An open working philosophy
Curiosity and care.
Shared understanding.
We explore mathematics with AI, sharing questions, arguments, and tools for people to learn from and build on. Careful explanation, generous exchange, and respect for the mathematical community guide our work.
Three questions guide each judgment: Is the argument sound in its stated scope? Does it help people understand or do mathematics? Does it treat sources and people responsibly? These are distinct obligations; strength in one does not erase a failure in another.
AI-assisted mathematics deserves unusually careful scrutiny. We owe readers complete arguments, justified assumptions, accurate credit, and serious attempts to find mistakes. We also owe them the central idea: how it connects to mathematics they know, why it matters, and what they can reuse.
Useful lemmas, methods, and interfaces may contribute as much as the final answer. A large computation or machine-checked proof can be valuable; explain its role and organize it so others can build on it. Neither brute force nor difficult mathematics is automatically a failing. Machine checking is a method of checking, not a rank of mathematical worth.
We respect ongoing work, including preprints. Explain why an intervention is worthwhile, credit its origins, and share the approach so others can explore it on their own terms. Avoid automated priority races and floods of review requests. Legitimate overlap, disagreement, and criticism remain part of research; we explain our contribution without claiming another researcher’s endorsement. Mathematicians owe us neither a response nor free labor. Criticism should make the mathematics clearer while treating people fairly.
Learning from Tao
We draw substantially on Terence Tao’s 24 July 2026 ICM lecture and accompanying essay. His capability conjectures concern what research tasks AI can do, when, and at what cost, supervision, success, correctness, and quality. His conditional discussion asks what mathematics should serve as capabilities grow.
His emphasis on understanding, theory, education, and community guides us: producing a proof is only part of making mathematical knowledge useful.
From a problem to shared knowledge
- Open problemsProof generation
- Unverified solutionsProof verification
- Verified solutionsProof exposition
- Well-written solutionsProof publication
- Accepted solutionsProof canonicalization
- Definitive solutions
Two phases, one purpose
| Phase | What we commit to |
|---|---|
| 1 Responsible contribution | Rigor, understandable ideas, reusable tools, considerate collaboration, honest credit, and open correction from the beginning. Share approaches that help people do their own mathematics, beyond delivering answers. |
| 2 A commons built from the commons | Keep every Phase 1 commitment and extend it through the production system. All training material for models doing this work—including pretraining and later training—must be publicly inspectable and meet the commons’ commitments. Make research inputs, derivations, and outputs openly reusable, with source acknowledgment and accountable stewardship. |
Phase 2 is a goal, not a claim about our present models. Open weights alone are insufficient. Inspectable training history and independent regeneration should make the lineage examinable. Minimally directed AI mathematics could have a separate commons collection without assigning a human mathematical author just for initiating a run.
Sharing the work
Publications: human-led work Joshua can explain and defend in a talk; or clearly labeled AI-lab work that is machine-checked or extends an AI-lab research line. Both require rigorous justification, inspectable evidence, and serious adversarial review. An extension does not prove itself.
Claims: ongoing work with its evidence and limitations. We reserve theorem, lemma, and proposition for proved results with a publication reference, including others’ work. Labels apply to an exact contribution and version; they do not transfer to every claim in a paper.
Author-first responses: when our work is principally a response to someone’s active preprint, first prepare a useful, carefully checked contribution to share privately with its authors. Our starting default is a twelve-month embargo from that first substantive share, with earlier release by agreement. Expiry triggers a review, not automatic publication. Private embargoed work and its derivatives are excluded from ordinary research searches, reuse, public claims, and awards. A citation or overlapping topic alone does not trigger an embargo. Existing public work needs a separate review of every public copy; we do not describe it as private merely because a listing disappears.
Other approaches belong here too. We welcome alternative philosophies, practical strategies, teaching materials, and criticism of our approach. We can link to public work with credit. For private submissions, we ask permission before publishing, respect chosen attribution, and agree substantive edits. Sharing a perspective does not imply endorsement.
We check contributions daily. Send a proposal or public link to joshuagay.automate@gmail.com: what you advocate, whom it helps, and how it could work.
Working philosophy · 10 September 2026. Our AI-lab publication route differs from Tao’s expectation that authors can give an expert talk. Our phases and commons proposal are our own. No endorsement by Tao is implied.