Mathematician – Proof Formalization & AI Research (Remote Contract)

About The Role What if your deep knowledge of formal mathematics could directly shape how the most advanced AI systems in the world reason, prove, and think? We're looking for mathematicians with a passion for rigorous proof and formal systems to help build the mathematical foundations that frontier AI depends on. This is a fully remote, flexible contract role working at the intersection of pure mathematics, logic, and cutting-edge AI research. If you live and breathe formal proof — and especially if you know your way around Lean 4 — this is a rare opportunity to do deeply meaningful technical work on your own schedule, from anywhere in Canada. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week What You'll Do Formalize advanced mathematical arguments and theorems in Lean 4, spanning a wide range of mathematical disciplines Contribute to the growth and quality of large-scale formal mathematical libraries, including mathlib Construct clean, readable, and well-structured formal proofs that translate informal mathematical reasoning into rigorous machine-checkable form Audit and verify existing formal proofs for correctness, completeness, and logical integrity Work at the frontier of AI research, helping train the next generation of mathematically capable language models Who You Are Hold a Master's degree or PhD in Mathematics or a closely related field Possess a strong background in rigorous mathematical proof writing and logical reasoning Have hands-on experience with formal proof assistants — Lean 4 strongly preferred Can fluently translate informal mathematical ideas into structured, machine-verifiable formal proofs Self-motivated and comfortable working independently in a remote, asynchronous environment Nice to Have Prior experience with proof verification, theorem proving, or mathematical formalization projects Familiarity with mathlib or other large-scale formal mathematical libraries Background in data annotation, data quality evaluation, or AI training workflows Experience across multiple mathematical domains — topology, algebra, analysis, logic, and beyond Why Join Us Work on frontier AI research alongside the world's leading AI labs and research teams Fully remote and flexible — structure your work around your life, not the other way around Freelance autonomy with the intellectual depth of meaningful, high-stakes technical work Contribute directly to formal mathematical libraries that will outlast any single project Gain rare exposure to how cutting-edge large language models are built and trained Potential for ongoing work and contract extension as new projects launch

Formalize advanced mathematical theorems and arguments using Lean 4 to contribute to large-scale libraries like mathlib. Audit existing formal proofs and help train next-generation AI language models in mathematical reasoning.

Requires a Master's or PhD in Mathematics or a related field with strong experience in rigorous proof writing. Proficiency in formal proof assistants, specifically Lean 4, is strongly preferred.

Identified from the job description. Confirm important requirements above.

• Lean 4
• Formal Proof
• Mathematical Logic
• Theorem Proving
• Mathlib
• Proof Verification
• Formalization
• Mathematical Reasoning

• Science & Research
• Technology
• Software
• Data & Analytics

Minimum education

Master’s degree

Minimum experience

2+ years

Apply by

Sep 13, 2026

Posting language

English

Working hours

40 hours per week

Location requirements

Country, Toronto, Ontario, Canada

Seniority

Entry level