Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Charlotte (AR); Remote; USD 110,000 - 165,000; Part time

Job summary

Alignerr seeks researchers to translate informal mathematical arguments into Lean 4 formal proofs for AI training, blending deep mathematics with machine-verifiable formalization.

Remote hourly contract, 10–40 hours/week, emphasizes rigorous proof scripts, collaboration with AI researchers, and advancing mechanized mathematics for next‑gen AI systems.

Qualifications

• Hold a Master’s degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing across one or more of: algebra, analysis, topology, logic, or discrete mathematics.
• Hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred.
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics.
• Able to translate dense, informal mathematical arguments into precise, structured formal proofs.
• Intellectually energized by working at the frontier — where tools struggle and human insight still matters most

Responsibilities

• Translate informal mathematical proofs into clean, structured, machine‑verifiable Lean 4 formalizations
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying hidden assumptions, gaps, and formalizable sub‑structures
• Construct formalizations that stress‑test the limits of existing proof assistants, especially where automation breaks down
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Skills

Rigorous proof writing

Lean 4

Formal verification

Mathematical reasoning

Education

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

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

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

About The Role

What if your deep mathematical expertise could directly shape how AI understands and generates formal proofs — pushing the boundaries of what machines can reason about?

We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs for cutting‑edge AI research. This role sits at the frontier of mathematics and computer science, tackling proofs that often lie beyond what automated systems can currently handle.

This is a fully remote, flexible contract role built for researchers who love precision, structure, and the intellectual challenge of making rigorous human reasoning legible to machines.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week

What You'll Do

• Translate informal mathematical proofs into clean, structured, machine‑verifiable Lean 4 formalizations
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying hidden assumptions, gaps, and formalizable sub‑structures
• Construct formalizations that stress‑test the limits of existing proof assistants, especially where automation breaks down
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
• 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
• Have a strong foundation in rigorous proof writing across one or more of: algebra, analysis, topology, logic, or discrete mathematics
• Have hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into precise, structured formal proofs
• Intellectually energized by working at the frontier — where tools struggle and human insight still matters most

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 where automated reasoning frequently requires manual scaffolding
• Background in data annotation, data quality, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators

Why Join Us

• Work on genuinely frontier problems — proofs that push the limits of what machines can verify
• Collaborate with teams building cutting‑edge AI models at leading research labs
• Fully remote and flexible — work when and where you do your best thinking
• Freelance autonomy with meaningful, intellectually stimulating work
• Gain rare exposure to how advanced AI models are trained on formal mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch