Formal Verification Scientist (Lean 4 & Mathlib)

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

Job summary

Alignerr is seeking a Formal Verification Scientist to translate advanced mathematical arguments into Lean 4 proofs, working with AI research teams on mechanized mathematics. This is a fully remote, hourly contract.

You will collaborate across disciplines, stress-test proof assistants, and produce readable scripts aligned with Mathlib idioms. Ideal candidates have a strong math background 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 assistants — Lean 4 strongly preferred.
• Deep enthusiasm for formal verification and the future of mechanized mathematics.
• Able to translate dense, informal arguments into structured, precise formal proofs.
• Mathematically mature and comfortable working at the boundary of what tools can currently express.

Responsibilities

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations.
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that stress-test the limits of existing proof assistants, especially where automation fails.
• Collaborate with AI researchers to design and refine formal verification strategies and pipelines.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Mathlib idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
• Investigate where automated provers break down — and articulate exactly why.
• Create Lean proofs that surface deeper patterns and generalizations implicit in the original mathematics.

Skills

Mathematics

Formal reasoning

Proof writing

Translate informal arguments

Education

Master's degree in Mathematics/Logic/Theoretical CS

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your mathematical expertise could directly shape how AI reasons, proves, and understands the world's most complex ideas? We're looking for Formal Verification Scientists to translate advanced mathematical arguments into precise, machine-verifiable proofs in Lean 4 — working at the very edge of what proof assistants can do. This is a fully remote, flexible contract role built for mathematicians who are passionate about formal verification and want their work to matter. You'll collaborate with leading AI research teams, helping define the frontier of mechanized mathematics.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that stress-test the limits of existing proof assistants, especially where automation fails
• Collaborate with AI researchers to design and refine formal verification strategies and pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Mathlib idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate where automated provers break down — and articulate exactly why
• Create Lean proofs that surface deeper patterns and 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 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 assistants — Lean 4 strongly preferred
• Deep enthusiasm for formal verification and the future of mechanized mathematics
• Able to translate dense, informal arguments into structured, precise formal proofs
• Mathematically mature and comfortable working at the boundary of what tools can currently express

Nice to Have

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

Why Join Us

• Work alongside world‑leading AI research labs on genuinely frontier problems
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with meaningful, intellectually rich work
• Direct exposure to how cutting‑edge AI models are trained and evaluated
• Contribute to work that expands what machines can understand and verify
• Potential for ongoing work and contract extension as new projects launch