Applied Formal Methods Researcher (Lean 4)

About The Role
What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal methods experts to translate rigorous human-written arguments into machine-verifiable Lean 4 proofs — working at the very edge of what automated reasoning can do.
This is a fully remote, flexible contract role designed for mathematically mature problem-solvers who find real satisfaction in the precision and structural beauty of formal verification.
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 generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test the limits of existing proof assistants — especially where tools struggle or fail
Investigate where automated provers break down and articulate the underlying reasons (complexity, missing lemmas, library gaps, etc.)
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 proof assistant idioms
Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Formalize classical proofs and compare machine-verifiable structures against textbook arguments
Surface deeper patterns and 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 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 proof systems — Lean 4 strongly preferred
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, informal mathematical arguments into clean, structured formal proofs
Thrive working independently on technically demanding, open-ended problems
Nice to Have
Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
Experience contributing to large-scale formalization projects (e.g., 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 directly with leading AI research teams and labs on cutting-edge projects
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, technically challenging work
Contribute to research that is actively advancing the frontier of mechanized mathematics and AI reasoning
Potential for ongoing work and contract extension as new projects launch

Work arrangement
No