About the Role
What if your deep mathematical training could directly shape how AI understands and constructs formal proofs? We're looking for mathematicians with hands-on experience in formal verification to work at one of the most exciting intersections in modern AI research — mechanized mathematics.
You'll translate rigorous human-written arguments into machine-verifiable Lean 4 proofs, explore the boundaries of what automated provers can and cannot do, and help build the datasets that train the next generation of AI reasoning systems.
This is a fully remote, flexible contract role designed for mathematicians who love precision, structure, and the intellectual challenge of formal verification.
- 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 readability
- Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
- Construct formalizations that probe and test the limits of existing proof assistants, particularly where automation breaks down
- Investigate why automated provers fail on specific problems — whether due to complexity, missing lemmas, or insufficient libraries — and document your findings clearly
- Collaborate with AI researchers to refine strategies for improving formal verification pipelines
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Develop highly reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Create Lean proofs that expose deeper patterns or generalizations implicit in the original mathematics
Who You Are
- Holder of a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Strong foundation 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), with Lean 4 strongly preferred — experience with Coq, Isabelle/HOL, or Agda also considered
- Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate dense, informal mathematical arguments into precise, machine-checkable formal proofs
- Self-directed and comfortable working independently in an asynchronous, remote environment
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 requires manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training workflows
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
The Ideal Candidate
You're a mathematically mature problem-solver who thrives at the frontier of formal verification. You find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify. You appreciate precision and structural beauty — and you're energized by the challenge of resolving gaps that automated tools cannot yet bridge.
Why Join Us
- Work directly on cutting-edge AI research projects alongside leading AI labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy: set your own pace within a 10–40 hour weekly range
- Gain rare exposure to how advanced AI reasoning systems are built and trained
- Contribute to research that is actively pushing the frontier of what machines can prove
- Potential for ongoing work and contract extension as new projects launch