Applied Formal Methods Researcher (Lean 4)

Job summary

Translate informal mathematical arguments into readable, reproducible Lean 4 proofs, and analyze proofs for assumptions, gaps, and formalizable structures. Investigate limitations of automated provers, document findings, and collaborate on formal verification strategies and proof pipelines.

Job details

About The Role What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate rigorous human arguments into machine-verifiable Lean 4 proofs — working at the very edge of what automated reasoning can do today. This is a fully remote, flexible contract role designed for people who find genuine satisfaction in the precision and structural elegance of formal mathematics. No AI background required — just deep mathematical maturity and hands-on experience with proof assistants. 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 — identifying hidden assumptions, logical gaps, and formalizable sub-structures Construct formalizations that probe the limits of existing proof assistants, especially where automation breaks down Investigate why automated provers struggle — complexity, missing lemmas, insufficient libraries — and document your findings clearly Collaborate with researchers to design, refine, and evaluate formal verification strategies and pipelines Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms Guide proof decomposition, lemma selection, and structuring decisions for complex formal models Formalize classical proofs and compare machine-verifiable structures against textbook arguments Surface deeper patterns or generalizations implicit in the original mathematics Who You Are Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field Strong foundation in rigorous proof writing across 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 strongly preferred Genuinely enthusiastic about formal verification, proof assistants, and mechanized mathematics Able to translate dense informal arguments into clean, precise formal proofs Comfortable working independently in an asynchronous, remote environment 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 Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding Prior experience with data annotation, data quality, or evaluation workflows Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies The Ideal Candidate You're a mathematically mature problem-solver who thrives at the frontier of formal verification. You find deep satisfaction in taking an elegant human argument and expressing it in a form a machine can verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. Why Join Us Work on cutting-edge AI projects alongside leading research labs Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, intellectually stimulating work Gain direct exposure to how advanced AI models are trained on formal mathematical reasoning Contribute to work that is genuinely pushing the boundaries of mechanized mathematics Potential for ongoing work and contract extension as new projects launch

What you’ll do

Translate informal mathematical arguments into readable, reproducible Lean 4 proofs, and analyze proofs for assumptions, gaps, and formalizable structures. Investigate limitations of automated provers, document findings, and collaborate on formal verification strategies and proof pipelines.

Requirements

Requires a master's degree or higher in mathematics, logic, theoretical computer science, or a related field, along with strong rigorous proof-writing skills. Candidates need hands-on experience with Lean or another proof assistant, with Lean preferred, and the ability to work independently in a remote environment.

Benefits

• Fully Remote Work
• Flexible Schedule
• Freelance Autonomy
• Exposure to Advanced AI Research
• Potential for Ongoing Work and Contract Extension

Listed skills

• analysis · Preferred

Other relevant skills

Identified from the job description. Confirm important requirements above.

• Lean 4
• Formal Verification
• Mathematical Proof Writing
• Proof Assistants
• Formalization
• Logic
• Algebra
• Analysis
• Topology
• Discrete Mathematics
• Type Theory
• Proof Automation
• Proof Decomposition
• Lemma Selection
• Asynchronous Collaboration

Job areas

• Science & Research
• Technology
• Software
• Education

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