Open Math Model: Developing AI for the Mathematical Community

The SAIR Foundation believes that, as artificial intelligence profoundly reshapes the landscape of scientific discovery, it should remain firmly anchored in the core principles of science: open academic exchange, rigorous peer validation, and deep respect for intellectual contribution.

These principles take practical form in Open Math OS, the operating system for collaborative math research and scientific computing. It brings open frontier models, a scientific compute cloud, and collaboration tools into one system, with the mathematical community in control of its data.

1. Why It Matters to Mathematicians and the World

From Black Box to Community-Owned Infrastructure

Mathematics has always advanced through transparency: every theorem and every proof must be open to intense scrutiny, verification, and extension by peers. SAIR Foundation holds that the future of AI-assisted mathematics—the vision of Math 2.0—requires community-owned infrastructure. Researchers must be able to independently inspect, continually refine, and run the models they rely on within environments they control, rather than becoming chronically dependent on the opaque, closed-source APIs of commercial entities, where the underlying reasoning algorithms remain hidden. The same conviction underlies Open Math OS, which is built on leading open-weight models rather than closed commercial APIs.

Built for the Daily Work of Research

Open problems in mathematics have been used as benchmarks to train the capability of many AI models. SAIR’s Open Math Model takes a fundamentally different approach. Its first phase is precisely calibrated to the real “daily pain points” of working mathematicians. The model puts practical utility first: helping researchers parse exceptionally complex, multi-page arguments, cross-reference extensive literature, explore novel mathematical examples, generate specialized code, and, crucially, advance the formalization of proofs in rigorous verification languages.

Open Math OS brings this work together in one place. Each project has its own cloud machine, running around the clock with more than 100 tools for mathematics and scientific computing already installed, Lean and Mathlib among them. When a problem demands more, Ultramath lets a researcher set several agents to work on it in parallel, while the judgment of what holds remains with the mathematician.

Democratizing the Frontier

The Open Math Model initiative is global by design. It is open to researchers across all institutions, regions, and career stages. By deliberately lowering the barrier to entry and democratizing access to advanced computing power and AI tools, SAIR Foundation ensures that brilliant minds everywhere can take part in the next frontier of mathematical discovery.

2. Safeguards for the Creators of Knowledge

SAIR’s Open Math Model is built on a rigorously defended ethical framework designed to protect the creators of knowledge.

The Community Owns Its Data

SAIR Foundation explicitly affirms that the mathematical community inherently owns its data and retains absolute authority over how it is used. That authority is exercised through the Open Math Model community, which sets the rules for how data is collected and used. The foundation operates on a strict opt-in model: only with explicit, prior consent and under formally established agreements will a researcher’s data be used for model training. Researchers hold the ultimate power to decide exactly what they share, setting firm boundaries on how AI engages with their intellectual output. Open Math OS makes these boundaries the default: projects, files, and chats remain private until researchers choose to share them, and training on their work stays off unless they explicitly consent.

Ownership and Credit Stay with Authors

Academic credit is the primary currency of the scientific world. SAIR Foundation guarantees that ownership of any independent or pre-existing work contributed to the initiative remains entirely with its original authors. This guarantee extends to Open Math OS: whatever is created there remains its authors’ own, along with the credit for its ideas. Researchers will also receive explicit, traceable attribution and recognition for the mathematical concepts, intuitions, and results they provide. The Contributor Network will record these contributions in a transparent, timestamped account of each member’s work.

Governed by the Community, Independent of Capital

The trajectory, priorities, and ethical boundaries of Open Math Model are governed directly by the mathematical community itself. SAIR Foundation openly acknowledges the necessity of partnering with industry to secure crucial computing resources, but it enforces one non-negotiable prerequisite: the complete protection of the community’s research independence. Its governance structure guarantees that the pursuit of scientific truth and academic integrity will never be subordinated to corporate profit motives or commercial timelines.

Ultimately, SAIR Foundation sets out to prove a vital premise: it is entirely possible to train world-class, state-of-the-art mathematical AI models without sacrificing researchers’ copyright or undermining the spirit of open academic reciprocity. Through this initiative, AI takes its rightful place as a true and respectful collaborator to scholars, rather than an extractive predator of their intellectual legacy.

Open Math OS: Infrastructure for Math 2.0

The operating system for collaborative math research and scientific computing—built on open frontier models, with the mathematical community in control of its data

Today we are launching Open Math OS. It brings open frontier models, a scientific compute cloud, and collaboration tools together in one system, so mathematicians and AI agents can work on research side by side. Within three months of launch, we plan to provide free compute to 10,000 mathematicians, beginning with 1,000 research teams by November 2026.

Math 2.0 is how we describe the next stage of mathematical research: mathematicians working with AI agents, with scientific computing and formal verification part of everyday practice. The infrastructure beneath that work will shape who controls the data, who receives credit, and who gets to take part. We believe it should be built the way mathematics itself is built: in the open, and accountable to the community it serves.

Why we built it

Mathematics advances through discoveries that others can examine and build upon. Few fields share as openly: researchers post preprints on arXiv, work through problems in public on MathOverflow, and build formal libraries such as Mathlib line by line. That culture rests on reciprocity: what is shared openly is built upon openly, and credit flows back to its source.

