Mathematical Formalization Specialist

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about rigorous proof? We're looking for mathematicians with hands-on experience in formal proof systems — especially Lean — to help push the boundaries of what machine-verifiable mathematics can express and automate.

This is a fully remote, flexible contract role at the intersection of pure mathematics and cutting-edge AI research. You'll be working on problems that sit beyond the reach of automated provers, helping map the frontier of formal verification.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: Flexible

What You'll Do

• Translate informal mathematical proofs into Lean (and related proof systems), with a focus on clarity, structure, and machine-verifiable correctness
• Analyze proofs across domains — 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
• 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
• Advise on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate failure modes of automated provers and articulate the underlying reasons — missing lemmas, insufficient libraries, complexity barriers, and more

Must-Have

Who You Are

• 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
• Genuine enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to translate dense, informal mathematical arguments into clean, structured formal proofs

Nice To Have

• Familiarity with type theory, the Curry-Haworth correspondence, and proof automation tools
• Experience contributing to large-scale formalization projects such as mathlib
• Exposure to theorem provers where automated reasoning frequently requires manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

Ideal Candidate

You're a mathematically mature problem‑solver who finds genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify. You appreciate precision and structural beauty — and you're energized by the challenge of resolving gaps that automated tools cannot yet bridge. You work well independently, think in lemmas, and care about getting it exactly right.

Sample Work

• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down and articulate why
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Why Join Us

• Work on cutting-edge AI research projects alongside leading AI labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute to AI development at the frontier of formal reasoning and mathematical intelligence
• Potential for ongoing work and contract extension as new projects launch