Applied Formal Methods Researcher (Lean 4)

Alignerr Corp.; United States; Remote; USD 83,000 - 165,000; Full time

Job summary

Alignerr Corp. is hiring Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs, working at the frontier of proof assistants and automation.

This fully remote, hourly contract targets mathematicians who thrive at the intersection of abstract reasoning and precise formalization, with 10–40 hours per week and flexible scheduling.

Qualifications

• Masters or higher in Mathematics, Logic, Theoretical Computer Science, or a related field.
• Strong proof-writing across algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, or Agda; Lean 4 preferred.
• Enthusiasm for formal verification, proof assistants, and mechanized mathematics.
• Translate informal arguments into precise, structured formal proofs with clarity.

Responsibilities

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility.
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that stress-test the limits of existing proof assistants — especially where automated tools struggle or fail.
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Investigate automated prover breakdowns and articulate root causes — complexity gaps, missing lemmas, insufficient libraries, and more.
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics.

Skills

Proof writing

Mathematical maturity

Strong communication

Education

Master's degree or higher

Tools

Lean (Lean 4)

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your mathematical expertise could directly shape how the world's most advanced AI systems reason, verify, and understand formal logic? We're looking for Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs — working at the absolute frontier of what proof assistants can express and automate.

This is a fully remote, flexible contract role built for mathematicians who live at the intersection of abstract reasoning and precise formalization. If you find deep satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify — this role was designed for you.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that stress-test the limits of existing proof assistants — especially where automated tools struggle or fail
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate automated prover breakdowns and articulate root causes — complexity gaps, missing lemmas, insufficient libraries, and more
• Create Lean proofs that 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
• Possesses a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Has hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into precise, structured formal proofs with minimal ambiguity
• Mathematically mature and energized by working at the boundary of what formal tools can currently handle

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 evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to interdisciplinary teams

Why Join Us

• Work directly on cutting-edge AI projects alongside world-leading research labs
• Fully remote and flexible — structure your hours around your life, not the other way around
• Freelance autonomy with the depth and intellectual rigor of frontier research work
• Gain exposure to advanced LLMs and the formal reasoning pipelines being built to train them
• Potential for ongoing contract extension as projects evolve and scale