Mathematical Formalization Specialist

Alignerr Corp.; Chicago (IL); Remote; USD 83,000 - 179,000; Full time

Job summary

Alignerr is seeking a Mathematical Formalization Specialist to translate rigorous mathematics into Lean and related proof systems, ensuring machine-verifiable proofs with mathematical rigor. The role emphasizes collaboration with AI research labs, exploring frontiers of formal verification, and advancing proof automation in a fully remote setup.

You will formalize informal arguments, analyze proof gaps, and contribute to scalable formalization projects, leveraging Lean, Coq, and other proof

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Hands-on experience with formal proof systems and Lean (Lean 3 or Lean 4) is strongly preferred.

Responsibilities

• Translate informal mathematical proofs into Lean and related proof systems with precision and rigor.
• Analyze domain-specific proofs to identify gaps and formalizable sub-structures.
• Construct formalizations that probe the limits of proof assistants where automation fails.
• Collaborate with researchers to design strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with mathematical best practices.
• Provide expert guidance on proof decomposition and lemma selection.
• Investigate why automated provers break down and document causes.

Skills

Lean proof systems

Formal verification

Proof writing

Research collaboration

Education

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

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

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

• 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