Google Research says its multi-agent system running on Gemini 4 Argon “generated the first formalization of the Birkhoff conjecture, a dynamical-systems problem open since 1927”, 99 years by our arithmetic. The result is one of several machine-checked math results Google listed in a blog post on 13 November.
The same system, Google says, “fully autonomously produced an end-to-end, machine-checked formalization of the Weil conjectures” in “about 1.8 million lines of Lean, produced across 28,800 subagent invocations”: about 62.5 lines per call, by our arithmetic.
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An evergreen Business Engineer explainer on what AI agents are and how they work. It teaches the general idea only and does not discuss Google’s math results.
The key insight: As we read the post, the scale is in the checking rather than the claims: Google says one formalization ran to about 1.8 million lines of Lean across 28,800 subagent calls, and a proof of a 2013 conjecture ran to 50 million lines, work Google describes as done with human experts.
Google describes formalization in Lean 4 as turning “a proof into code that a computer kernel checks line by line”, so that “the proof only compiles if every logical step holds”. The post credits a multi-agent framework called LEAP, built with Google Cloud AI and paired with Gemini 4 Argon.
Besides Birkhoff and Weil, Google says the system formalized for the first time “the 3D Bochner–Riesz conjecture”, which it calls “a central problem in harmonic analysis open for more than 50 years”, “finding and fixing a gap in a recently released informal proof along the way”.
The post also lists “resolving the C¹ regularity of infinity-harmonic functions in three and higher dimensions”, which it describes as “an open question for about 20 years”, and verifying “a UCLA group’s informal proofs of the 40-year-old Jamison Caterpillar Conjecture”. It says the system produced the first formalization of a recent proof of Hilbert’s tenth problem over general rings of integers, in over 919,000 lines of Lean.
Years each problem had been open, as Google Research’s 13 November post states them; the Birkhoff (1927) and Courtade-Kumar (2013) year counts are our arithmetic. Google describes Birkhoff and Bochner-Riesz as formalized, C1 regularity as resolved and Courtade-Kumar as proved.
A 2013 Conjecture in 50 Million Lines
Separately, Google says researchers from Google, CUHK, USC and CMU used its Long Proof pattern “to prove information theory’s 2013 Courtade–Kumar conjecture in full generality”. It says Gemini models “developed most of the new analytical bounds and interval-arithmetic certificates”, and that the team “formalized the entire proof in Lean 4, producing 50 million lines of code”.
That is about 28x the length of the Weil formalization, by our arithmetic, and the three formalizations with line counts in the post add up to about 52.7 million lines. Our October piece on Google Research’s earlier five open math results covers the previous round.
Beyond Math, and Who Gets Access
The post reports results outside math as well. It says a two-week Argon campaign added “about 800,000 lines of safe Rust that pass all kernel unit tests and boot on arm64 hardware” to Google’s Zircon microkernel port. It also says authors of 578 submissions to the STOC 2027 computer science conference opted in to its Deep Review feedback tool.
Google says external users “can use Gemini 4 models with /teamwork and /boost in Antigravity and Deep Review today”, and that it has opened applications giving “10,000 academic researchers six months of free access to our highest usage tier”. Our piece on Gemini 4 Hydrogen’s pricing covers one of the models named.
The Structural Read
As we read it, Google separates formalizing an existing proof from resolving a problem: it lists the Birkhoff, Weil and Bochner–Riesz items as formalizations, and the C¹ regularity and Courtade–Kumar items as resolved or proved.
As we read the access terms, Google is pairing the results with distribution: it says the tools are available in Antigravity today and that it has opened applications for 10,000 academic researchers to get six months of free access to its highest usage tier.
Google Research, Advancing science & engineering with Antigravity’s /teamwork, 13 November 2026
“Formalizing mathematics in Lean 4 turns a proof into code that a computer kernel checks line by line.”
Three Implications
FOR MATHEMATICIANSGoogle says the system found and fixed a gap in a recently released informal proof of the 3D Bochner–Riesz conjecture while formalizing it.
FOR RESEARCHERSGoogle says 10,000 academic researchers can apply for six months of free access to its highest usage tier.
FOR SOFTWARE TEAMSGoogle says a two-week campaign added about 800,000 lines of safe Rust to its Zircon microkernel port that pass all kernel unit tests.
The framework says: “The surface, not the model, governs autonomy.”
As we read it, Google’s post credits its results to multi-agent harness patterns such as /teamwork and LEAP running on Gemini 4 models; the framework does not discuss Google’s math results.
What Is Not Established
The post does not say who wrote the proof of the Birkhoff conjecture that was formalized, and it does not describe any independent review of the results. Google says “All of this work is done in collaboration with human experts”.
A formalization checks an existing proof; Google describes the C¹ regularity and Courtade–Kumar items as resolved or proved, and the Birkhoff, Weil and Bochner–Riesz items as formalizations. Our piece on Terence Tao’s view of OpenAI’s 372 proofs covers the debate over AI math claims. Google was not contacted for this piece.
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Google says its Gemini 4 agents produced the first machine-checked formalization of the Birkhoff conjecture, open since 1927, and a 1.8-million-line formalization of the Weil conjectures across 28,800 subagent calls, while a team using its tools proved the 2013 Courtade–Kumar conjecture in 50 million lines of Lean.
A note on sourcing. The results, line counts and access terms come from Google Research’s blog post “Advancing science & engineering with Antigravity’s /teamwork” of 13 November 2026, read in full on 14 November. Year counts, ratios and totals are our arithmetic. Google was not contacted for this piece.
Gennaro Cuofano is a CRO and tech executive who has worked in AI since late 2015, starting with bringing NLP, natural-language generation, voice and chatbot products to the marketing industry. His background is in law and finance: he holds a Master's degree in Law and an International MBA with an emphasis on corporate finance (LUISS Business School and the University of San Diego, 2012), and worked as a financial analyst at a real-estate investment firm in San Diego and as an assistant controller. His work focuses on business model strategy, business engineering and, more broadly, structural analysis: how companies make money, read from their own filings. He created FourWeekMBA and leads research there and at The Business Engineer, his newsletter on AI and business strategy, with over 95,000 subscribers and more than 1,000 published analyses. His writing has also appeared on Entrepreneur (for example, How to Digitize a Family Business in Europe) and HackerNoon. Find him on LinkedIn and Substack. See how we source.
