Researcher - Lean 4 & Formal Proof Systems
Posted Today by Alignerr
Negotiable
Undetermined
Remote
Birmingham, England, United Kingdom
Summary: The role of Researcher in Lean 4 & Formal Proof Systems involves translating complex mathematical proofs into machine-verifiable formalizations using Lean 4, contributing to the advancement of AI reasoning and formal verification. This fully remote position is tailored for individuals with a strong mathematical background who thrive on intellectual challenges and precision. The researcher will collaborate with AI teams to refine verification strategies and explore the limits of existing proof assistants. The commitment ranges from 10 to 40 hours per week, offering flexibility in work hours.
Key Responsibilities:
- Translate informal mathematical proofs into clean, correct, machine-verifiable Lean 4 formalizations
- Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable substructures
- Construct formalizations that test the boundaries of existing proof assistants, especially where automation breaks down
- Collaborate with AI researchers to design and refine formal verification strategies and pipelines
- Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
- Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
- Formalize classical and advanced proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Key Skills:
- 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 formal systems — Lean 4 strongly preferred
- Enthusiasm for formal verification, proof assistants, and mechanized mathematics
- Ability to translate dense, informal mathematical arguments into precise, structured formal proofs
- Self-directed and comfortable working independently on complex, open-ended problems
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling (nice to have)
- Experience contributing to large-scale formalization projects such as Mathlib (nice to have)
- Strong communication skills for explaining formalization decisions, edge cases, and proof strategies (nice to have)
Salary (Rate): £170.00 hourly
City: Birmingham
Country: United Kingdom
Working Arrangements: remote
IR35 Status: undetermined
Seniority Level: undetermined
Industry: IT
Researcher – Lean 4 & Formal Proof Systems (AI Training)
About The Role
What if your deep mathematical expertise could directly shape how AI reasons, proves, and understands the most rigorous structures in all of science? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — working at the absolute frontier of what proof assistants can express and automate. This is a fully remote, flexible contract role designed for researchers who love precision, structural elegance, and the intellectual challenge of pushing formal systems beyond their current limits.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into clean, correct, machine-verifiable Lean 4 formalizations
- Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable substructures
- Construct formalizations that test the boundaries of existing proof assistants, especially where automation breaks down
- Collaborate with AI researchers to design and refine formal verification strategies and pipelines
- Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
- Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
- Formalize classical and advanced 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
- 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 4 strongly preferred
- Are genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Can translate dense, informal mathematical arguments into precise, structured formal proofs
- Are self-directed and comfortable working independently on complex, open-ended problems
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
- Experience contributing to large-scale formalization projects such as Mathlib
- Exposure to theorem provers in settings where automated reasoning frequently fails or requires manual scaffolding
- Prior experience with data annotation, data quality, or AI evaluation systems
- Strong communication skills for explaining formalization decisions, edge cases, and proof strategies
Why This Role Stands Out
- Work directly at the intersection of advanced mathematics and cutting-edge AI research
- Collaborate with world-leading AI research teams and labs
- Gain deep exposure to how frontier large language models are trained and evaluated
- Fully remote and asynchronous — work on your own schedule, from anywhere
- Freelance autonomy with the substance of genuinely meaningful, high-impact research work
- Potential for ongoing contract extension as projects grow and evolve