Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr Corp.; United States; Remote; MXN 1,526,000 - 3,307,000; Part time

Job summary

Alignerr is seeking a Formal Verification Scientist to translate advanced mathematics into Lean 4 formalizations at the edge of what proof assistants can automate. This is a remote, hourly contract role designed for mathematicians who value precision and elegant formal structures.

You will collaborate with AI researchers, develop readable Lean proofs, and push the limits of formal verification in mechanized mathematics.

Qualifications

• Master's or higher in Mathematics, Logic, Theoretical CS or closely related field.
• Strong proof-writing and formalization skills.
• Experience with Lean, Coq, Isabelle/HOL, or similar proof systems.
• Deep interest in formal verification and mechanized math.
• Ability to translate informal proofs into structured Lean proofs.

Responsibilities

• Translate informal mathematical proofs into Lean 4 with emphasis on clarity and correctness.
• Analyze proofs to identify gaps and formalizable sub-structures.
• Construct formalizations at the frontier of proof assistants where automation struggles.
• Collaborate with AI researchers to design verification strategies and pipelines.
• Develop readable, reproducible Lean proof scripts following best practices.

Skills

Mathematical rigor

Proof writing

Formal reasoning

Communication

Education

Master's degree or higher in Mathematics, Logic, Theoretical CS

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deepest mathematical expertise could directly shape how AI understands and reasons about rigorous proof? We're looking for Formal Verification Scientists to translate advanced human mathematics into machine-verifiable Lean 4 formalizations — working at the exact boundary of what proof assistants can currently express and automate.

This is a fully remote, flexible contract role for mathematicians who thrive on precision, structural elegance, and pushing the limits of what formal systems can do. If you find genuine satisfaction in taking a dense, beautiful argument and expressing it in a form a machine can verify — 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 with an emphasis on clarity, correctness, and structural integrity
• Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the frontier of existing proof assistants — especially where automated tools struggle or fail
• Collaborate with AI researchers to design, refine, and evaluate formal verification strategies and 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
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate and articulate precisely where automated provers break down — and why
• 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
• Strong foundation in rigorous proof writing 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 comparable proof systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, structured formal proofs with precision
• Naturally detail‑oriented and methodical — you notice exactly where an argument breaks down

Nice to Have

• Prior experience with data annotation, data quality, or evaluation systems
• 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 requires manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

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