Google's Gemini 4 agents and Antigravity /teamwork tackle open problems in math and science

Google says teams across the company and at academic partner institutions have used its Gemini 4 model family — Argon, Carbon and Hydrogen — together with the multi-agent /teamwork feature in its Antigravity environment to make progress on research problems that had sat open for years. A Google Research blog post describes results in information theory, formal verification, optimization, quantum computing and streaming algorithms, along with molecular structure discoveries, kernel optimization and infrastructure gains it says are already in production.

How /teamwork works

The post attributes the design to two shortcomings of current language models: single generations are unreliable, leaving a wide gap between one attempt and a correct answer, and models lose track of detail over multi-day tasks as attention spreads across growing context windows.

/teamwork addresses the first problem by exploring many candidates in parallel and checking them against external falsifiers — the Lean 4 proof checker, unmodified software test suites, execution simulators, web search and hardware counters — which decide which answers actually hold. It handles the second by partitioning context: each specialist agent sees only the files and tools its step needs, coordinators hand work to fresh successors, and critic and auditor agents re-check results from clean contexts, without the reasoning of the agent that produced them.

Workflows are written as declarative, self-improving natural-language patterns, with each prompt routed to the best-fitting pattern — from distributed coding and iterative problem-solving, packaged separately as /boost, to long proof and document review. Google says the remaining features reach external Antigravity users in the coming weeks.

Proving the Courtade–Kumar conjecture

The headline result is a proof of the Courtade–Kumar conjecture, open in information theory since 2013. Researchers from Google, CUHK, USC and CMU used the Long Proof pattern, which implements a harness called Stellar Colosseum inside Antigravity. The conjecture states that when a random bit string passes through a noisy channel, no compression of the input to a single bit preserves more information than a "dictator function" that copies one input bit.

The collaboration was interactive rather than one-shot. Gemini first found counterexamples to a generalized version of the conjecture from an earlier CUHK paper, the post says. The CUHK team then proposed a candidate function reducing the problem to a 14-variable optimization, along with a key lower bound. Gemini 4 Argon and earlier models partitioned the parameter space, produced most of the new analytical bounds and interval-arithmetic certificates, and extended the proof from balanced to unbalanced functions without human input. The full proof was then formalized in Lean 4, totaling 50 million lines of code.

Results across theory

Other open problems were posed directly to Gemini 4 and to multi-agent harnesses; Google says the human authors verified, simplified and edited the resulting proofs and algorithms for publication. Highlights from the post:

• Adaptive data analysis: a harness running Gemini 4 Argon independently proved and Lean-verified near-optimal sample bounds for statistical queries chosen adaptively from earlier answers, closing a gap open since 2014 and yielding the first nearly space-optimal streaming algorithm that stays accurate against adaptive adversaries on streams with both insertions and deletions.
• Quantum computing: a new construction settles a 2014 question with the first n-bit Boolean functions needing strictly more than n/2 quantum queries at constant error, and pins down the exact overhead for symmetric functions.
• Matrix multiplication: a deterministic algorithm resolves the main open question from STOC 2024, achieving its target speedup over cubic time for combinatorial Boolean matrix multiplication and triangle detection, where only logarithmic savings had been found in the previous fifty years.
• Sparse sketches: stacked sketches answer a 2025 open question, compressing a matrix to linear dimension while preserving every direction of an r-dimensional subspace using only √log r nonzeros per row — quadratically fewer than the log r previously required and nearly matching a new lower bound.
• Streaming graphs: Stellar Colosseum answers a question left open by FOCS 2022 with the first single-pass streaming algorithm for cut sparsification of weighted graphs under dynamic edge-weight updates, achieving near-optimal memory, update time and reconstruction time simultaneously.
• Optimization and arithmetic: a deterministic algorithm for online inverse linear optimization reaches optimal regret while cutting runtime from exponential to polynomial in the dimension, and separate multi-agent campaigns simplified the Turing-machine bound for n-bit integer multiplication below n log n.

A geometry lower bound also shows that approximating all pairwise distances among n points within any constant factor can require polynomially more than n edges, even with extra Steiner points and arbitrarily many hops.

Why it matters

Two things separate this from the usual run of AI-does-math announcements. Verification is built in: the strongest claims come with Lean 4 formalizations or checks against untouched test suites, so they do not rest on trusting a model's output. And the architecture targets the real failure modes of agents — unreliable single generations and context decay over long horizons — using parallel exploration and strict context isolation.

If the tools hold up once external researchers get them, the bottleneck in parts of theoretical work could shift from generating candidate arguments toward framing problems and reviewing formalizations. The results are self-reported by Google, and independent scrutiny of the published papers will be the real test.