Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Oxford; Remote; GBP 83,000 - 124,000; Part time

Job summary

Alignerr is seeking a Researcher to transform informal mathematical proofs into Lean 4 formalizations, pushing the boundaries of mechanized mathematics. You will analyze proofs for gaps, craft machine-verifiable representations, and guide lemma selection and proof structure in collaboration with AI researchers.

Remote, hourly contract with 10–40 hours per week, requiring strong mathematical training and experience with Lean 4 (or Lean 3) and other proof assistants.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or related field.
• Proven ability to write rigorous formal proofs and document them clearly.
• Experience with Lean (Lean 4 preferred) and formal verification.
• Familiarity with proof assistants and the frontier of mechanized mathematics.

Responsibilities

• Translate informal proofs into machine-verifiable Lean 4 formalizations.
• Analyze generic and domain-specific proofs for gaps and assumptions.
• Create readable, reproducible proof scripts aligned with Lean idioms.
• Investigate reasons automated provers fail and identify remedies.
• Collaborate with AI researchers to design and evaluate verification pipelines.
• Support proof decomposition and lemma selection strategies.

Skills

Lean 4

Formal verification

Proof writing

Mathematical modelling

Communication skills

Education

Master's degree or higher in Mathematics, Logic, TCS

Tools

Lean 4

Lean 3

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 how AI understands and constructs formal proofs? We're looking for mathematicians and formal verification experts to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — working at the true frontier of what proof assistants can express and automate.

This is a fully remote, flexible contract role for researchers who love rigor, structure, and pushing the boundaries of mechanized mathematics.

• 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


• Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable substructures


• Construct formalizations that test the limits of existing proof assistants, especially where automation struggles or fails


• Investigate and articulate why automated provers break down — whether due to complexity, missing lemmas, or insufficient libraries


• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms


• Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models


• Collaborate with AI researchers to design, refine, and evaluate formal verification pipelines


• Create Lean 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


• 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), with Lean 4 strongly preferred — experience with Coq, Isabelle/HOL, or Agda also valued


• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics


• Able to translate dense, informal mathematical arguments into clean, structured, machine-checkable proofs


• Intellectually curious and motivated by working where automated tools reach their limits

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 in contexts where manual scaffolding is frequently required


• Background in data annotation, evaluation systems, or AI training workflows


• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work directly on cutting‑edge AI research projects alongside leading AI labs


• Fully remote and flexible — work when and where it suits you


• Freelance autonomy with the structure of meaningful, high‑impact research tasks


• Gain exposure to how advanced LLMs are trained and evaluated on formal reasoning


• Contribute to mapping the frontier of what formal verification can express and automate


• Potential for ongoing work and contract extension as new projects launch