Remote Applied Formal Methods Researcher (Lean 4)

Alignerr Corp.; United States; Remote; USD 83,000 - 165,000; Full time

Job summary

Alignerr Corp. is hiring Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs, working at the frontier of proof assistants and automation.

This fully remote, hourly contract targets mathematicians who thrive at the intersection of abstract reasoning and precise formalization, with 10–40 hours per week and flexible scheduling.

Qualifications

• Masters or higher in Mathematics, Logic, Theoretical Computer Science, or a related field.
• Strong proof-writing across algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, or Agda; Lean 4 preferred.
• Enthusiasm for formal verification, proof assistants, and mechanized mathematics.
• Translate informal arguments into precise, structured formal proofs with clarity.

Responsibilities

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility.
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that stress-test the limits of existing proof assistants — especially where automated tools struggle or fail.
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Investigate automated prover breakdowns and articulate root causes — complexity gaps, missing lemmas, insufficient libraries, and more.
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics.

Skills

Proof writing

Mathematical maturity

Strong communication

Education

Master's degree or higher

Tools

Lean (Lean 4)

Coq

Isabelle/HOL

Agda

Job description

Alignerr Corp. is hiring Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs, working at the frontier of proof assistants and automation.

This fully remote, hourly contract targets mathematicians who thrive at the intersection of abstract reasoning and precise formalization, with 10–40 hours per week and flexible scheduling.