Google's Antigravity 'Teamwork' multi-agent framework with Gemini 3.7 Flash solves seven open CS/math problems, incl. part of Knuth's cycles problem
On Aug 27, 2026 Google announced updates to Teamwork, a multi-agent orchestration framework in its Antigravity coding environment. Using Gemini 3.7 Flash (with 3.1 Pro), its "Long Proof" pattern produced results on seven open problems in theoretical computer science and math, including the first proofs for two simpler constructions in the even case of Knuth's "Claude's Cycles" problem (40+ and 70+ page proofs, one formally verified in Lean). It scored 71% on Google's TCSBench, built a cycle-accurate RISC-V CPU simulator that boots xv6, and had optimizations merged into Eigen and ParlayHash.
Key facts
- Teamwork: agents propose, critique and refine each other's work for hours or days; patterns chosen automatically (Iterative Coding, Distributed Coding, Long Proof, Self-Verification inspired by DeepMind's Aletheia, Document Review); available as /teamwork-preview on all paid Antigravity plans
- Seven results (Google): improved coreset bounds for lp subspace approximation (FOCS 2025 open problem, arXiv:2608.26047); conditional lower bound for sparse least-squares (JMLR 2021 problem, arXiv:2608.02588); near-closing the complexity gap for Chamfer similarity (arXiv:2607.20393); provable Hadamard quantization with ~5.93x smaller leading constant (arXiv:2608.02564); independent reproduction of the Erdős unit-distance breakthrough without internet access; near-optimal lower bound for prefix-matrix factorizations (arXiv:2608.08238); Knuth's cycles, even case (GitHub dpwoodru/knuthCycles)
- Verification: Google says all results were reviewed and confirmed by human experts except the Knuth result, where the 40-page proof was formally verified in Lean; five papers are on arXiv
- TCSBench (Google-internal benchmark of open/challenging TCS problems): 71% with Gemini 3.7 Flash + 3.1 Pro, up from 67.7% with 3.6 Flash + 3.1 Pro
- Systems: cycle-accurate out-of-order RISC-V simulator built from scratch; boots xv6 to a shell; 0.71% cycle alignment error vs. BOOM hardware ground truth; runs 100+ standard benchmarks
- Open source: SIMD fast path for single-row/column GEMV merged into Eigen; 'Swiss Parlay' ideas for ParlayHash (2x insert throughput at 64 threads, 25% less memory per element) landed upstream
Science result
- Field
- computer-science / theoretical computer science / combinatorics
- Problem
- Seven open problems incl. lp subspace-approximation coresets (FOCS), sparse convex optimization lower bounds (JMLR), prefix-matrix factorizations, and the even case of Knuth's Hamiltonian-cycle decomposition ('Claude's Cycles')
- Result
- New bounds or proofs for six problems plus an independent rediscovery of the Erdős unit-distance result; for Knuth's problem, first proofs for two simpler constructions of the even case (40+ and 70+ pages)
- AI system
- Gemini 3.7 Flash, Gemini 3.1 Pro, Antigravity Teamwork
- Human role
- AI-driven multi-agent search and proof writing; humans set objectives and reviewed results
- Verification
- Human expert review (Google) for most results; Lean formalization for the 40-page Knuth proof; arXiv preprints, not yet peer-reviewed
- Status
- pending
What happened
Google updated Teamwork, the multi-agent framework in its Antigravity IDE first shown at Google I/O, and published results meant to show that orchestrating many cheap Flash-model agents can match much larger models on hard, long tasks. Its Long Proof pattern generates competing proof strategies, pairs each with a "falsifier" agent that tries to break it, splits the chosen strategy into subproblems, and runs tournaments of improved drafts. It keeps a registry of pitfalls across rounds.
The headline math result touches the problem from Donald Knuth's February 2026 "Claude's Cycles" note: decomposing the 3D torus digraph into three Hamiltonian cycles. Claude had found the construction for odd m, and the even case was left largely open. Teamwork produced the first proofs for two simpler even-case constructions, and Google says the 40-page proof was checked in Lean. Other results appear as arXiv preprints on problems posed at FOCS and in JMLR. In engineering, Teamwork wrote a RISC-V out-of-order CPU simulator that boots an operating system and contributed performance patches that maintainers accepted into Eigen and ParlayHash.
Why it matters
It is another data point in the summer-2026 wave of AI-assisted results on open problems. This one comes from a cheap "Flash" model plus orchestration rather than a frontier flagship, and it lands on a problem first opened up by a rival lab's model. Caveats: the problems are mostly specialized TCS questions, the preprints are not peer-reviewed, and TCSBench is Google's own benchmark.
Changelog
- 2026-09-30: created (official-blog audit)
Related events
- Donald Knuth's 'Claude's Cycles': Claude Opus 4.6 solves an open Hamiltonian-cycle problem ('Shock! Shock!') ★★★★
- Google releases Gemini 3.7 Flash at half the price of 3.6 Flash ★★★
- OpenAI model disproves Erdős's 80-year-old unit distance conjecture ★★★★★
Sources (6)
- officialGoogle Antigravity blog: Teamwork: When AI becomes a research partner
- officialGoogle blog: Antigravity Teamwork with Gemini 3.7 Flash
- docsAntigravity docs: Teamwork
- codeKnuth cycles even-case proofs (GitHub dpwoodru/knuthCycles)
- paperarXiv:2608.26047: coresets for lp subspace approximation
- paperTCSBench paper (arXiv:2608.09538)
id: 2026-08-27-antigravity-teamwork-open-problems · updated 2026-09-30 · open in the interactive timeline