Applied Formal Methods Researcher (Lean 4)

Alignerr Corp.; Charlotte (AR); Remote; USD 83,000 - 152,000; Part time

Job summary

Alignerr is seeking mathematicians and formal verification specialists to translate rigorous human arguments into Lean 4 proofs, working at the edge of automated reasoning. This is a fully remote, flexible hourly contract requiring 10–40 hours per week and centered on precision and verifiability of formal proofs.

Ideal candidates hold a Master’s or higher in Mathematics, Logic, or related fields with strong proof-writing skills and experience with Lean, Coq, Isabelle/HOL, or Agda.

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 comparable proof systems — Lean 4 strongly preferred.
• Genuinely enthusiastic about formal verification, proof assistants, and mechanized mathematics.
• Able to take a dense, informal mathematical argument and express it precisely in a form a machine can verify.

Responsibilities

• Translate informal mathematical proofs into Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility.
• Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures.
• Construct formalizations that probe and expose the limits of current proof assistants, especially where automation breaks down.
• Investigate why automated provers fail — complexity barriers, missing lemmas, insufficient libraries — and articulate those findings clearly.
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments.
• Uncover deeper patterns or generalizations implicit in the original mathematics through the formalization process.

Skills

Formal verification

Proof writing

Analytical thinking

Strong communication

Mathematical maturity

Education

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

Tools

Lean 3/4

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for mathematicians and formal verification specialists to translate rigorous human arguments into machine-verifiable Lean 4 proofs — working at the very edge of what automated reasoning can achieve.

This is a fully remote, flexible contract role designed for mathematically mature researchers who find elegance in precision and satisfaction in bridging the gap between human intuition and formal logic.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility
• Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
• Construct formalizations that probe and expose the limits of current proof assistants, especially where automation breaks down
• Investigate why automated provers fail — complexity barriers, missing lemmas, insufficient libraries — and articulate those findings clearly
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
• Uncover deeper patterns or generalizations implicit in the original mathematics through the formalization process

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 comparable proof systems — Lean 4 strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, informal mathematical argument and express it precisely in a form a machine can verify

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 manual scaffolding
• Prior experience with data annotation, data quality, or AI evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs at the frontier of AI and formal mathematics
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually challenging work
• Contribute directly to shaping how AI reasons about mathematics at a foundational level
• Collaborate with a global team of researchers pushing the boundaries of mechanized proof
• Potential for ongoing work and contract extension as new projects launch