Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr Corp.; Boston (MA); Remote; USD 96,000 - 165,000; Part time

Job summary

Alignerr Corp. is seeking a Formal Verification Scientist to translate complex mathematical proofs into Lean 4 formalizations, pushing the boundaries of proof automation.

This fully remote hourly contract role invites mathematicians who love rigorous reasoning to work on challenging AI-oriented verification tasks. You'll translate and test proofs, collaborate with AI researchers, and produce readable, reproducible Lean scripts.

Qualifications

• Mastery of rigorous proof writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean 3 or Lean 4, Coq, Isabelle/HOL, Agda, or comparable proof systems.
• Ability to translate informal mathematical arguments into clean, machine-verifiable formal proofs.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with a focus on clarity, structure, and correctness
• Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants — especially where 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 where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Skills

Lean 4

Coq

Isabelle/HOL

Agda

Formal verification

Mathematical reasoning

Education

Master's degree or higher in Mathematics or related field

Job description

About The Role

What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for Formal Verification Scientists to translate complex, human-written mathematical proofs into precise, machine-verifiable formalizations using Lean 4 — working at the absolute frontier of what proof assistants can express and automate.

About The Role

What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for Formal Verification Scientists to translate complex, human-written mathematical proofs into precise, machine-verifiable formalizations using Lean 4 — working at the absolute frontier of what proof assistants can express and automate.

This is a fully remote, flexible contract role for mathematicians who are passionate about rigorous proof construction and the power of formal verification. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can understand, this role was built for you.

• 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 a focus on clarity, structure, and correctness
• Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants — especially where 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 where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Who You Are

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as 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 — Lean 4 strongly preferred
• Able to translate informal mathematical arguments into clean, structured, machine-verifiable formal proofs
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Mathematically mature and comfortable working independently at the edge of current knowledge

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 evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to cross-functional collaborators

Why Join Us

• Work on cutting‑edge AI projects alongside world‑leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Contribute directly to expanding what AI can understand, verify, and reason about mathematically
• Potential for ongoing work and contract extension as new projects launch