Mathematical Formalization Specialist

Alignerr; Pittsburgh (Allegheny County); On-site; USD 83,000 - 124,000; Full time

Job summary

Alignerr seeks a Mathematical Formalization Specialist to translate informal arguments into Lean proofs (Lean 3/4). You will analyze proofs, identify gaps, and develop formalizations that test proof assistants’ limits, collaborating with AI researchers to improve verification pipelines.

The role emphasizes precision, structure, and independent work in a fully remote, flexible contract. Master's or higher in Mathematics or related fields is required, with hands-on Lean or similar systems

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on experience with Lean (strongly preferred), Coq, Isabelle/HOL, Agda, or comparable formal proof systems.

Responsibilities

• Translate informal mathematical proofs into Lean proofs with emphasis on clarity, structure, and correctness.
• Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that probe the limits of proof assistants, especially where automation breaks down.

Skills

Lean

Formal proof writing

Analytical thinking

Education

Master's degree in Mathematics/Logic/Theoretical CS

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Job description

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

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