What if your mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate advanced mathematical arguments into precise, machine-verifiable Lean 4 proofs — working at the very frontier of what proof assistants can express and automate.
This is a fully remote, flexible contract role for mathematically mature problem-solvers who find deep satisfaction in bridging human intuition and machine precision.
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
Work at the limits of existing proof assistants, tackling cases where automated tools struggle or fail entirely
Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines
Develop proof scripts aligned with mathematical best practices and proof assistant idioms
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
Investigate and articulate where and why automated provers break down — complexity, missing lemmas, library gaps, and beyond
Formalize classical proofs and compare machine-verifiable structures against textbook arguments
Who You Are
Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Deep 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
Passionate about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, informal mathematical arguments into clean, structured formal proofs
You appreciate precision, structural elegance, and the challenge of resolving gaps that automated tools cannot yet bridge
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 regimes where automated reasoning frequently fails or requires extensive manual scaffolding
Prior experience with data annotation, evaluation systems, or AI training workflows
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work on cutting-edge AI research projects alongside world-leading labs
Fully remote and flexible — structure your own hours and work from anywhere
Freelance autonomy with access to genuinely frontier-level mathematical and AI problems
Contribute to work that defines the boundary of what formal verification and AI can achieve together
Potential for ongoing work and contract extension as new projects launch
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