Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Charlotte (AR); Remote; USD 55,000 - 83,000; Part time

Job summary

Alignerr Corp. is seeking a Researcher to translate deep mathematical reasoning into Lean 4 formalizations for AI training. This remote contract role suits researchers who value precision and rigorous, machine-verifiable proofs.

You will work across algebra, topology, logic, and discrete math to push the boundaries of what automated systems can handle, with flexible hours between 10 and 40 per week. Lean 3/4, Coq, Isabelle/HOL, and Agda experience is highly valued as you contribute to frontier

Qualifications

• Requires strong mathematical background and formal proof experience.
• Experience translating informal arguments into machine-verifiable proofs.

Responsibilities

• Translate informal mathematical proofs into Lean 4 formalizations.
• Analyze proofs across domains (algebra, analysis, topology, logic, discrete math).
• Construct formalizations that stress-test proof assistants where automation breaks down.
• Collaborate with researchers to refine verification strategies.
• Develop readable, reproducible proof scripts aligned with best practices.
• Provide guidance on proof decomposition, lemma selection, and structuring techniques.
• Investigate why automated provers fail and explain the reasons.
• Create Lean proofs that reveal deeper patterns or generalizations in the mathematics.

Skills

Mathematical reasoning

Formal thinking

Clear communication

Education

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

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 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