AI is putting that reciprocity to the test. Large AI systems are trained on vast amounts of public text, including mathematics that researchers shared freely, yet the most widely used systems are closed: their weights are not released and their training data is not fully disclosed. Under the default terms of some consumer AI services, what researchers type in, including unpublished ideas, conjectures, and failed attempts, can be used to train future models unless they opt out.

AI output can look rigorous and still be wrong. Without verification, the cost of checking falls on readers and reviewers. Progress in mathematical AI is often measured on competition problems rather than on the daily work of research. And that work is scattered: a model in one window, computation on a laptop, a proof assistant to install and maintain, a draft in LaTeX, collaborators across institutions and time zones.

We built Open Math OS to bring that work together, on principles the mathematical community can hold us to.

Models, compute, data, and people—in one system

Open frontier models

Frontier reasoning, built in the open. Open Math OS runs open-weight models from third-party developers, currently Kimi K3, DeepSeek V4.1 Flash, and GLM 5.3 Flash, with adjustable reasoning depth for each task. Open weights let the community inspect, improve, and run these models, so research need not depend on a single vendor. With Ultramath, “Ultracode for math,” several agents work on one problem in parallel: they pursue different approaches, share findings, and return proposed solutions to your chat. You decide what holds.

Scientific compute cloud

A mathematical laboratory for every project. Every project runs on its own cloud machine, 24/7, even when your laptop is closed. Each comes with 100+ preinstalled tools for mathematics and scientific computing, including Lean 4 and Mathlib (v4.34), SageMath, PARI/GP, SymPy, and LaTeX. You work in the browser with no local setup, and your files and results are there when you return.

Data sovereignty

The mathematical community, in control. Open Math OS upholds a core principle of Open Math Model: the mathematical community owns its data and decides how it is used. Our commitments:

Private by default. Your projects, files, and chats stay private until you share them.

Consent before training. We use your work for model training only with your explicit consent, on terms agreed in advance. You choose what to share and for what purpose.

Rules set in public. The community will decide, through open governance, how data is collected and used.

Credit stays with you. You keep ownership of your work and credit for your ideas.

Collaboration tools

Mathematicians and AI agents. One research team. Teams bring members together; each project keeps one goal in focus, with its own chats and cloud files. Divide the work, from proving lemmas to revising the paper, while people and agents share the same projects, files, and conversations. Share a chat by link, with its full history, so colleagues can follow the reasoning behind a result.

Built for mathematical rigor

Open Math OS keeps mathematicians in charge of what counts as a result. Agents propose; mathematicians review and decide. Lean and Mathlib are available in every project, so formalized proofs can be machine-checked rather than taken on trust. Our aim is understanding, not just answers: tools that help researchers pursue investigations they could not otherwise undertake.

We are building for the everyday work of research mathematicians, not benchmark puzzles. The first phase of Open Math Model targets understanding difficult arguments, checking references, exploring examples, writing code, and formalizing proofs. We will measure the value of the models we build by reliable assistance, verifiable results, and the cost of sustained use.

Open by design

Mathematics is built in the open. Its tools should be too. Open Math OS is part of Open Math Model, the initiative we started at SAIR Foundation to unite mathematicians in shaping open models, research tools, and their governance. It follows the commitments of our Open Statement:

Models shaped by the community. Researchers will help determine how the initiative’s models are trained, what they are evaluated on, and how they serve research and education, guided by shared scientific priorities.

Open development. These models will have open-licensed weights and code, published training methods, and reproducible evaluations, with training data from documented sources under compatible permissions. Releases will report failures and limitations alongside successes, and independent teams will be able to reproduce the work and adapt the models to their own mathematical needs.

Shared intellectual property. Models, code, and tools developed through the initiative will be shared under open licenses such as Apache 2.0, MIT, or CC BY 4.0, with ownership and attribution for jointly developed work to be agreed with contributors from the outset.

Accountable governance. Governance rules and decisions will be public, with clear ways for members to propose changes, take part in decisions, and hold leaders accountable. Partnerships with industry for compute and other resources must preserve the community’s research independence.

Open participation. We welcome researchers across institutions, regions, and career stages.

Shape what comes next

Put Open Math OS to work on real research tasks and explore its strengths and gaps. Share what you learn through feedback, bug reports, and improvements. And help set the direction: we are forming five community subcommittees, and we invite mathematicians to join them.

Compute: secure and allocate resources for model training and inference.

Data Governance: set policies for how data is collected, documented, and used.

Harness, Tools & Benchmarks: build open tools, agentic harnesses, and benchmarks for mathematical reasoning.

Training: coordinate research on, and training of, open math models.

Events, Education & Partnerships: grow participation through events, competitions, education, and partnerships with universities and research institutions.

Members will help set priorities, propose initiatives, and carry out the work.

Build Math 2.0. Together.

Open Math OS is available to individual researchers and teams of all sizes. Thanks to our donors, compute can be offered for free, and our current infrastructure is ready to support over 10,000 mathematicians. Free compute is a first step toward making open models and affordable compute a shared foundation for mathematical research.

To get started, sign in with your SAIR account, introduce your team and research, and begin once approved. Read our Open Statement at sair.foundation/open-math-model, join the Open-Math-Model channel on the SAIR Foundation Zulip, or write to us at math@sair.foundation.

We want to show that capable mathematical AI can be built without compromising researchers’ ownership, credit, or the openness of their field. AI should be a collaborator that strengthens mathematicians and the commons they share. Whatever we build next, we will always stand with the mathematical community.