Applied Formal Methods Researcher (Lean 4)

Alignerr Corp.; Birmingham; Remote; GBP 69,000 - 103,000; Part time

Job summary

Alignerr is seeking Applied Formal Methods Researchers to translate rigorous human mathematical arguments into Lean 4 formalizations — supporting machine-verifiable proofs at the frontier of automated reasoning. This fully remote, flexible contract role is designed for mathematicians who love precision, structure, and the challenge of bridging human intuition with machine-verifiable logic.

Responsibilities include translating informal proofs into Lean 4, analyzing proofs for gaps, constructing

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong proof-writing skills 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 systems.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity, structure, and correctness.
• Analyze proofs across domains—identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test and expose the limits of existing proof assistants.
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Investigate breakdowns in automated provers and articulate why they occur—complexity, missing lemmas, insufficient libraries.
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments.

Skills

Formal verification enthusiasm

Independent working

Clear communication

Education

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

Tools

Lean 4

Lean 3

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for Applied Formal Methods Researchers to translate rigorous human mathematical arguments into machine-verifiable Lean 4 formalizations — working at the very frontier of what automated reasoning can express and achieve.

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for Applied Formal Methods Researchers to translate rigorous human mathematical arguments into machine-verifiable Lean 4 formalizations — working at the very frontier of what automated reasoning can express and achieve. This is a fully remote, flexible contract role designed for mathematicians who love precision, structural elegance, and the intellectual challenge of bridging human intuition with machine-verifiable logic.

• 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 proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and expose the limits of existing proof assistants, especially where automated tools struggle or fail
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate breakdowns in automated provers and articulate why they occur — complexity, missing lemmas, insufficient libraries, and more
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments

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 proof systems — Lean 4 strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, structured, machine-verifiable proofs
• Naturally detail-oriented, precise, and comfortable working independently

Nice to Have

• 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 fails or requires 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

Why Join Us

• Work at the cutting edge of AI research alongside world-leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Gain direct exposure to how advanced AI models are trained and evaluated
• Contribute to a field that is actively redefining the boundaries of mathematical reasoning and AI capability
• Potential for ongoing work and contract extension as new projects launch