Applied Formal Methods Researcher (Lean 4)

Alignerr; Denver (CO); Remote; USD 55,000 - 110,000; Full time

Job summary

Alignerr is seeking Applied Formal Methods Researchers to translate rigorous mathematical arguments into Lean 4 proofs for AI verification. This fully remote hourly contract suits mathematicians who enjoy precision, proof assistants, and impactful work at the frontier of automated reasoning.

You will translate informal proofs, analyze gaps, and develop machine-verifiable formalizations while collaborating with AI researchers to refine verification pipelines. Lean experience is highly preferred.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Proven ability to write rigorous proofs and formal arguments across algebra, analysis, topology, logic, or discrete mathematics.
• Experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistants.

Responsibilities

• Translate informal mathematical proofs into machine-verifiable Lean 4 formalizations.
• Analyze proofs to identify gaps, assumptions, and formalizable sub-structures.
• Construct formalizations that stress-test modern proof assistants and explain why automated provers fail.

Skills

Proof writing

Mathematical rigor

Formal reasoning

Education

Master's degree or higher in Mathematics/Logic/Theoretical CS

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical expertise could directly shape how AI reasons about the hardest problems in formal verification? We\'re looking for Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs — working at the exact frontier where human mathematical intuition meets the limits of automated reasoning.

About The Role

What if your deep mathematical expertise could directly shape how AI reasons about the hardest problems in formal verification? We\'re looking for Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs — working at the exact frontier where human mathematical intuition meets the limits of automated reasoning.

This is a fully remote, flexible contract role for mathematicians who thrive on precision, love proof assistants, and want their work to matter at the cutting edge of AI research.

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

What You\'ll Do

• Translate informal mathematical proofs into clean, correct, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that stress-test the limits of modern proof assistants, especially where automation breaks down
• Investigate and articulate why automated provers fail — whether due to complexity, missing lemmas, or library gaps
• Collaborate with AI researchers to design and refine formal verification pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices
• Guide proof decomposition strategies, lemma selection, and formal model structuring
• Formalize classical results 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
• Deeply comfortable with 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 proof assistants — Lean strongly preferred
• Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take dense, informal arguments and express them with machine-level precision
• A mathematically mature problem-solver who finds satisfaction in resolving the gaps automated tools cannot yet bridge

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 in regimes where automated reasoning frequently requires manual scaffolding
• Prior experience with data annotation, evaluation systems, or AI training workflows
• Strong communication skills for explaining formalization decisions and reasoning strategies

Why Join Us

• Work directly on cutting-edge AI research projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the \ structure of meaningful, technically demanding work
• Contribute to defining what the next generation of mechanized mathematics can express and automate
• Potential for ongoing work and contract extension as new projects launch