About The Role
What if your deep mathematical intuition and mastery of formal proof systems could directly shape how AI understands and reasons about mathematics? We're looking for Formal Verification Scientists to translate advanced human-written proofs into precise, machine-verifiable formalizations — helping map the outer edge of what proof assistants can express, capture, and automate.
This is a fully remote, flexible contract role ideal for mathematicians who live at the intersection of rigorous proof construction and cutting-edge computer science.
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 generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail entirely
Collaborate with AI 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 and articulate where automated provers break down — due to complexity, missing lemmas, or insufficient libraries
Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Who You Are
Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Have 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 systems — Lean 4 strongly preferred
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, informal mathematical arguments into clean, structured, machine-verifiable proofs
Mathematically mature and energized by working at the frontier — where automated tools run out and human insight takes over
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 AI evaluation systems
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work on cutting-edge AI research projects alongside leading AI labs and research teams
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually stimulating work
Contribute directly to expanding the frontier of formal verification and mechanized mathematics
Gain rare exposure to how advanced AI models are trained on mathematical reasoning
Potential for ongoing work and contract extension as new projects launch