Mathematician – Formal Proof & AI Research (Remote Contract)

Alignerr Corp.; Amsterdam; Remote; EUR 83,000 - 165,000; Full time

Benefits offered by this job

Remote work

Flexible hours

Job summary

Alignerr Corp. is seeking mathematicians with a passion for rigorous proof and formal systems to help build the mathematical foundations used by frontier AI research. This is a fully remote, hourly contract role focusing on formal mathematics, logic, and AI applications.

Experience with Lean 4 and large math libraries will be essential. You will formalize advanced theorems, contribute to mathlib, and craft machine-checkable proofs while auditing existing developments for logical integrity.

Qualifications

• Must have strong track record in formal mathematical proofs.
• Proficient in Lean 4 and translating informal reasoning into machine-checkable proofs.
• Ability to work independently in a remote, asynchronous setup.

Responsibilities

• Formalize advanced mathematical arguments in Lean 4 across disciplines.
• Contribute to growth of large-scale formal libraries, including mathlib.
• Create clear, readable formal proofs translating informal reasoning.
• Audit existing formal proofs for correctness and completeness.
• Support AI research at the frontier by enabling language-model tooling.

Skills

Rigorous proof writing

Formal reasoning

Remote/independent work

Education

Master's or PhD in Mathematics

Tools

Lean 4

Proof assistants

Job description

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. The Netherlands has one of Europe's strongest traditions in mathematical logic and formal systems — if you know your way around Lean 4 and want to do deeply meaningful work, this opportunity is for you.

• 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