Star Fleet AI solves 27 Erdős problems with 20 parallel GPT-5.6 instances

Star Fleet is a novel AI system designed to tackle the most difficult open problems in mathematics. It operates as a Mac desktop app that controls up to 20 custom agentic harnesses called 'starships' in parallel. Each starship runs its own GPT-5.6 instance on a dedicated 60-vCPU server and works on a separate math problem. The system is built from scratch in TypeScript & Bun, and each starship has access to x86-64 CPU bursts of up to 2,000 vCPUs, H100 GPU bursts, the world's largest corpus of Lean 4 premises (theorems & lemmas) searchable via Gemini embeddings, a Firecrawl.dev index of arXiv papers, a Claude Fable proof-verifier agent, and a local memory system (Ton 618) that weaves every verified premise into a dependency graph for compounding proofs.

The system has already solved 27 Erdős problems, with a notable success on Erdős Problem #123. This problem asks whether for any pairwise-coprime integers 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 difficulty arises from the divisibility antichain condition, which previous approaches struggled with. Star Fleet's solution uses a reduction scheme and a finite-seed check, encoded as a Lean theorem `Erdos123.erdos_123`. By running multiple parallel instances with diverse search strategies, the system found the required constructive proof. This demonstrates that AI can now contribute to frontier mathematical research by combining large-scale computation with formal verification.