Researcher - Lean 4 & Formal Proof Systems

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

The Role
What if your deep mathematical expertise could directly shape how AI reasons about formal proofs — pushing the frontier of what machines can understand and verify?

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 intersection of mathematics and computer science, working on problems that lie beyond the reach of current automated provers.

This is a fully remote, flexible contract role built for researchers who love rigor, precision, and the challenge of expressing elegant human reasoning in a form a machine can trust.

Organization:
Alignerr

Type:
Hourly Contract

Location:

Remote

Commitment: 10–40 hours/week

What You'll Do

Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness

Analyze domain-specific and general mathematical arguments — identifying gaps, hidden assumptions, and formalizable sub-structures

Construct formalizations that test and extend the limits of existing proof assistants, especially where automation breaks down

Investigate failure modes in automated provers and articulate precisely why they occur — complexity barriers, missing lemmas, insufficient libraries

Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms

Collaborate with researchers to design and refine strategies for improving formal verification pipelines

Create Lean proofs that reveal deeper patterns or generalizations implicit in original mathematical arguments

Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models

Who You Are

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics

Hands‑on experience with Lean (Lean 3 or Lean
4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean 4 strongly preferred

Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics

Ability to take dense, informal arguments and express them in clean, structured, machine-verifiable form

Self‑directed and comfortable working at the frontier, where the right path isn't always obvious

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, evaluation systems, or AI training workflows

Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

Work on cutting-edge AI research projects in collaboration with leading AI labs

Fully remote and flexible — work when and where it suits you

Freelance autonomy with the structure of meaningful, intellectually demanding work

Contribute directly to expanding what AI can understand and verify in advanced mathematics

Potential for ongoing work and contract extension as new projects launch