What if your deepest mathematical instincts could directly shape how the next generation of AI understands and reasons about formal proof? We're looking for expert mathematicians to translate rigorous human arguments into machine-verifiable Lean 4 formalizations — working at the very frontier of what proof assistants can do.
This is a fully remote, flexible contract role built for mathematicians who live and breathe formal reasoning. If you find satisfaction in taking a dense, elegant proof and expressing it in a form a machine can verify — this is your role.
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 systems) with a focus on clarity, structure, and correctness
Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test and expand the limits of existing proof assistants
Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
Investigate where automated provers break down — and articulate precisely why
Create Lean proofs that reveal deeper patterns or generalizations implicit in classical mathematics
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 systems — Lean strongly preferred
Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate informal arguments into clean, structured, machine-verifiable proofs
Mathematically mature and comfortable working at the intersection of mathematics and computer science
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, or evaluation systems
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work on genuinely cutting-edge AI projects alongside world-leading research labs
Fully remote and flexible — structure your hours around your life
Freelance autonomy with the depth and meaning of serious mathematical work
Rare opportunity to directly influence how AI systems reason about mathematics
Potential for contract extension as projects evolve and expand
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