Mathematical Formalization Specialist (Lean / Formal Proof Systems)
About the Role
What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems - particularly
Lean
- to work on some of the most intellectually demanding problems in AI development today.
This is a fully remote, flexible contract role working alongside leading AI research labs. You'll be translating rigorous human-written mathematics into machine-verifiable formal proofs, operating at the very edge of what proof assistants can currently express and automate.
- Organization
: Alignerr - Type
: Hourly Contract - Location
: Remote - Commitment
: Flexible What You'll Do- Translate informal mathematical proofs into
Lean
(and related proof systems) with precision, clarity, and structural rigor - Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that probe the limits of existing proof assistants - especially where automation fails
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide expert guidance on proof decomposition, lemma selection, and formal modeling strategies
- Investigate and articulate the reasons automated provers break down - whether due to complexity, missing lemmas, or library gaps
Who You Are
Must-Have:- 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 formal proof system - Lean strongly preferred - Deep enthusiasm for
formal verification
, proof assistants, and the mechanization of mathematics - Ability to translate dense, informal arguments into clean, structured, machine-verifiable proofs
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
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
Sample Work You Might Do- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
- Investigate where automated provers break down and document the underlying causes
- Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
- Help map the frontier of what formal verification can express, capture, and eventually automate
Why Join Us- Work on cutting-edge AI research projects alongside leading labs pushing the limits of machine reasoning
- Fully remote and flexible - work on your own schedule, from anywhere
- Freelance autonomy with the depth and challenge of genuinely frontier-level mathematical work
- Contribute to a field that is reshaping the reliability and rigor of AI at its core
- Potential for ongoing work and contract extension as new projects launch