One headline result is a full proof of the 2013 Courtade–Kumar conjecture, reported by researchers from Google, CUHK, USC and CMU; Gemini helped find counterexamples to an earlier generalization, develop analytical bounds and interval-arithmetic certificates, extend the result to unbalanced functions, and formalize the proof in 50 million lines of Lean 4 code.

Google’s LEAP framework, paired with Gemini 4 Argon, has also produced large machine-checked formalizations, including about 1.8 million Lean lines for the Weil conjectures and more than 919,000 lines for a proof of Hilbert’s tenth problem over general rings of integers.

The same effort formalized a proof of finite-time blowup for the 3D Navier–Stokes equations and reported formalizations or verification involving the Birkhoff and 3D Bochner–Riesz conjectures, infinity-harmonic functions, the KdV equation and other conjectures.

Other highlighted theoretical advances span online inverse linear optimization, integer multiplication, the splay-tree Deque Conjecture and approximate leave-one-out cross-validation for non-smooth sparse penalties.

Additional results include near-optimal, Lean-verified sample bounds for adaptive data analysis; a construction resolving a 2014 quantum-query question; deterministic speedups for Boolean matrix multiplication and triangle detection; and new work on sparse distance networks, matrix sketches and single-pass streaming for dynamic cut sparsification.

Google’s Deep Review also provided manuscript feedback to 578 authors who opted in for STOC 2027; in a survey of 70 authors, 90% rated the feedback mostly or almost entirely factual, 90% said they would use it again, and more than 30% said it caught substantive proof bugs or mathematically significant typos.

In a separate demonstration of agent-led research, an autonomous team trained a 9×9 Go engine from a basic AlphaZero implementation, accelerating self-play 2,300-fold and reaching 1,885 Elo in under eight days—a gain of roughly 2,600 Elo.

Google says teams using Gemini 4 models and Antigravity’s /teamwork have advanced work across mathematics, science and systems engineering by splitting long tasks among specialized agents and checking results with tools such as proof assistants, tests, simulations and hardware measurements.

The /teamwork approach is designed to avoid the context loss and unreliable results that can come from one-shot generation: agents explore solutions in parallel with limited, task-specific context, while fresh critics or auditors check their work; Antigravity also offers the sequential coding workflow /boost and specialized research patterns.

A chemistry workflow combining 30 specialized agents with a physics-informed NMR spectral simulator achieved 95% top-1 exact-match and 100% top-3 accuracy on complex benchmark molecules, nearly doubling single-agent performance; separately, 29 agents converted 13 public tables into a 50-task causal-inference benchmark over 11.5 hours, with reviewers and auditors checking for flaws and shortcuts.

In systems engineering, FarArray-based applications handled graphs of up to one trillion edges, reporting 60–90 times higher throughput and 40–180 times faster performance at six times lower RAM than TCP key-value stores; other results included up to 14 times lower peak memory, 11–27 times faster Personalized PageRank, and TPU graph-neural-network kernels using up to 185 times less high-bandwidth memory with 8–15 times faster passes.

For TPU kernel optimization, DuoDiscover built 23-second proxy evaluators for workloads that take 7–32 minutes to evaluate on full hardware, reporting geometric-mean speedups of 4.09× across 17 JAXBench kernels and 2.99× across seven Pallas inference kernels.