Mathematical Formalization Specialist

About the Role

What if your deep mathematical expertise could directly shape how AI reasons, verifies, and understands proof — at the frontier of what machines can currently do?

We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human-written arguments into machine-verifiable Lean proofs. This is rare, high-impact work that sits at the intersection of pure mathematics and cutting-edge AI research — and it's work that automated tools simply cannot do alone.

This is a fully remote, flexible contract role. If you're a mathematician who gets excited by precision, structural elegance, and the challenge of making a machine understand a beautiful proof, this is the role for you.

Organization

Alignerr

Type

Hourly Contract

Location

Remote

Commitment

Flexible — work on your own schedule

What You'll Do

• Translate informal mathematical proofs into Lean (Lean 3 or Lean 4) with an emphasis on clarity, structure, and correctness
• Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that probe and test the limits of existing proof assistants — especially where automation breaks down
• 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 structuring strategies for formal models

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 (strongly preferred), Coq, Isabelle/HOL, Agda, or comparable formal proof systems
• Passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, well-structured formal proofs independently
• Naturally precise, detail-oriented, and intellectually curious about the edge cases automated tools can't handle

Nice to Have

• Familiarity with type theory, the Curry–Howard correspondence, or proof automation techniques
• Experience contributing to large-scale formalization projects such as mathlib
• Exposure to theorem provers in contexts where manual scaffolding is required
• Strong ability to articulate formalization decisions, edge cases, and reasoning strategies in writing

Sample Work You Might Do

• Formalize classical theorems and compare machine-verifiable structures against standard textbook arguments
• Investigate where automated provers break down — and clearly articulate why (missing lemmas, insufficient libraries, complexity barriers, etc.)
• Construct Lean proofs that surface deeper patterns or implicit generalizations within the original mathematics

Why Join Us

• Work on genuinely frontier problems — tasks where automated tools fail and human mathematical expertise is irreplaceable
• Fully remote and flexible — structure your work around your schedule
• Contribute directly to AI research that advances the reliability and reasoning capabilities of next-generation models
• Freelance autonomy with the structure of meaningful, intellectually stimulating task-based work
• Potential for ongoing work and contract extension as new research projects launch