Researcher - Lean 4 & Formal Proof Systems

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

Benefits offered by this job

Fully remote

Flexible hours

Freelance autonomy

Collaborative research

Contract extensions

Job summary

Alignerr is seeking a Researcher to translate dense mathematical proofs into Lean 4 formalizations, shaping AI reasoning at the edge of human and machine logic.

The role is an hourly contract, fully remote, with 10–40 hours per week and flexible scheduling. You will work with AI researchers to push the boundaries of proof automation and contribute high-quality formal artifacts.

Qualifications

• Master's degree or higher in Mathematics, Logic, or theoretical CS.
• Strong foundation in rigorous proof construction across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean, Coq, Isabelle/HOL, or similar proof assistants.

Responsibilities

• Translate informal proofs into Lean 4 formalizations that are machine-verifiable.
• Analyze proofs across domains to identify gaps and formalizable sub-structures.
• Create formalizations that push proof assistants beyond current automation limits.
• Collaborate with AI researchers to design verification strategies.
• Develop clean, readable, and reproducible Lean scripts following math practice.
• Guide proof decomposition, lemma selection, and structuring techniques.
• Investigate automated prover failures and explain the reasons.
• Produce Lean proofs revealing deeper patterns or generalizations.

Skills

Formal verification

Mathematical reasoning

Lean expertise

Education

Master's degree in Mathematics/Logic/CS

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Job description

Researcher — Lean 4 & Formal Proof Systems (AI Training)

About The Role

What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification experts to translate sophisticated proofs into Lean 4 - working at the exact boundary where human mathematical intuition meets machine-verifiable logic.

This is a rare opportunity to contribute to cutting-edge AI research by helping build training data that pushes proof assistants beyond their current limits. If you find satisfaction in taking a dense, elegant argument and expressing it with machine-level precision, this role was made for you.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10-40 hours/week (flexible)

What You'll Do

• Translate informal mathematical proofs into rigorous, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains - identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that probe the limits of existing proof assistants, especially where automation fails
• Collaborate with AI researchers to design and refine formal verification strategies
• Develop clean, readable, reproducible proof scripts aligned with mathematical best practices
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate and articulate where automated provers break down - and why
• 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
• Possess a strong foundation in rigorous proof construction 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 proof assistants - Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, structured formal proofs independently

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 in contexts where automated reasoning fails or requires extensive manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training pipelines
• Strong communication skills for articulating formalization decisions, edge cases, and proof strategies

Why Join Us

• Work at the frontier of formal verification and AI research - problems here are genuinely unsolved
• Fully remote and flexible - structure your hours around your life
• Freelance autonomy with the substance of impactful, intellectually demanding work
• Collaborate with researchers at leading AI labs on projects that matter
• Contribute directly to advancing what AI systems can reason about and verify
• Potential for ongoing work and contract extension as new projects launch