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