Lean 4 Proof Engineer - Mathematical Formalization

About The Role

What if your mastery of rigorous mathematics could directly shape how AI reasons, proves, and understands the deepest structures of human knowledge?

We're looking for mathematicians with hands-on experience in formal proof systems to help map the frontier of machine-verifiable mathematics — formalizing advanced proofs in Lean 4 for some of the most ambitious AI research happening today.

This is a fully remote, flexible contract role built for mathematically mature problem-solvers who find genuine satisfaction in translating elegant human arguments into precise, machine-checkable form.

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 assistants) with an emphasis on clarity, structure, and correctness
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — 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
• Investigate why automated provers break down — complexity, missing lemmas, insufficient libraries — and articulate those findings clearly
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• 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
• Possess a strong foundation in rigorous proof writing and mathematical reasoning across core areas
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistants — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, elegant human argument and express it in a form that a machine can verify
• Self-motivated and able to work independently in an asynchronous, remote environment

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, quality evaluation, or AI training workflows
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work at the genuine frontier of formal mathematics and AI — proofs that matter, problems that are hard
• Fully remote and flexible — structure your work around your life
• Freelance autonomy with the substance of meaningful, technically demanding work
• Collaborate with researchers working on cutting-edge AI models and LLM training
• Gain rare exposure to how advanced AI systems are built and evaluated at the mathematical level
• Potential for ongoing work and contract extension as new projects launch