Mathematical Formalization Specialist

Alignerr Corp.; United States; On-site; MXN 1,011,000 - 1,770,000; Full time

Benefits offered by this job

Fully remote

Flexible schedule

Job summary

Alignerr Corp. is seeking a Mathematical Formalization Specialist to translate rigorous human arguments into Lean-based machine-verifiable proofs. You will work with AI researchers to refine formal verification strategies while maintaining clean, readable proof scripts.

The role emphasizes deep mathematical knowledge, experience with Lean/Coq/Isabelle/HOL/Agda, and the ability to work independently on complex formalization projects in a fully remote setting.

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 math.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems—Lean strongly preferred.
• Deep enthusiasm for formal verification, proof assistants, and mechanized mathematics.
• Ability to translate dense informal arguments into clean, structured, machine-verifiable formalizations.
• Work independently with precision and consistency.

Responsibilities

• Translate informal mathematical proofs into Lean (and related proof assistants) with clarity and correctness.
• Analyze proofs to identify gaps, assumptions, and formalisable sub-structures.
• Construct formalizations that push the limits of proof assistants where tools struggle.
• Collaborate with AI researchers to design verification strategies and pipelines.
• Develop readable, reproducible proof scripts aligned with best practices.
• Advise on proof decomposition, lemmas, and structuring techniques for formal models.
• Investigate where automated provers break down and explain why.

Skills

Lean expertise

Proof writing

Formal verification

Independent worker

Education

Master's degree in Mathematics/Logic/CS

Tools

Coq

Isabelle/HOL

Agda

Lean

Job description

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

What if your mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human-written arguments into machine-verifiable proofs — working at the very edge of what automated tools can do today.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: Flexible — work on your own schedule

What You'll Do

• Translate informal mathematical proofs into Lean (and related proof assistants) with a focus on clarity, structure, and correctness
• Analyze domain-specific and general proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that push the limits of existing proof assistants, especially where tools struggle or fail
• Collaborate with AI researchers to design and refine formal verification strategies and pipelines
• Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices
• Advise on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond

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 (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
• Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Can reliably translate dense informal arguments into clean, structured, machine-verifiable formalizations
• Work independently with precision and consistency

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 in contexts where automated reasoning requires significant manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies to collaborators

Why This Role

• Work on cutting-edge AI research projects alongside leading AI labs and researchers
• Fully remote and flexible — structure your work around your life, not the other way around
• Apply your deepest mathematical skills to problems that genuinely matter and that automated tools cannot yet solve
• Contribute to the advancement of formal verification and AI reliability at the frontier of modern mathematics
• Potential for ongoing work and contract extension as new research projects launch