Applied Formal Methods Researcher (Lean 4)

About The Role
What if your deep mathematical training could directly shape how AI reasons, proves, and understands the most complex ideas in human knowledge? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — helping map the frontier of what machines can verify, and building the foundation for the next generation of AI reasoning systems.
This is a fully remote, flexible contract role for mathematicians who are passionate about formal verification and want their expertise to matter beyond the page.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4
Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable substructures
Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
Collaborate with researchers to design and refine strategies for improving formal verification pipelines
Develop highly readable, reproducible proof scripts aligned with mathematical best practices
Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Formalize classical proofs and compare machine-verifiable structures against textbook arguments
Investigate where automated provers break down and articulate exactly why — complexity, missing lemmas, insufficient libraries, and beyond
Who You Are
Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Possess 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 comparable proof systems — Lean strongly preferred
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Skilled at translating dense, informal arguments into clean, structured, machine-readable proofs
A mathematically mature problem-solver who finds satisfaction in resolving gaps that automated tools cannot yet bridge
Nice to Have
Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
Experience with large-scale formalization projects such as Mathlib
Exposure to theorem provers where automated reasoning frequently requires manual scaffolding
Prior experience with data annotation, quality evaluation, or AI training workflows
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work at the intersection of advanced mathematics and cutting-edge AI research
Collaborate with world-leading AI research teams and labs
Fully remote and flexible — work on your own schedule from anywhere
Freelance autonomy with meaningful, intellectually rigorous work
Gain direct exposure to how frontier AI models are trained and evaluated
Potential for ongoing engagement and contract extension as projects evolve

Work arrangement
Yes