Researcher - Lean 4 & Formal Proof Systems

Researcher — Lean 4 & Formal Proof Systems (AI Training)
About The Role
What if your deepest mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — pushing the boundaries of what proof assistants can express, capture, and automate.
This is a fully remote, flexible contract role built for researchers who thrive on rigor, precision, and intellectual challenge. If you find satisfaction in taking a dense, elegant human 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 proofs across domains — 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
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
Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond
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 math
Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 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 independently
Naturally precise, patient, and driven by structural elegance and logical completeness
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, evaluation systems, or AI training workflows
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 and top AI teams
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually stimulating work
Operate at the true frontier of formal verification and mechanized mathematics
Contribute directly to how next-generation AI systems reason about mathematics and logic
Potential for ongoing work and contract extension as new projects launch

Work arrangement
No