About this role · Stem
About the Role What if your mathematical expertise could directly shape how AI reasons, verifies, and understands proofs at the highest level? We're looking for mathematicians with hands-on experience in formal proof systems — especially Lean — to help push the boundaries of what machine-verifiable mathematics can express and automate. This is a fully remote, flexible contract role working at the intersection of advanced mathematics and cutting-edge AI research. If you find deep satisfaction in translating elegant human arguments into precise, machine-checkable formalizations, this role was built for you. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: Flexible, task-based What You'll Do - Translate informal mathematical proofs into Lean (and related proof assistants) with an emphasis on clarity, structure, and correctness - Analyze proofs across a range of domains — identifying gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that test and extend the limits of existing proof assistants, especially where automated tools struggle or fail - Collaborate with researchers to design and evaluate strategies for improving formal verification pipelines - Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Provide expert guidance on proof decomposition, lemma selection, and formal model structuring - Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and more Who You Are - Hold 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) — experience with Coq, Isabelle/HOL, or Agda also valued - Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics - Able to translate dense, informal arguments into clean, well-structured formal proofs - Mathematically mature — you thrive working at the frontier, not just within established territory 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 in settings where automated reasoning frequently fails or requires manual scaffolding - Strong communication skills for documenting formalization decisions, edge cases, and reasoning strategies Sample Work You Might Do - Formalize classical or research-level proofs and compare machine-verifiable structures against informal textbook arguments - Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics - Map the frontier of formal verification by identifying and analyzing the limits of current proof assistants Why Join Us - Work on genuinely frontier problems at the intersection of mathematics and AI - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, intellectually rigorous work - Contribute to AI research that advances the reliability and reasoning capabilities of next-generation models - Potential for ongoing work and contract extension as new projects launch