Mathematical Formalization Specialist

Alignerr; Austin (CO); On-site; USD 83,000 - 165,000; Part time

Benefits offered by this job

Remote work

Flexible schedule

Freelance autonomy

Job summary

Alignerr is seeking a Mathematical Formalization Specialist to advance machine-verifiable mathematics using Lean and related proof systems. This fully remote, flexible hourly contract role collaborates with AI research teams to push the boundaries of formal verification and automated reasoning.

You will translate informal proofs into Lean, identify gaps, build formalizations, and craft readable proof scripts that align with best practices in proof assistants.

Qualifications

• Extensive experience writing rigorous formal proofs.
• Hands-on experience with Lean (Lean 3/4) and related proof systems.
• Ability to translate dense informal arguments into clean, machine-verifiable proofs.
• Interest in formal verification and AI research along with clear communication.

Responsibilities

• Translate informal mathematical proofs into Lean (and related proof systems).
• Analyze generic and domain-specific proofs to identify gaps and formalizable sub-structures.
• Build formalizations that stress-test the limits of existing proof assistants.
• Collaborate with researchers to improve formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with best practices.
• Advise on proof decomposition, lemma selection, and structuring techniques.

Skills

Formal proof writing

Mathematical maturity

Translate informal proofs

Strong communication

Education

Master's degree or higher in Mathematics or related field

Tools

Lean (Lean 3/Lean 4)

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 help push the boundaries of what machine-verifiable mathematics can express and automate.

This is a fully remote, flexible contract role working alongside leading AI research teams. You'll tackle proofs that sit beyond the reach of current automated tools, helping map and expand 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 precision, clarity, and structural elegance
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Build formalizations that stress-test the limits of existing proof assistants — especially where automation fails
• Collaborate with researchers to design and refine 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

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 formal proof system — Lean strongly preferred
• Genuine enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to translate dense informal arguments into clean, structured, machine-verifiable proofs

Nice To Have

• Familiarity with type theory, the Curry-Howard correspondence, or proof automation tooling
• Experience contributing to large-scale formalization projects such as mathlib
• Exposure to theorem provers in contexts where automated reasoning frequently fails or requires manual scaffolding
• Strong communication skills for articulating 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 human argument and expressing it in a form a machine can verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving the gaps that automated tools cannot yet bridge. You're excited to work at the intersection of pure mathematics and cutting-edge AI research.

Sample Work

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

Why Join Us

• Work on genuinely cutting-edge AI research alongside leading labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Contribute to projects that advance the reliability and mathematical depth of AI systems
• Potential for ongoing work and contract extension as new projects launch