What if your deep mathematical training could directly shape the future of AI - and help machines understand the most rigorous arguments the human mind can produce?
We're looking for expert mathematicians with hands‑on experience in formal proof systems to translate advanced mathematical reasoning into machine‑verifiable Lean 4 code. This role sits at the frontier of what proof assistants can express, capture, and automate - and you'll be the one mapping that frontier.
This is a fully remote, flexible contract role for mathematicians who care deeply about precision, structure, and the art of formal argumentation.
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 correctness and clarity
Analyze proofs across domains - identifying hidden assumptions, logical gaps, and formalizable sub‑structures
Construct formalizations that test and expose the limits of existing proof assistants
Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines
Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
Guide proof decomposition, lemma selection, and structuring techniques for formal models
Investigate where automated provers break down - and articulate precisely why
Create Lean proofs that reveal deeper patterns or generalizations implicit in the original 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 4 strongly preferred
Thrive at the intersection of mathematics and formal computer science
Take satisfaction in translating dense, elegant human arguments into forms a machine can fully verify
Appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge
Nice to Have
Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
Experience contributing to large-scale formalization projects (e.g., Mathlib)
Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
Prior experience with data annotation, quality evaluation, or AI training workflows
Strong communication skills for articulating formalization decisions, edge cases, and proof strategies
Why Join Us
Work directly on cutting-edge AI research alongside leading labs and researchers
Fully remote and flexible - work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually rigorous work
Operate at the frontier of mechanized mathematics - pushing what formal verification can achieve
Potential for ongoing work and contract extension as new projects launch
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