Applied Formal Methods Researcher (Lean 4)

About The Role
What if your deep mathematical training could directly shape how AI understands and constructs rigorous proofs? We're looking for Applied Formal Methods Researchers to formalize advanced mathematics in Lean 4 — working at the precise boundary where human mathematical reasoning meets machine verifiability.
This is a fully remote, flexible contract role built for mathematicians who live at the intersection of proof theory and computation. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify — this role was made for you.
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 — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test the limits of existing proof assistants, especially where automation struggles or fails
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
Formalize classical proofs and compare machine-verifiable structures against textbook arguments
Investigate where automated provers break down — and articulate precisely why
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 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 strongly preferred
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate informal mathematical arguments into clean, structured formal proofs
Comfortable working independently in an asynchronous, remote environment
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 the world's leading AI research labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually rigorous work
Direct impact on how AI systems learn to reason about advanced mathematics
Exposure to state-of-the-art large language models and how they're trained on formal reasoning
Potential for ongoing work and contract extension as new projects launch

Work arrangement
Yes