Researcher - Lean 4 & Formal Proof Systems

Job summary

Translate informal mathematical arguments into clear, correct, machine-verifiable Lean 4 proofs, and identify gaps, assumptions, and structures that can be formalized. Collaborate on improving formal verification strategies, evaluate where automated provers fail, and create readable, reproducible proof scripts.

Job details

Researcher — Lean 4 & Formal Proof Systems (AI Training) About The Role What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — working at the cutting edge of what proof assistants can express, capture, and automate. This is a fully remote, flexible contract role designed 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 Lean 4 formalizations with an emphasis on clarity, structure, and correctness Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more 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 Have a strong foundation in rigorous proof writing and mathematical reasoning 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 systems — Lean 4 strongly preferred Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to translate dense, informal arguments into clean, structured formal proofs with precision and care Nice to Have Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools Experience with large-scale formalization projects such as Mathlib Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding Prior experience with data annotation, data quality evaluation, or AI training workflows Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us Work on cutting-edge AI projects alongside leading research labs and AI teams Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, intellectually rigorous work Contribute directly to expanding the frontier of what formal verification and AI can achieve together Potential for ongoing work and contract extension as new projects launch

What you’ll do

Translate informal mathematical arguments into clear, correct, machine-verifiable Lean 4 proofs, and identify gaps, assumptions, and structures that can be formalized. Collaborate on improving formal verification strategies, evaluate where automated provers fail, and create readable, reproducible proof scripts.

Requirements

A master's degree or higher in mathematics, logic, theoretical computer science, or a related field is required, along with strong proof-writing and mathematical reasoning skills. Hands-on experience with Lean or a comparable proof assistant is required, with Lean 4 preferred, as is the ability to formalize dense mathematical arguments precisely.

Benefits

• Fully Remote Work
• Flexible Schedule
• Freelance Autonomy
• Potential for Ongoing Work and Contract Extension

Listed skills

• Lean · Preferred
• Flexible · Preferred
• Training · Preferred
• analysis · Preferred
• Communication · Preferred
• Communication Skills · Preferred
• enthusiastic · Preferred
• future · Preferred
• Organization · Preferred
• precision · Preferred
• Strong Communication · Preferred
• Strong communication skills · Preferred

Other relevant skills

Identified from the job description. Confirm important requirements above.

• Lean 4
• Formal Proof Writing
• Mathematical Reasoning
• Formal Verification
• Proof Assistants
• Proof Decomposition
• Lemma Selection
• Type Theory
• Curry-Howard Correspondence
• Proof Automation
• Mathlib
• Coq
• Isabelle/HOL
• Agda
• Data Quality Evaluation
• AI Training

Job areas

• Science & Research
• Technology
• Software
• Education

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