Mathematician – Formalization & AI Foundations (Remote Contract)

Alignerr Corp.; Warszawa; Remote; PLN 138,000 - 248,000; Part time

Job summary

Alignerr Corp. is seeking mathematicians to shape the mathematical foundations behind frontier AI through rigorous formal systems. This is a fully remote, hourly contract role with 10–40 hours per week.

You will formalize proofs in Lean 4, contribute to large-scale libraries like mathlib, and translate informal reasoning into machine-checkable formal arguments. Work is independent, asynchronous, and at the cutting edge of AI research.

Qualifications

• Master's degree or PhD in Mathematics or closely related field.
• Strong background in rigorous proof writing and logical reasoning.
• Hands-on experience with formal proof assistants (Lean 4 preferred).
• Ability to translate informal ideas into machine-verifiable formal proofs.

Responsibilities

• Formalize advanced mathematical arguments and theorems in Lean 4.
• 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

Skills

Rigorous proof writing

Logical reasoning

Self-motivation

Education

Master's degree or PhD in Mathematics

Tools

Lean 4

mathlib

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. Poland has one of the world's most celebrated mathematical traditions — rooted in logic, set theory, and foundations. If you know your way around Lean 4 and want to apply that tradition to frontier AI, this role is built 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