Today we're publicly releasing OrthoSolver — a new AI system purpose-built for formal mathematical reasoning. OrthoSolver operates natively inside Lean 4, the leading interactive theorem prover, and is designed to accelerate proof discovery, verify complex theorems, and make formal mathematics accessible to a much wider audience.
Why formal reasoning?
Large language models have made impressive strides in generating natural-language mathematics. But plausible-sounding proofs are not the same as correct proofs. In formal mathematics, every logical step is machine-checked — there is no room for hand-waving, hidden assumptions, or subtle errors.
We believe this kind of rigor is not just valuable for pure mathematics. Formal verification is the foundation of trustworthy software, safe AI systems, and any domain where correctness cannot be left to chance.
What OrthoSolver can do
OrthoSolver works as a copilot inside your Lean 4 workflow. Given a proof goal, it searches for valid tactic sequences that close the goal — or, when the problem is more open-ended, it proposes intermediate lemmas and proof strategies. Key capabilities include:
- Tactic prediction — Given a proof state, OrthoSolver suggests the most promising next tactics, ranked by likelihood of closing the goal.
- Multi-step proof search — For harder goals, OrthoSolver performs tree search over tactic sequences, exploring thousands of candidate paths in seconds.
- Lemma synthesis — When a direct proof is out of reach, OrthoSolver can propose helper lemmas that decompose the problem into manageable pieces.
- Autoformalization — Translate informal mathematical statements written in natural language or LaTeX into formal Lean 4 definitions and theorem statements.
How it works
At its core, OrthoSolver combines a transformer language model trained on millions of formal proofs with a Monte Carlo tree search algorithm adapted for the proof-search setting. The language model provides a learned prior over which tactics are likely to succeed, while the tree search explores and verifies candidate proofs against the Lean kernel.
Every proof OrthoSolver produces is checked by Lean's type checker before it is returned to the user. There are no approximations — if OrthoSolver says a proof is complete, it is mathematically guaranteed to be correct.
Benchmarks
On the MiniF2F benchmark (a standard evaluation suite of competition-level math problems formalized in Lean), OrthoSolver solves 71.4% of problems — a significant improvement over prior state-of-the-art systems. On Mathlib's test split, OrthoSolver closes 58% of proof goals in under 30 seconds.
What's next
This release is only the beginning. We are actively working on extending OrthoSolver's capabilities to longer, multi-step proofs, improving its ability to reason about novel mathematical structures, and integrating it more deeply into the Lean ecosystem.
We're also committed to open research. We will be publishing a detailed technical report in the coming weeks, and we plan to contribute our training infrastructure and datasets back to the Lean community.
If you'd like to try OrthoSolver or learn more about what we're building, get in touch.