Applied Formal Methods Researcher (Lean 4)

Alignerr Corp.; Cambridge; Remote; GBP 83,000 - 165,000; Part time

Job summary

Alignerr is seeking an Applied Formal Methods Researcher to translate rigorous proofs into Lean 4 formalizations, contributing to cutting-edge AI research and formal verification. This fully remote, hourly-contract role invites mathematicians with a passion for proof assistants to shape AI foundations and collaborate with AI researchers on verification pipelines.

You'll work 10–40 hours per week, designing clear proof scripts and identifying gaps in proof libraries, with potential for ongoing

Qualifications

• 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.
• Experience with Lean and/or other proof assistants is highly desirable.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4.
• Analyze proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that push the limits of proof assistants and automated tools.
• Collaborate with AI researchers to improve formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with best practices.
• Provide guidance on proof decomposition, lemma selection, and structuring techniques.
• Investigate why automated provers struggle and articulate the limitations.
• Formalize classical proofs to reveal deeper patterns.

Skills

Rigorous proof writing

Formal verification

Independent work

Mathematical maturity

Clear communication

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical training could directly shape how AI reasons, proves, and understands the foundations of mathematics? We're looking for Applied Formal Methods Researchers to translate rigorous human-written proofs into machine-verifiable formalizations in Lean 4 — working at the cutting edge of AI research and formal verification.

About The Role

What if your deep mathematical training could directly shape how AI reasons, proves, and understands the foundations of mathematics? We're looking for Applied Formal Methods Researchers to translate rigorous human-written proofs into machine-verifiable formalizations in Lean 4 — working at the cutting edge of AI research and formal verification.

This is a fully remote, flexible contract role designed for mathematicians who are passionate about proof assistants and want their expertise to have a real, lasting impact on the future of AI.

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

What You'll Do

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related systems) with an emphasis on clarity, structure, and correctness
• Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that probe the limits of existing proof assistants — especially where automated 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 proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate why — whether due to complexity, missing lemmas, or insufficient libraries
• Formalize classical proofs and 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
• Possess 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 formal systems — Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate complex informal arguments into clean, structured, and correct formal proofs
• Mathematically mature and comfortable working independently at the frontier of what proof assistants can express

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
• Prior exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
• Background in data annotation, data quality, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators

Why Join Us

• Work directly on cutting-edge AI projects alongside the world's leading AI research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the depth and meaning of frontier research
• Contribute to work that is actively shaping the future of mathematical reasoning in AI
• Potential for ongoing engagement and contract extension as new projects launch