Researcher — Lean 4 & Formal Proof Systems (AI Training)
About The Role
What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — working at the cutting edge of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role designed for researchers who love rigor, structure, and pushing the boundaries of mechanized mathematics.

Organization: Alignerr

Type: Hourly Contract

Location: Remote

Commitment: 10–40 hours/week

What You'll Do

Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations 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 automated 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

Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more





Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Who You Are

Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Have a strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete mathematics

Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred

Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics

Able to translate dense, informal arguments into clean, structured formal proofs with precision and care

Nice to Have

Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools

Experience with 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, data quality evaluation, or AI training workflows

Robust communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

Work on cutting-edge AI projects alongside leading research labs and AI teams

Fully remote and flexible — work when and where it suits you

Freelance autonomy with the structure of meaningful, intellectually rigorous work

Contribute directly to expanding the frontier of what formal verification and AI can achieve together

Potential for ongoing work and contract extension as new projects launch

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📌 Researcher - Lean 4 & Formal Proof Systems (Quebec City)
🏢 Alignerr
📍 Quebec City