Applied Formal Methods Researcher (Lean 4)

Alignerr Corp.; Glasgow; Remote; GBP 55,000 - 110,000; Part time

Job summary

Alignerr is seeking an Applied Formal Methods Researcher to translate complex human-written proofs into machine-verifiable formalizations using Lean 4 and related systems. You will analyze proofs across domains, identify gaps, and design formalizations that push the boundaries of automated reasoning.

This remote hourly contract offers flexible hours (10–40 per week) and collaboration with AI researchers to advance mechanized mathematics.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Hands-on experience with formal proof systems and rigorous proof writing.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems).
• Analyze proofs across domains—identifying hidden assumptions, logical gaps, and formalizable sub-structures.
• Construct formalizations that test and expose the limits of existing proof assistants.
• Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines.
• Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices.
• Guide proof decomposition strategies—including lemma selection and formal modeling decisions.

Skills

Lean 4

Formal verification

Proof systems

Theoretical CS

Education

Master's degree or higher in Mathematics/Logic/Theoretical Computer Science

Tools

Lean 3/4

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your mathematical expertise could directly shape how AI reasons about the hardest problems in mathematics? We're looking for Applied Formal Methods Researchers to translate complex human-written proofs into machine-verifiable formalizations — working at the very frontier of what automated reasoning can do.

• 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 proof systems)
• Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
• Construct formalizations that test and expose the limits of existing proof assistants
• Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
• Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices
• Guide proof decomposition strategies — including lemma selection, structuring techniques, and formal modeling decisions
• Investigate where automated provers break down and articulate why — whether due to complexity, missing lemmas, or library gaps
• Create Lean proofs that surface deeper patterns and 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 comparable formal systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the long-term potential of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured formal proofs

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

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 challenging work
• Contribute directly to advancing the frontier of AI mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch
• Global collaboration with a team at the intersection of mathematics and AI