About the Role
What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human arguments into machine-verifiable formalizations — working at the bleeding edge of what proof assistants can express, capture, and automate.
This is a fully remote, flexible contract role built for mathematicians who are passionate about precision, formal verification, and the challenge of pushing modern proof assistants to their limits.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: Flexible
What You'll Do
- Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
- Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that 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 clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Advise on proof decomposition, lemma selection, and structuring techniques for formal models
Who You Are
- Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Have 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 formal systems — Lean strongly preferred
- Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate dense informal arguments into clean, well-structured formal proofs
- Self-directed and reliable when working independently on technically demanding tasks
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 breaks down or requires manual scaffolding
- Strong communication skills for articulating formalization decisions, edge cases, and proof strategies
Sample Work You Might Do
- Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
- Investigate where automated provers break down — and document exactly why (complexity, missing lemmas, library gaps, etc.)
- Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
- Help map the frontier of what current formal verification tools can and cannot yet handle
Why Join Us
- Work on genuinely cutting-edge AI projects alongside leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually rigorous work
- Contribute to a growing field where your expertise directly advances the reliability and reasoning capability of AI systems
- Potential for ongoing work and contract extension as new formalization projects launch