Parallel agents crack Erdős problems by isolation

Twenty independent Codex agents, each running on dedicated 60-vCPU servers with Lean 4 and formal verification tools, have proposed 27 solutions to Erdős problems using an isolation-based multi-agent architecture. The Star Fleet Math project avoids shared agent contexts, instead relying on machine-checkable proofs and human review to ensure correctness, demonstrating a scalable pattern for parallel problem-solving in mathematics.

AI https://sourcefeed.dev/c/ai Article Parallel agents crack Erdős problems by isolation Twenty independent Codex harnesses, Lean gates, and heavy tool sandboxes show how multi-agent work actually scales. Priya Nair https://sourcefeed.dev/u/priya nair A Mac app spinning up twenty agentic "starships," each on its own 60-vCPU box with a dedicated model instance, is easy to read as pure spectacle. The more useful reading is architectural. Star Fleet Math https://www.starfleetmath.com/ is a TypeScript and Bun control plane that farms independent open problems to isolated agents, arms each one with Lean 4, SAT/SMT solvers, computer algebra systems, vector-searchable premises, and burst compute, then refuses to accept an answer until a formal proof and often a human pass. That pattern, not any single lemma, is what developers should steal. The headline number is twenty parallel sessions aimed at Erdős problems https://www.erdosproblems.com/ . The project lists 27 proposed solutions. Whether every write-up survives community scrutiny is a separate question. What is already clear is the unit of work: one hard, self-contained problem per agent, with machine-checkable correctness as the merge criteria. Isolation is the product Each starship runs on a dedicated server 60 vCPUs, 120 GiB RAM preloaded with CaDiCaL, kissat, Z3, Google CP-SAT, SageMath, PARI/GP, GAP, Macaulay2, and full Rust, CUDA C++, and Lean 4 toolchains. On demand it can burst to roughly 2,000 vCPUs for sharded search jobs, or to H100s for massively parallel search. Premises live in what the project calls a large Lean 4 corpus, indexed in plain English via embeddings and a Chroma store. ArXiv and GitHub are crawled and searchable. Long-term memory "Ton 618" weaves every verified theorem into a dependency graph so later proofs can reuse earlier ones instead of rediscovering them. Verification is layered. A Claude-based proof-reviewer harness sits in front of human review; after automated approval, an iMessage path can still pull in a human Colin for a second look. The agent is not trusted. The Lean kernel and the human are. That is the opposite of the usual multi-agent demo where three chatbots argue in a shared context until someone declares victory. Here, agents never share a workspace. They share a growing library of verified facts. Parallelism is safe because the problems are independent and the acceptance test is mechanical. Why math is a good stress test Erdős problems are a clean workload for this design. There are over 1,100 listed on the public site; roughly 40% are already solved in the human literature. Many remaining items are number-theoretic statements that can be stated crisply and, in principle, formalized. The project says it avoided problems that already had informal or partial answers online. The write-up for Erdős Problem 123 https://www.erdosproblems.com/123 is a useful window into what the agents actually do. The question asks whether, for pairwise-coprime integers a, b, c 1, every sufficiently large integer is a sum of distinct terms a^i b^j c^k with no selected term dividing another. The divisibility antichain condition is what breaks naive induction. The reported approach moves to a single homogeneous exponent level where distinct monomials cannot divide each other , builds arithmetic progressions of primitive homogeneous subset sums via edge codes and van der Waerden / Hales–Jewett arguments from Mathlib, then controls baseline and width carefully enough to seed a correction induction. The result is stated as a Lean theorem erdos 123 under the nondegenerate hypothesis a, b, c 1. You do not need to buy every step of that argument from a blog post. You do need to notice the workflow: search and computer algebra propose structure, Lean formalization is the finish line, and verified lemmas feed the shared graph. Without the formal gate, twenty parallel agents would mostly produce twenty plausible PDFs. What transfers to ordinary software work Most developers will never rent twenty 60-vCPU sandboxes for open conjectures. The portable pieces are still sharp. Pick independent units. Parallel Codex sessions pay off when tasks do not thrash the same files or the same mental model: three modules' test suites, a long refactor plus two bugfixes, a scaffold job beside a docs pass. Shared context is for collaboration; isolation is for throughput. Enforce isolation the boring way. The practical baseline is still git worktrees, one checkout per agent, each on its own branch: git worktree add ../app-auth feature/auth git worktree add ../app-login-fix bugfix/login git worktree add ../app-tests scaffold/tests cd ../app-auth && codex Terminal multiplexers keep the panes visible. The official Codex desktop app macOS/Windows and multi-session workspaces add kanban status and visual diffs. All of these exist because a single agent is almost never the bottleneck; review and collision avoidance are. Define a real done signal. Math has Lean. Software needs something analogous: typecheck + tests + linters + a required review policy, preferably auto-run in the agent sandbox before a human is paged. If "done" is vibes, parallel agents just multiply half-finished branches. Compound verified artifacts. Star Fleet's dependency graph of premises is the math version of a curated internal package registry, a golden path library, or a set of approved architecture ADRs that agents must cite. Unverified agent output should not pollute that store. Budget for tools, not just tokens. The interesting cost center here is not only model calls. It is the SAT solvers, algebra systems, premise search, and CPU/GPU bursts that make search feasible. For code agents, the equivalent is sandboxes with the real toolchain, package cache, language servers, and when useful property-based or fuzz harnesses. A naked chat window is underpowered for the same reason a naked LLM is underpowered for number theory. Limits that still matter This is not a closed-form proof that frontier models "solved" twenty famous open problems in the sense a journal referee would accept. The site itself frames entries as solutions proposed, formalized in Lean, with human review in the loop. Many Erdős items have long partial histories; careful problem selection reduces contamination but does not eliminate evaluation risk. Formalization quality still depends on how the intended statement was encoded, which is a classic footgun. The economics are also specialized. Twenty dedicated mid-size servers plus GPU/CPU bursts is a research budget, not a default CI shape. Everyday teams should start with two to four worktree-isolated sessions and a strict CI gate, then scale only where review latency, not model latency, is the constraint. Still, the direction is right. Agentic systems get more useful when you stop asking one agent to be a genius in a shared mess and start treating them like workers on independent tickets, with heavy tools and a compiler that can say no. Star Fleet is an extreme instance of that idea aimed at open mathematics. The same skeleton, stripped of H100 bursts and iMessage pages, is how serious multi-agent coding setups should look: isolate, tool heavily, verify hard, and only then merge. If you are already running one coding agent all day, the next lever is not a bigger prompt. It is a second worktree, a clearer done check, and a place for verified intermediate results to accumulate. Sources & further reading - Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel https://www.starfleetmath.com/ — starfleetmath.com - hckr news - Hacker News sorted by time https://hckrnews.com/ — hckrnews.com - How to Run Multiple Codex Agents in Parallel | Nimbalyst https://nimbalyst.com/blog/how-to-run-multiple-codex-agents-in-parallel/ — nimbalyst.com - GitHub - teorth/erdosproblems: A community database for the problems on the erdosproblems.com site · GitHub https://github.com/teorth/erdosproblems — github.com Priya Nair https://sourcefeed.dev/u/priya nair · AI & Developer Experience Writer Priya covers AI frameworks, developer productivity tooling, and the startup ecosystem across South and Southeast Asia, bringing a researcher's rigour and a practitioner's empathy to every story. She is deeply sceptical of benchmarks and asks hard questions so her readers don't have to. Discussion 0 No comments yet Be the first to weigh in.