Leo: Revolutionizing Mathematical Proofs with AI Assistance
In the realm of pure mathematics, proofs have long been the gold standard of rigor, yet they remain stubbornly human endeavors. Theorems are often scribbled on blackboards or typed in LaTeX, conveying intuition through natural language and diagrams rather than machine-verifiable logic. This informality, while elegant, creates bottlenecks: verifying complex proofs by hand is error-prone, collaboration across proofs is cumbersome, and scaling to massive theorems feels Sisyphean. Enter Leo, a startup founded by former DeepMind researchers, which promises to bridge this gap by deploying AI to formalize mathematics at scale.
Leo emerged from the frustration of its founders, who cut their teeth on DeepMind’s FunSearch project. That effort, which garnered headlines in late 2023 for discovering new solutions to combinatorial problems, highlighted AI’s potential in math but fell short of full proof generation. Johan Henriksson, Leo’s CEO and a key FunSearch contributor, recalls the limitations vividly. “We realized that to really push the boundaries, we needed to formalize everything,” he says. Joined by co-founders Jakob Moosbauer and Alex Davies, both DeepMind alumni with PhDs in mathematics and machine learning, Henriksson launched Leo in early 2026. Their mission: transform informal mathematical sketches into fully verified proofs using interactive AI tools.
At the heart of Leo’s approach lies Lean, an open-source proof assistant developed by Microsoft Research. Lean encodes mathematics in a dependently typed programming language called Lean 3, where every statement and proof step must compile without errors. This formalization enables machine checking but demands expertise that few mathematicians possess. Lean’s mathlib library, a vast repository of formalized theorems crowdsourced by thousands, serves as Leo’s training corpus. The startup fine-tunes large language models (LLMs) on this dataset, creating assistants that “speak” Lean fluently.
Leo Assistant, the flagship product, is a chat-based interface reminiscent of ChatGPT but specialized for proof formalization. Users input informal problem statements or proof sketches in English, and the AI generates Lean code, explains its reasoning, and iterates based on feedback. “It’s like having a brilliant grad student who never sleeps,” quips Moosbauer. The tool shines in geometry, a domain historically resistant to formalization due to its reliance on diagrams and intuition.
A compelling demonstration came at the International Mathematical Olympiad (IMO) level. Leo tackled Problem 3 from the 1988 IMO, a geometry challenge involving cyclic quadrilaterals and angle chasing. Traditional solutions span pages of diagrams and casework; Lean’s formal version requires precise encoding of Euclidean axioms from mathlib’s geometry module. In under 10 minutes of interaction, Leo Assistant produced a verified proof, handling edge cases like degenerate triangles automatically. Similarly, for IMO 2008 Problem 3 on polynomial inequalities, the AI navigated Diophantine approximations and AM-GM inequalities with minimal guidance.
This prowess stems from Leo’s training regimen. Models are instructed not just to generate code but to reason step-by-step, mirroring human proof strategies. Reinforcement learning from human feedback (RLHF) refines outputs, prioritizing concise, tactic-based proofs over verbose expansions. Tactics, Lean’s proof automation primitives like “simp” for simplification or “ring” for algebraic identities, allow compact proofs that unfold into thousands of logical steps under the hood.
Yet Leo is no panacea. Current limitations include hallucinated proofs on novel theorems and struggles with heavy computation, such as those in number theory. “AI formalizers excel at routine tactics but falter on creative leaps,” notes Kevin Buzzard, a Lean evangelist at Imperial College London. Leo counters this by integrating with external solvers like Z3 for automated reasoning and by encouraging hybrid workflows: humans supply high-level strategy, AI handles drudgery.
The startup’s ambitions extend beyond assistance. Leo envisions a “formal math web,” where theorems link like hyperlinks, enabling unprecedented discovery. Imagine querying “prove Fermat’s Last Theorem using only elliptic curves,” with the AI assembling a modular proof from mathlib components. Early adopters, including university researchers, report 10x speedups in formalization. One user formalized a 50-page algebraic geometry paper in weeks, not months.
Funding fuels this vision: Leo raised $5 million in seed capital from investors like Thrive Capital and Nat Friedman, valuing the company at $25 million. The team, now 12 strong, operates remotely from Berlin and London. Partnerships with Lean maintainers ensure alignment with mathlib’s evolution, including the shift to Lean 4.
Critics worry about over-reliance on AI, potentially deskilling mathematicians. Henriksson counters: “Formal math amplifies human insight, not replaces it. Informal proofs will always exist for communication; formal ones ensure truth.” As AI encroaches on creative domains, Leo positions itself at the vanguard, democratizing rigor for the next generation of theorems.
By making formal verification conversational and efficient, Leo could accelerate fields from cryptography to machine learning theory, where bug-free math underpins security and reliability. Whether it fully upends mathematical practice remains to be seen, but one thing is clear: the blackboard era may be giving way to the AI-assisted proof.
What are your thoughts on this? I’d love to hear about your own experiences in the comments below.