Applied Formal Methods Researcher (Lean 4)

About The Role
What if your deep mathematical training could directly shape how AI reasons, proves, and thinks? We're looking for formal methods researchers to translate complex human mathematical arguments into machine-verifiable proofs in Lean 4 — working at the precise frontier where human ingenuity meets the limits of automated reasoning.
This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof construction and the future of mechanized mathematics.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal mathematical proofs into formal, machine-verifiable Lean 4 proofs with an emphasis on clarity, correctness, and structural elegance
Analyze domain-specific and general proofs to identify hidden assumptions, logical gaps, and formalizable sub-structures
Construct challenging formalizations that probe the limits of current proof assistants — especially where automation breaks down
Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
Develop clean, reproducible proof scripts aligned with mathematical best practices and Lean idioms
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
Investigate failure modes in automated provers and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and beyond
Create formalizations that surface deeper patterns or generalizations implicit in the original mathematics
Who You Are
Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Deeply fluent 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 proof assistants — Lean strongly preferred
Genuinely passionate about formal verification, proof assistants, and the long-term future of mechanized mathematics
Able to bridge the gap between intuitive human arguments and precise formal representations
Nice to Have
Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
Experience contributing to large-scale formalization projects such as Mathlib
Exposure to theorem provers where automated reasoning frequently fails or requires substantial manual scaffolding
Prior experience with data annotation, data quality evaluation, or AI training workflows
Strong ability to communicate formalization decisions, edge cases, and reasoning strategies clearly in writing
Why This Role Stands Out
This isn't routine annotation work. You'll operate at the cutting edge — tackling proofs that automated systems cannot yet handle, mapping the frontier of what formal verification can express, and contributing directly to how next-generation AI models learn to reason mathematically. If you find deep satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify, this role was built for you.
Why Join Us
Work on genuinely frontier AI research alongside leading labs
Fully remote and asynchronous — work on your own schedule, from anywhere
Freelance autonomy with meaningful, intellectually stimulating work
Contribute to shaping how AI models understand and generate formal mathematics
Potential for contract extension as projects evolve and expand

Work arrangement
Yes