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

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