Researcher - Lean 4 & Formal Proof Systems

About Alignerr

At Alignerr, we partner with the world’s leading AI research teams and labs to build and train cutting-edge AI models.

Position: Researcher - Lean 4 & Formal Proof Systems

We are seeking mathematicians with deep training in rigorous proof construction and hands-on experience with formal proof languages, especially Lean. This role sits at the intersection of mathematics and computer science, focusing on translating human-written mathematical arguments into precise, machine-verifiable formalizations. You will work on proofs that often lie beyond the current capabilities of automated provers, helping us map the frontier of what formal verification can express, capture, and automate.

What You’ll Do

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness.
• Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants, especially where tools struggle or fail.
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models.

Sample Work You Might Do

• Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
• Investigate where automated provers break down, and articulate why (complexity, missing lemmas, insufficient libraries, etc.).
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.

Requirements

• Master’s degree (or higher) in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems, with Lean strongly preferred.
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.
• Ability to translate informal arguments into clean, structured formal proofs.

Preferred Qualifications

• Prior experience with data annotation, data quality, or evaluation systems.
• Familiarity with type theory, Curry-Howard correspondence, and proof automation tools.
• Experience with large-scale formalization projects (e.g., mathlib).
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding.
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies.

Ideal Candidate

A mathematically mature problem-solver who enjoys working at the frontier of formal verification; someone who finds satisfaction in taking a dense, elegant human argument and expressing it in a form that a machine can understand. You appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge.

Why Join Us

• Competitive pay and flexible remote work.
• Collaborate with a team working on cutting-edge AI projects.
• Exposure to advanced LLMs and how they’re trained.
• Freelance perks: autonomy, flexibility, and global collaboration.
• Potential for contract extension.

Key skills/competency

• Lean 4
• Formal Verification
• Mathematical Proofs
• Theorem Proving
• Logic
• Type Theory
• Proof Assistants
• AI Research
• Mathematical Reasoning
• Problem Solving