Formal Verification Scientist (Lean 4 & Mathlib)
About The Role What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human arguments into machine-verifiable Lean 4 formalizations — pushing the boundary of what automated reasoning can express and verify. This is a fully remote, flexible contract role for mathematicians who love precision, structural elegance, and working at the cutting edge of mechanized mathematics.
- 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 proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
- Construct formalizations that test and extend the limits of existing proof assistants, especially where automated tools struggle or fail
- Investigate and articulate where and why automated provers break down — whether due to complexity, missing lemmas, or library gaps
- Develop Lean proof scripts that reveal deeper patterns and generalizations implicit in the original mathematics
- Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
- Provide expert guidance 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 proof systems — Lean 4 strongly preferred
- Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Can translate dense, informal mathematical arguments into precise, machine-verifiable formal structures
- Work independently with strong self-direction and attention to detail
Nice to Have
- Experience with large-scale formalization projects such as Mathlib
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Exposure to theorem provers where automated reasoning frequently requires manual scaffolding
- Prior experience with data annotation, evaluation, or quality assessment workflows
- Strong communication skills for documenting formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work directly with world-leading AI research teams on genuinely frontier problems in formal mathematics
- Fully remote and flexible — structure your hours around your life, with 10–40 hours per week
- Freelance autonomy with the intellectual depth of serious mathematical research
- Gain exposure to how advanced LLMs are trained and evaluated on formal reasoning tasks
- Contribute to work that expands the boundary of what machines can understand and verify
- Potential for ongoing work and contract extension as projects evolve