Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr; United States; On-site; USD 83,000 - 131,000; Part time

Job summary

Alignerr seeks a Formal Verification Scientist to translate rigorous mathematics into Lean 4 proofs, shaping machine-verifiable formalizations for advanced AI systems.

You will analyze proofs, extend Lean 4 capabilities, and collaborate with AI researchers to refine verification pipelines, delivering readable and robust formalizations.

Qualifications

• Master’s degree or higher in Mathematics, Logic, or theoretical CS.
• Strong proof-writing skills across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (3 or 4), Coq, Isabelle/HOL, or Agda.

Responsibilities

• Translate informal proofs into Lean 4 proofs with clarity and correctness.
• Analyze proofs to identify gaps, assumptions, and formalizable sub-structures.
• Construct formalizations that push limits of proof assistants.
• Collaborate with AI researchers to improve formal verification pipelines.
• Develop readable, reusable Lean scripts aligned with best practices.

Skills

Proof writing

Formal verification

Mathematics background

Lean familiarity

Education

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

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical expertise could directly shape how the world's most advanced AI systems understand and reason about formal proof? We're looking for Formal Verification Scientists to translate rigorous human-written mathematics into machine-verifiable Lean 4 proofs — working at the very frontier of what proof assistants can express, capture, and automate.

About The Role

What if your deep mathematical expertise could directly shape how the world's most advanced AI systems understand and reason about formal proof? We're looking for Formal Verification Scientists to translate rigorous human-written mathematics into machine-verifiable Lean 4 proofs — working at the very frontier of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role designed for mathematicians who live and breathe formal reasoning. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify — this role was made 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 an emphasis on clarity, structure, and correctness
• Analyze generic and domain-specific proofs — identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that push the limits of existing proof assistants, especially in areas where tools struggle or fail
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop clean, 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 precisely why — whether due to complexity, missing lemmas, or library limitations
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• 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
• 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 a comparable formal proof system — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, well‑structured formal proofs independently
• Thrive working at the intersection of mathematics and computer science, where precision is non‑negotiable

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 substantial manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies to interdisciplinary teams

Why Join Us

• Work directly with world-leading AI research labs on genuinely frontier problems
• Fully remote and flexible — structure your work around your life, not the other way around
• Freelance autonomy with the intellectual depth of high‑stakes mathematical research
• Gain exposure to how advanced AI models are trained and where formal mathematics fits into that process
• Contribute to a body of work that maps the boundary of what machines can and cannot yet verify
• Potential for ongoing collaboration and contract extension as new projects launch