Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr Corp.; Seattle (WA); Remote; USD 83,000 - 165,000; Part time

Job summary

Alignerr Corp. seeks a Formal Verification Scientist to translate advanced proofs into machine-verifiable Lean formalizations.

This fully remote, hourly contract role is ideal for mathematicians who operate at the intersection of rigorous proof and cutting-edge computer science. You'll work on translating informal arguments into structured proofs, analyze gaps, and test proof assistants’ limits, collaborating with AI researchers to refine verification pipelines.

Qualifications

• Master’s degree or higher in mathematics, logic, or a closely related field.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems.
• Ability to translate dense informal mathematical arguments into clean, structured proofs.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete math.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity and correctness.
• Analyze generic and domain-specific proofs, identifying gaps and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants, especially where automation struggles.
• Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof idioms.
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
• Investigate where automated provers break down due to complexity or missing libraries.
• Create Lean proofs that reveal deeper patterns or generalizations in the original mathematics.

Skills

Proof writing

Formal verification

Mathematical maturity

Communication

Education

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

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical intuition and mastery of formal proof systems could directly shape how AI understands and reasons about mathematics? We're looking for Formal Verification Scientists to translate advanced human-written proofs into precise, machine-verifiable formalizations — helping map the outer edge of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role ideal for mathematicians who live at the intersection of rigorous proof construction and cutting-edge computer science.

• 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 proof systems) with an emphasis on clarity, structure, and correctness
• Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail entirely
• 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 proof assistant idioms
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate and articulate where automated provers break down — due to complexity, missing lemmas, or insufficient libraries
• Create Lean proofs that reveal 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
• Have 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 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured, machine‑verifiable proofs
• Mathematically mature and energized by working at the frontier — where automated tools run out and human insight takes over

Nice to Have

• Familiarity with type theory, the Curry‑Howard correspondence, and proof automation tools
• Experience with 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, or AI evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on cutting‑edge AI research projects alongside leading AI labs and research teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute directly to expanding the frontier of formal verification and mechanized mathematics
• Gain rare exposure to how advanced AI models are trained on mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch