Applied Formal Methods Researcher (Lean 4)

About The Role
What if your mathematical expertise could directly shape how the world's most advanced AI systems reason, verify, and understand formal logic? We're looking for Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs — working at the absolute frontier of what proof assistants can express and automate.
This is a fully remote, flexible contract role built for mathematicians who live at the intersection of abstract reasoning and precise formalization. If you find deep satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify — this role was designed for you.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility
Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that stress-test the limits of existing proof assistants — especially where automated tools struggle or fail
Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Investigate automated prover breakdowns and articulate root causes — complexity gaps, missing lemmas, insufficient libraries, and more
Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
Who You Are
Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Possesses a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
Has hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean 4 strongly preferred
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate informal arguments into precise, structured formal proofs with minimal ambiguity
Mathematically mature and energized by working at the boundary of what formal tools can currently handle
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, data quality evaluation, or AI training workflows
Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to interdisciplinary teams
Why Join Us
Work directly on cutting-edge AI projects alongside world-leading research labs
Fully remote and flexible — structure your hours around your life, not the other way around
Freelance autonomy with the depth and intellectual rigor of frontier research work
Gain exposure to advanced LLMs and the formal reasoning pipelines being built to train them
Potential for ongoing contract extension as projects evolve and scale

Work arrangement
Yes