Researcher — Lean 4 & Formal Proof Systems (AI Training)

About The Role

What if your deep mathematical training could directly shape how AI reasons about formal proofs — pushing the boundaries of what machines can verify, understand, and learn

We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into Lean 4, working on problems that sit beyond the current reach of automated provers. This isn't routine annotation work — it's frontier research at the intersection of mathematics and computer science, contributing directly to the development of cutting-edge AI systems.

This is a fully remote, flexible contract role. If you find beauty in rigorous proof structure and satisfaction in making a machine understand what only a human mathematician could express, this role was built for you.

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, correctness, and structure
Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
Construct formalizations that stress-test the limits of existing proof assistants, especially where automated tools struggle or fail entirely
Investigate and articulate why automated provers break down — whether due to complexity, missing lemmas, or insufficient library coverage
Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
Collaborate with AI researchers to refine strategies for improving formal verification pipelines
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
Surface deeper patterns or generalizations implicit in the original mathematics through the formalization process

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 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 a comparable proof assistant — Lean 4 strongly preferred
Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Can translate dense, informal mathematical arguments into clean, structured formal proofs independently
Are comfortable working at the frontier — where the tools don't always cooperate and creativity is required

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 scenarios where automated reasoning frequently fails or requires significant manual scaffolding
Prior experience with data annotation, data quality evaluation, or AI training workflows
Strong written communication skills for explaining formalization decisions, edge cases, and proof strategies to interdisciplinary collaborators

Why Join Us

Work on genuinely hard, intellectually stimulating problems at the frontier of formal verification and AI research
Collaborate with researchers working on some of the most advanced AI models being built today
Gain unique exposure to how large language models are trained and evaluated on mathematical reasoning
Fully remote and flexible — work on your own schedule from anywhere in the world
Freelance autonomy: choose your hours, work independently, and engage with a global research community
Potential for ongoing work and contract extension as new projects launch

Researcher - Lean 4 & Formal Proof Systems