Star Fleet Math: An AI System That's Actually Solving Open Math Problems

Star Fleet Math is a new AI system that tackles the world's hardest open mathematics problems using Lean 4. It's a Mac desktop app that orchestrates up to 20 parallel agentic harnesses—called "starships"—each running a dedicated GPT-5.6 instance on a 60-vCPU server. The entire system is built from scratch in TypeScript and Bun.

Each starship has access to a serious arsenal: CPU bursts of up to 2,000 vCPUs for sharded search, H100 GPU bursts for massively parallel search, a large corpus of Lean 4 premises searchable via Gemini embeddings and Chroma vector DB, a Firecrawl index of arXiv and GitHub, a proof-verifier agentic harness using Claude Fable, and a local long-term memory system called Ton 618 that builds a dependency graph of verified theorems. The sandbox comes preloaded with SAT/SMT solvers (CaDiCaL, kissat, Z3), Google's CP-SAT, computer algebra systems (SageMath, PARI/GP, GAP, Macaulay2), and full Rust, CUDA C++, and Lean 4 toolchains.

Star Fleet has already proposed a solution to Erdős Problem #123, a number theory problem with a $250 prize. The problem asks: for pairwise coprime integers a,b,c≥1, is every large integer the sum of distinct numbers of the form a^k b^l c^m (k,l,m≥0), with the extra condition that no selected term divides another?

The core difficulty and the breakthrough

The divisibility condition is what makes this problem hard. Ordinary completeness arguments break down because terms from different scales tend to be comparable by divisibility, while a divisibility antichain can be too sparse to fill consecutive integers. Earlier work had developed a reduction scheme using correction and induction, but it left a stubborn finite-seed problem: you first need to represent every integer in a multiplicatively wide interval [N, CN], and the induction only propagates that interval, not constructs it.

The key insight was to work on a single homogeneous exponent level (i+j+k = D). On the same level, two distinct monomials can never divide each other, so every subset is automatically primitive. This turns the problem into an additive question about subset sums, making primitiveness free as long as all pieces stay on the same degree. The team then used an edge-code construction to get c^n primitive subset sums with distinct residues modulo c^n and bounded carry, then applied finite van der Waerden (from Mathlib's Hales-Jewett theorem) to get arbitrarily long exact arithmetic progressions of primitive homogeneous subset sums.

The real breakthrough came from exploiting unused monomials on the same exact homogeneous level—an "optional interior shell"—to turn one arithmetic progression into a large lattice interval, then fill residues with face corrections. The final result: for every pairwise-coprime triple a,b,c>1, every sufficiently large integer is a sum of distinct terms a^i b^j c^k such that no selected term divides another. The theorem is formalized in Lean 4 as Erdos123.erdos_123 : Erdos123.IntendedStatement.

Star Fleet is currently working on 27 Erdős problems, 630 Frontier Math problems, and 14 Millennium problems. The system's architecture—combining massive parallel compute, formal verification in Lean 4, and a growing dependency graph of proven theorems—is a glimpse into how AI-assisted mathematics might work at scale.