20 Codex Accounts, 20 Erdős Problems, One Lean 4 Proof Factory

Colin Snyder’s Star Fleet Math system solved 27 Erdős problems by running 20 parallel GPT-5.6 instances, each on a dedicated 60-vCPU server, inside a single macOS desktop app. The architecture is unusual. The results are concrete. And the implications for how AI interacts with formal mathematics are worth examining closely.

Star Fleet is not a research lab project. It is a personal build by Snyder, advised by Mike Kim, inspired by the Ignis system and previously built with Dhruv Agarwal and Nitin Kesarwani at the New Turing Institute. The entire stack is written in TypeScript and Bun. Each of the 20 “starships” operates independently on a separate Erdős problem, with access to CPU bursts of up to 2,000 vCPUs for search programs, H100 GPU bursts for massively parallel search, and a local Lean 4 premise corpus that Snyder claims is the world’s largest.

The system also indexes arXiv papers via Firecrawl, wraps Claude Fable in a proof-verifier agent, and uses an iMessage API to ask Snyder himself for review after Fable approves. A local long-term memory system called Ton 618 weaves every verified Lean 4 premise into a dependency graph so proofs compound.

The headline result: 27 solution proposals for Erdős problems, 0 for Frontier Math, 0 for the Millennium problems. The site lists a specific solved problem: Erdős Problem #123, a $250 prize problem in number theory. The question asks whether, for pairwise-coprime integers a,b,c > 1, every sufficiently large integer is a sum of distinct numbers of the form a^i b^j c^k where no selected term divides another.

Snyder’s team formalized the proof in Lean 4. The final theorem Erdos123.erdos_123 : Erdos123.IntendedStatement compiles with only the standard Lean axiom set — [propext, Classical.choice, Quot.sound] — and no sorryAx placeholders. That is a fully verified formal proof, not a heuristic argument.

The proof itself is worth reading for its architecture. The problem resists standard induction because the divisibility condition makes terms from different scales incomparable. Earlier approaches got stuck on a “finite seed” problem: you need to represent every integer in a multiplicatively wide interval before induction can propagate. Snyder’s solution introduces an “optional interior shell” — monomials on the same homogeneous exponent level that can be added or omitted without breaking primitiveness — to amplify the interval width linearly with the number of optional terms.

This is the kind of structural insight that mathematicians recognize as clever. The fact that a system of 20 GPT-5.6 agents working in parallel produced it raises questions about what “AI-assisted mathematics” means.

The architecture is not a single model reasoning through a problem. It is a coordination layer on top of 20 independent reasoning instances, each with its own compute sandbox, search tools, and proof verifiers. Snyder describes each starship as having access to SAT/SMT solvers (CaDiCaL, kissat, Z3), Google’s CP-SAT, computer algebra systems (SageMath, PARI/GP, GAP, Macaulay2), and the full Rust, CUDA C++, and Lean 4 toolchains. The models generate candidate proofs. The tools verify them. The human reviews edge cases.

This is not a “GPT-5 solved 27 Erdős problems” story. It is a “carefully engineered multi-agent system with heavy compute and human oversight solved 27 Erdős problems” story. The distinction matters for how the field thinks about capability.

The compute cost is not disclosed, but 20 instances each on a 60-vCPU server with H100 burst capability is not cheap. The system also uses GPT-5.6, which is not a publicly available model. Snyder built this for himself, not as a product. The economics of reproducing this at scale are unclear.

The site lists 27 solution proposals but does not claim all are verified to the same standard as Problem #123. The verification pipeline — Fable reviews, then Snyder reviews — is human-in-the-loop, not fully automated. Some solutions may be partial or informal.

What matters is the precedent. A single developer with enough compute, good engineering taste, and a willingness to build a bespoke agentic harness can now produce verified formal proofs for open problems in number theory. The bottleneck is no longer mathematical insight alone. It is the ability to coordinate models, tools, and verification into a working pipeline.

The Lean 4 formalization is the key detail. A heuristic solution to an Erdős problem is interesting. A Lean 4 proof that compiles with no placeholders is a different category — it is machine-checkable, shareable, and composable with other formal mathematics. The Mathlib community can inspect it. Other researchers can build on it.

This is the direction AI-assisted mathematics has been moving. The AlphaProof results from DeepMind, the work on Lean Copilot, the various autoformalization projects — all point toward a future where formal verification is the default, not an afterthought. Snyder’s system is a concrete demonstration that the stack works for nontrivial open problems.

The open question is whether this approach generalizes. The 27 solved problems are all Erdős problems, which tend to be discrete and combinatorial. The system scored 0 on Frontier Math and the Millennium problems. The architecture may be better suited to problems where search and case analysis dominate, rather than deep structural insight.

Snyder’s system also raises questions about how the mathematics community should handle AI-generated proofs. The traditional peer-review process is not designed for proofs produced by a 20-agent system with a single human reviewer. The Lean 4 formalization solves the verification problem — the proof is machine-checked — but the social question of credit, attribution, and trust remains.

For now, the takeaway is straightforward. A macOS app running 20 GPT-5.6 instances on beefy servers solved 27 open problems in number theory and formalized at least one of them in Lean 4. The proof compiles. The system works. The field should pay attention to the architecture, not just the headline.