About The Role
What if your deep mathematical expertise could directly shape how AI reasons, proves, and thinks? We're looking for Applied Formal Methods Researchers to translate rigorous human-written mathematics into machine-verifiable Lean 4 proofs — working at the exact frontier where formal verification meets the limits of modern AI.
This is a fully remote, flexible contract role built for mathematicians who love precision, structural beauty, and the challenge of expressing elegant arguments in a form a machine can actually verify.
Job Details
* Organization: Alignerr
* Type: Hourly Contract
* Location: Remote
* Commitment: 10–40 hours/week
What You'll Do
* Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness
* Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
* Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail
* 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 guidance on proof decomposition, lemma selection, and structuring techniques for formal models
* Formalize classical proofs and compare machine‐verifiable structures against textbook arguments
* Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and beyond
* Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Who You Are
* Holder of a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
* Deeply grounded in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
* Experienced with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable 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, structured formal proofs with precision
* A methodical 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 with large‐scale formalization projects such as Mathlib
* Exposure to theorem provers where automated reasoning frequently fails or requires significant manual scaffolding
* Prior experience with data annotation, data quality, or evaluation systems
* Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
* Work directly on cutting‐edge AI projects alongside leading research labs
* Fully remote and flexible — work when and where it suits you
* Freelance autonomy with the intellectual depth of meaningful, frontier‐level work
* Direct exposure to how advanced AI models are trained and where mathematical reasoning fits in
* Contribute to defining the boundary of what mechanized mathematics can express and verify
* Potential for ongoing work and contract extension as new projects launch
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