Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; United States; Remote; MXN 1,018,000 - 3,053,000; Part time

Job summary

Alignerr Corp. is seeking a Lean 4 Proof Engineer to translate advanced mathematics into formal Lean proofs. The role emphasizes rigorous proof construction, collaboration with AI researchers, and creating readable proof scripts that adhere to formal verification best practices.

The position is a remote hourly contract with flexible hours and the opportunity to work on cutting-edge formalization projects and large-scale proof systems.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong proof-writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems.
• Passion for formal verification and mechanized mathematics.
• Ability to translate dense informal arguments into clean formal proofs.

Responsibilities

• Translate informal proofs into Lean 4 formalizations with clarity, correctness, and structure.
• Analyze domain-specific and general proofs to identify gaps and formalizable sub-structures.
• Construct formalizations that test the limits of proof assistants where automation struggles.
• Collaborate with AI researchers to design, refine, and evaluate verification strategies.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
• Investigate where automated provers break down and articulate underlying reasons.
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics.

Skills

Lean

Proof assistants

Mathematics

Formal verification

Coq

Isabelle/HOL

Agda

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or related field

Tools

Coq

Isabelle/HOL

Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization

About The Role

What if your mathematical expertise could directly shape the future of AI reasoning? We're looking for Lean 4 Proof Engineers to translate advanced human-written mathematics into precise, machine-verifiable formalizations — working at the cutting edge of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role built for mathematicians who love rigorous proof construction and want their work to matter beyond the page.

• 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 systems) with a focus on clarity, correctness, and structure
• Analyze domain-specific and general proofs to identify 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 AI researchers to design, refine, and evaluate formal verification strategies
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that surface 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 mathematics
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense informal arguments into clean, precisely structured formal proofs
• A mathematically mature problem-solver who finds satisfaction in expressing an elegant human argument 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, evaluation systems, or data quality workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

Why Join Us

• Work at the frontier of AI research alongside world-leading research labs and teams
• Fully remote and flexible — structure your work around your life, not the other way around
• Freelance autonomy with intellectually meaningful, high-impact work
• Direct exposure to how cutting-edge large language models are trained and evaluated
• Contribute to work that is genuinely pushing the boundaries of what machines can understand and verify
• Potential for ongoing contract extension as new projects launch