems.

Broad incumbents

• OpenAI: OpenAI's o-series reasoning models and GPT-5 Pro target general-purpose reasoning and have been demonstrated solving Erdos-style problems in collaboration with Harmonic itself. As a broader AI lab with massive compute and enterprise distribution, OpenAI is a horizontal incumbent that competes with Harmonic in the reasoning-model category.
• Anthropic: Anthropic's Claude models with extended thinking target formal reasoning, code verification, and safety-critical use cases — overlapping directly with Aristotle's positioning. Anthropic is a broader incumbent with stronger enterprise distribution and a published safety-focused brand.
• xAI: xAI builds large-scale reasoning-focused models (Grok series) with an emphasis on math and code benchmarks. It competes for the same frontier-AI capital pool and researcher talent that Harmonic is recruiting against.
• Meta AI (FAIR): Meta's FAIR lab co-created the VERINA Code Verification Benchmark against which Aristotle set the SOTA, indicating overlapping research interests in formal verification. As a broad incumbent with open-weight releases, Meta AI is comparable in capability scope though not specialized in mathematical reasoning.
• Microsoft Research: Microsoft Research has active programs in Lean-based autoformalization and AI-assisted theorem proving (e.g., Llemma, integration of Lean into Copilot). It is a broad incumbent with deep formal-methods expertise that intersects with Harmonic's core technology stack.

Emerging players

• Numina: Numina is an open-source initiative building AI models for mathematics (notably the NuminaMath dataset and models that have topped math leaderboards). It is an emerging player in math-focused AI with partial overlap to Harmonic's mathematical-reasoning focus.
• Galois: Galois specializes in formal verification and provably correct software for safety-critical systems, an adjacent capability to Aristotle's formal-reasoning engine. It is an emerging player that could either compete with or partner with Harmonic in the verified-software vertical.

Others

• Mistral AI: Mistral AI builds frontier open-weight language models used in code and reasoning workflows. While not specialized in formal mathematical reasoning, it represents the open-model alternative that downstream developers may choose over a closed, API-only offering like Aristotle.
• Lean Focused Research Organization: The Lean FRO stewards the Lean 4 proof assistant that is the substrate for Aristotle's verified outputs. Harmonic's $300K donation establishes a partnership, but the FRO's governance direction and roadmap materially shape Harmonic's technical dependencies.

Market position

Strengths5 records

Weaknesses5 records

Competitive moat5 records

Key risks6 records

Key highlights6 records

Customer concentration

• Xx.com/HarmonicMath
• GitHubgithub.com/harmonic-ai
• YouTubeyoutube.com/@HarmonicMathemathics
• LinkedInlinkedin.com/company/harmonicmath

Revenue estimate

Valuation estimate

Number of profiles

Profiles2 records

Funding overview

Funding rounds3 records

Investors14 records

Funding detail is available on the Subscription and Enterprise plan.Contact sales →

M&A

Investments

M&A and investment is available on the Subscription and Enterprise plan.Contact sales →

Frequently asked questions about Harmonic