Mathematical Formalization Specialist (Lean / Formal Proof Systems)

Alignerr Corp.; United States; Remote; USD 110,000 - 207,000; Part time

Benefits offered by this job

Fully remote

Flexible schedule

Freelance autonomy

Ongoing project opportunities

Job summary

Alignerr seeks mathematicians with hands-on experience in formal proof systems to translate rigorous arguments into machine-verifiable Lean formalizations. This fully remote hourly contract role sits at the intersection of mathematics and computer science, with flex-time and task-based commitment.

You will translate dense mathematical arguments into structured formal proofs, collaborate with AI researchers, and push the boundaries of proof assistants like Lean, Coq, and Isabelle/HOL.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong proof-writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (3/4), Coq, Isabelle/HOL, or Agda.

Responsibilities

• Translate informal proofs into Lean and related systems with emphasis on clarity and correctness.
• Analyze proofs across mathematical domains to identify gaps and formalizable sub-structures.
• Construct formalizations that test the limits of proof assistants where automation struggles.
• Collaborate with AI researchers to improve formal verification pipelines.
• Develop clean, reproducible proof scripts aligned with proof-idioms and best practices.

Skills

Mathematical proof writing

Formal verification

Clear communication

Problem solving

Self-motivated

Education

Master's degree or higher in Mathematics/Logic/CS

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

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 — especially Lean — to tackle problems that sit beyond the reach of automated tools. This is a fully remote, flexible contract role at the intersection of mathematics and computer science. You'll work on genuinely hard problems, translating rigorous human arguments into machine‑verifiable formalizations that help map the frontier of what proof assistants can express, capture, and automate.

Organization & Contract Details

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: Flexible, task-based

What You'll Do

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze proofs across mathematical 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 AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models

Sample Work You Might Do

• Formalize classical proofs and compare machine‑verifiable structures against textbook arguments
• Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
• Write Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Required

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 comparable formal proof systems — 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–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

The 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 understand. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You don't just do mathematics — you think carefully about how mathematics is done.

Why Join Us

• Work on cutting‑edge AI research projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute directly to advancing the reliability and reasoning capabilities of next‑generation AI
• Potential for ongoing work and contract extension as new projects launch