Researcher - Lean 4 & Formal Proof Systems

Researcher – Lean 4 & Formal Proof Systems (AI Training)

About The Role

What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification experts 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 for researchers who love rigor, structural beauty, and the challenge of pushing formal systems to their limits.

• 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 — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants, particularly where automation breaks down
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Advise on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
• 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
• 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 translate dense informal arguments into clean, structured, and correct formal proofs
• Naturally precise and detail-oriented — you find satisfaction in resolving gaps that automated tools cannot yet bridge

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, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning 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, intellectually stimulating work
• Contribute directly to advancing the frontier of formal verification and AI mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch