Google reports seven Teamwork math results, with three reproduced by Flash

The other five results address distinct questions: better coreset construction bounds for ℓp subspace approximation when p>2; a conditional lower bound for sparse least-squares optimization; a nearly closed complexity gap for Chamfer similarity between vector embeddings; single-stage Hadamard quantization; and a near-optimal lower bound for prefix-matrix factorizations. Coresets are reduced representations of a dataset used to approximate calculations on the full set. Google says five resulting papers were available on arXiv and that human experts confirmed the results other than the Lean-verified Knuth proof.

Two of the papers show why the precise mathematical claim matters. The sparse least-squares paper, submitted August 3, establishes a conjectured limit on polynomial-time algorithms conditional on a specified Small-Set Expansion Hypothesis. It is a conditional lower bound on what algorithms can achieve, not an unconditional impossibility theorem or a faster optimization algorithm.

The quantization paper, also submitted August 3, removes a second processing stage from an earlier construction for representing high-dimensional vectors. It reports an approximately 5.93-fold reduction in the leading constant of a proved error bound and eliminates the residual stage's communication payload. That figure is not a measured 5.93-fold speedup in an AI application. The paper identifies similarity search, distributed learning and model compression as relevant uses of vector quantization.

Both papers say an automated Gemini-based system developed inside Google first obtained their proofs and that the human authors verified them and edited the presentation. Their explicit verification statements strengthen the evidence, while leaving human checking integral to the published results. These are author-reported checks, not reports of separate replications by users of the paid preview.

Company-reported TCSBench scores from Google Antigravity compare two model combinations. Google said mixed Flash–Pro support in the product's Long Proof pattern was still forthcoming. Source: Google Antigravity.

The framework carries more of the claim than Flash alone

Antigravity began as a coding platform, rather than a dedicated mathematics system. Google introduced it in November 2025 with agents able to plan, execute and verify tasks across an editor, terminal and browser. Its launch also offered model choice beyond Google's Gemini, including Anthropic's Claude Sonnet 4.5 and OpenAI's GPT-OSS. That history helps separate the platform's role from the capabilities of any one model.

In the research announcement, Gemini 3.1 Pro is the Google model credited with obtaining the original results. The three reproduced with the newer Flash model concern subspace approximation, vector-embedding comparisons and Hadamard quantization. Google presents Flash as its faster, more cost-efficient model for everyday developer work; the evidence here concerns what that model can do with extensive orchestration.

Teamwork's Long Proof pattern began as a standalone research harness before being incorporated into the product. The September Stellar Colosseum paper describes that harness as model-agnostic: it allocates inference across alternative research strategies, tests when a route is ready to break into subproblems and sends verification findings back to the affected part of an argument.

Google's implementation generates candidate strategies alongside dedicated attempts to falsify them. It then combines candidates and critiques, builds a dependency graph for proof sections and retains objections and failed drafts. The proposed advantage is better use of repeated inference and criticism, rather than a claim that any single model response has become a reliable research proof.

There is also continuity with earlier work. Google says Teamwork was first announced at Google I/O. Its separate Self-Verification pattern draws inspiration from Aletheia, an earlier autonomous mathematics agent that demonstrated research-level abilities in the FirstProof Challenge. Teamwork packages research, coding and document-review workflows into a framework that selects a pattern and adjusts agent counts as work progresses. Google itself says simpler multi-agent approaches can suffice for routine tasks; Teamwork is aimed at harder, open-ended work where agents can otherwise reinforce one another's mistakes.

On TCSBench, an evaluation of research-level theorem-proving tasks drawn from FOCS, STOC and SODA papers, Google reports 71% using Gemini 3.7 Flash together with 3.1 Pro, compared with 67.7% previously reported using 3.6 Flash and 3.1 Pro—a gain of 3.3 percentage points. Google says the benchmark was developed separately within the company and calls the result its highest internal score. That supports progress on this evaluation, not an independent ranking of competing research systems. The Colosseum abstract separately reports solving 218 of 222 Codeforces problems with Pro and execution feedback; that programming evaluation is distinct from the open research results.

Google's published introductory token rates expire December 31, 2026. These model prices do not establish the cost of a verified Teamwork discovery. Source: Google — Gemini 3.7 Flash launch.

Cheap tokens do not establish cheap discoveries

Google introduced Gemini 3.7 Flash on August 13, three weeks after Gemini 3.6 Flash, as a model for coding and agents. Its launch announcement priced it at $0.75 per million input tokens and $3.75 per million output tokens through December 31, 2026—half the original 3.6 Flash token prices. The same announcement specifies $1.50 and $7.50 respectively from January 1, 2027. Those are model token rates, not a quoted price for a Teamwork research campaign or an Antigravity subscription.

Google acknowledges that some mathematical results used more parallelism than the default product configuration. It says the Antigravity version balances cost and capability while retaining the workflow. The announcement does not provide enough campaign-level spending, token-use or failure-rate data to calculate cost per verified discovery or establish parity between the showcased runs and the paid preview.

The company's engineering examples offer other checks on useful output. Google says Teamwork with Gemini 3.7 Flash built a RISC-V processor simulator that boots the xv6 operating system and runs more than 100 standard RISC-V benchmarks. It reports an average cycle-alignment error of 0.71% on unseen workloads against BOOM execution ground truth. Its account describes comparison with a BOOM simulator and functional checking against a separate Spike reference simulator, whose source code was sandboxed to prevent cheating. The figure is not a measurement across physical chips in deployment.

Google also says changes reached Eigen, a C++ linear-algebra library, and ParlayHash, a concurrent hash table, through normal external code review. The Eigen change accelerated matrix-vector multiplication when the matrix has a single row or column and went through review with Gemini 3.6 Flash's assistance. For Swiss Parlay, Google reports twice ParlayHash's initial-insert throughput with 64 threads and 1.5 times its overall throughput with one thread. It also claims performance close to the sequential FlatHashMap table while using 25% less memory per element, without separately identifying the memory comparison's baseline.

Those examples broaden the evidence beyond mathematical arguments, but measure different things: simulation fidelity, accepted code and theorem correctness cannot be combined into a single success rate.

What researchers still need to establish

The August announcement made Teamwork available through /teamwork-preview on paid Antigravity plans and said additional improvements would roll out over subsequent weeks. Humans remain responsible for objectives and final acceptance, even when the agents iterate autonomously for hours or days.

At the time of the announcement, Google said support for combining Flash and Pro within Long Proof was still coming in a future update. That makes the configuration behind the benchmark another detail researchers need to check against the version they can use.

The next useful test is whether researchers can reproduce the mathematical results at disclosed resource levels using the accessible configuration. That requires the exact model mix and agent concurrency, the total tokens and elapsed time, unsuccessful attempts as well as successes, and expert or formal verification of the output. Without those details, neither the seven-result count nor the introductory token discount establishes what a paying user must spend to obtain a new, verified result.