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About The Role
What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for Applied Formal Methods Researchers to translate rigorous mathematical arguments into machine-verifiable proofs in Lean 4 — working at the very edge of what automated reasoning can do today.
This is a fully remote, flexible contract role built for mathematicians who live and breathe formal verification. You'll work on proofs that push proof assistants to their limits, helping map the frontier of mechanized mathematics and contributing to some of the most technically demanding AI research happening right now.
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 formalizations in Lean 4
Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test the boundaries of existing proof assistants, especially where automation breaks down
Investigate and articulate why automated provers struggle or fail — complexity, missing lemmas, library gaps, and beyond
Collaborate with researchers to design and refine strategies that improve formal verification pipelines
Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
Surface deeper patterns and generalizations that become visible only through formalization
Who You Are
Holds 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), Coq, Isabelle/HOL, Agda, or a comparable proof assistant — Lean strongly preferred
Able to translate dense, informal mathematical arguments into precise, structured formal proofs
Genuinely enthusiastic about formal verification, proof assistants, and the trajectory of mechanized mathematics
Mathematically mature and comfortable working at the frontier — where automated tools fall short and human insight is essential
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 manual scaffolding is frequently required
Prior experience with data annotation, evaluation systems, or data quality workflows
Strong written communication skills for documenting formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work on cutting-edge AI projects alongside leading research labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, technically demanding work
Contribute directly to advancing 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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