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About The Role
What if your deep mathematical training could directly shape how AI reasons, proves, and understands the world's hardest problems? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the precise intersection of rigorous mathematics and cutting-edge AI research.
This is a fully remote, flexible contract role for mathematicians who are passionate about formal verification and want their expertise to matter at the frontier 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, machine-verifiable Lean 4 formalizations
Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down
Investigate why automated provers fail — whether due to complexity, missing lemmas, or insufficient libraries — and articulate your findings clearly
Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant 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
Reveal deeper patterns or generalizations implicit in existing mathematical arguments
Who You Are
Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Possess 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 formal systems — Lean 4 strongly preferred
Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense informal arguments into clean, precise formal proofs with clarity and structure
A mathematically mature problem-solver who finds satisfaction in 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 where automated reasoning frequently fails or requires manual scaffolding
Prior experience with data annotation, evaluation systems, or data quality workflows
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work on cutting-edge AI projects alongside world-leading research labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually stimulating work
Gain exposure to advanced LLMs and how frontier AI systems are trained and evaluated
Contribute to work that genuinely advances the state of mechanized mathematics and AI reasoning
Potential for ongoing work and contract extension as new projects launch
Work arrangement
Yes
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