About The Role What if your deep mathematical training could directly shape how AI reasons, proves, and understands the most rigorous ideas in all of science? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the exact frontier where human mathematical intuition meets machine-verifiable logic. This is a fully remote, flexible contract role ideal for mathematicians who are passionate about formal verification and excited to push proof assistants beyond their current limits. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week

What You'll Do

Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures Construct formalizations that test and expose the limits of existing proof assistants Investigate where automated provers break down and articulate why — complexity, missing lemmas, library gaps, and beyond Collaborate with AI researchers to design and refine formal verification strategies and pipelines Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments Surface deeper patterns or generalizations implicit in the original mathematics Who You Are 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), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean 4 strongly preferred Ability to translate dense, informal mathematical arguments into clean, structured formal proofs Genuinely excited about formal verification, proof assistants, and the evolving landscape of mechanized mathematics

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 Prior exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding Experience with data annotation, data quality, or evaluation systems Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators The Ideal Candidate You're a mathematically mature problem-solver who finds deep satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving the gaps that automated tools cannot yet bridge. You thrive at the intersection of mathematics and computer science — and you want your expertise to matter.

Why Join Us

Work directly with leading AI research labs on cutting-edge formalization projects Fully remote and asynchronous — work when and where it suits you Freelance autonomy with the substance of genuinely meaningful, high-skill work Gain rare exposure to how advanced LLMs are trained on formal mathematical reasoning Contribute to work that is actively expanding what AI can understand and prove Potential for ongoing work and contract extension as new projects launch