Researcher - Lean 4 & Formal Proof Systems

Job summary

Translate informal mathematical arguments into clear, correct, machine-verifiable Lean 4 proofs, and develop formalizations that test the limits of existing proof assistants. Analyze prover failures, identify gaps and assumptions, and collaborate with researchers on strategies to improve formal verification workflows.

Job details

Researcher — Lean 4 & Formal Proof Systems (AI Training) About The Role What if your deep mathematical expertise could directly shape how AI reasons about formal proofs — pushing the frontier of what machines can understand and verify? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs for cutting-edge AI research. This role sits at the intersection of mathematics and computer science, working on problems that lie beyond the reach of current automated provers. This is a fully remote, flexible contract role built for researchers who love rigor, precision, and the challenge of expressing elegant human reasoning in a form a machine can trust. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness Analyze domain-specific and general mathematical arguments — identifying gaps, hidden assumptions, and formalizable sub-structures Construct formalizations that test and extend the limits of existing proof assistants, especially where automation breaks down Investigate failure modes in automated provers and articulate precisely why they occur — complexity barriers, missing lemmas, insufficient libraries Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms Collaborate with researchers to design and refine strategies for improving formal verification pipelines Create Lean proofs that reveal deeper patterns or generalizations implicit in original mathematical arguments Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models Who You Are Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean 4 strongly preferred Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics Ability to take dense, informal arguments and express them in clean, structured, machine-verifiable form Self-directed and comfortable working at the frontier, where the right path isn't always obvious Nice to Have Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools Experience contributing to large-scale formalization projects such as Mathlib Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding Prior experience with data annotation, evaluation systems, or AI training workflows Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us Work on cutting-edge AI research projects in collaboration with leading AI labs Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, intellectually demanding work Contribute directly to expanding what AI can understand and verify in advanced mathematics Potential for ongoing work and contract extension as new projects launch

What you’ll do

Translate informal mathematical arguments into clear, correct, machine-verifiable Lean 4 proofs, and develop formalizations that test the limits of existing proof assistants. Analyze prover failures, identify gaps and assumptions, and collaborate with researchers on strategies to improve formal verification workflows.

Requirements

A master's degree or higher in mathematics, logic, theoretical computer science, or a related field is required, along with strong rigorous proof-writing skills. Candidates should have hands-on experience with Lean or another formal proof system, with Lean 4 preferred, and be able to formalize dense mathematical arguments independently.

Benefits

• Fully Remote Work
• Flexible Schedule
• Freelance Autonomy
• Potential for Ongoing Work and Contract Extension

Listed skills

• precision · Preferred
• analysis · Preferred
• Organization · Preferred
• Training · Preferred
• Collaboration · Preferred
• Communication · Preferred
• future · Preferred
• Communication Skills · Preferred
• Strong communication skills · Preferred
• Strong Communication · Preferred
• Flexible · Preferred
• Lean · Preferred

Other relevant skills

Identified from the job description. Confirm important requirements above.

• Lean 4
• Formal Proof Systems
• Mathematical Proof Writing
• Formal Verification
• Proof Formalization
• Proof Decomposition
• Lemma Selection
• Automated Theorem Proving
• Type Theory
• Curry-Howard Correspondence
• Mathlib
• Coq
• Isabelle/HOL
• Agda
• Mathematical Reasoning
• Technical Communication

Job areas

• Science & Research
• Technology
• Software
• Education

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