Applied Formal Methods Researcher (Lean 4)

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

About The Role

What if your deep mathematical expertise could directly shape how the world's most advanced AI systems reason, prove, and think? We're looking for Applied Formal Methods Researchers to formalize challenging mathematical proofs in Lean 4 — working at the very frontier of mechanized mathematics and AI research.

About The Role

What if your deep mathematical expertise could directly shape how the world's most advanced AI systems reason, prove, and think? We're looking for Applied Formal Methods Researchers to formalize challenging mathematical proofs in Lean 4 — working at the very frontier of mechanized mathematics and AI research.

This is a fully remote, flexible contract role built for mathematicians who are passionate about formal verification and want their work to matter. No two days are the same — you'll be pushing the limits of what proof assistants can do, and the results feed directly into cutting‑edge AI development.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week

What You’ll Do

• 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

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 algebra, analysis, topology, logic, or discrete mathematics
• Have hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal proof system — Lean strongly preferred
• Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, elegant human argument and express it in a form a machine can understand and verify
• Comfortable working independently and asynchronously in a remote setting

Nice to Have

• Familiarity with type theory, the Curry‑Howard correspondence, and proof automation tools
• Experience contributing to large‑scale formalization projects such as Mathlib
• Exposure to theorem provers where automated reasoning frequently fails or requires significant manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators

Why Join Us

• Work on some of the most intellectually demanding problems at the intersection of mathematics and AI
• Fully remote and flexible — structure your work around your life, not the other way around
• Freelance autonomy with the satisfaction of meaningful, high-impact contributions
• Direct exposure to how advanced AI models are trained and evaluated
• Collaborate with researchers and mathematicians working on genuinely novel problems
• Potential for ongoing work and contract extension as new projects launch