Remote Lean 4 Formal Methods Researcher

Alignerr Corp.; Sheffield (TX); Remote; USD 14,000 - 55,000; Part time

Job summary

Alignerr is seeking an Applied Formal Methods Researcher to formalize challenging mathematical proofs in Lean 4, working at the frontier of mechanized mathematics and AI research. This is a fully remote, hourly contract role with 10–40 hours per week, offering intellectual challenge and flexible scheduling.

You will translate informal proofs into machine-verifiable Lean formalizations, analyze complex proofs across domains, and push the boundaries of what proof assistants can do.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal proof system.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations with an emphasis on clarity, structure, and correctness
• Analyze complex proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub‑structures
• Construct formalizations that stress‑test existing proof assistants, especially in areas where tools struggle or fail entirely
• Investigate the boundaries of automated reasoning — articulating why and where provers break down (complexity, missing lemmas, library limitations, etc.)
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Guide proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical results and compare machine‑verifiable structures against standard textbook arguments

Skills

Proof writing

Lean

Formal methods

Mathematical reasoning

Education

Master's degree or higher in Mathematics/Logic/Theoretical CS

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Alignerr is seeking an Applied Formal Methods Researcher to formalize challenging mathematical proofs in Lean 4, working at the frontier of mechanized mathematics and AI research. This is a fully remote, hourly contract role with 10–40 hours per week, offering intellectual challenge and flexible scheduling.

You will translate informal proofs into machine-verifiable Lean formalizations, analyze complex proofs across domains, and push the boundaries of what proof assistants can do.