Researcher - Lean 4 & Formal Proof Systems

About The Role

What if your deep mathematical training could directly shape how AI reasons about proofs — and push the boundary of what machines can formally verify? We're looking for mathematicians and formal methods researchers to translate sophisticated mathematical arguments into Lean 4, working at the cutting edge of AI research and mechanized mathematics. This is a fully remote, flexible contract role for people who find beauty in rigor — and satisfaction in making a machine understand what a human mind sees instantly.

Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week

What You'll Do

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems)
• 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 automation breaks down
• Collaborate with researchers to design, refine, and evaluate formal verification strategies
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate where automated provers fail — and articulate precisely why

Who You Are

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof construction across one or more core mathematical domains
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable proof assistant — Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, informal argument and express it in a form a machine can verify — without losing what makes the proof elegant

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 requires manual scaffolding
• Prior experience with data annotation, data quality, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, technically demanding work
• Contribute directly to advancing the capabilities of formal verification and AI reasoning
• Potential for ongoing work and contract extension as new projects launch