About The Role What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate rigorous human arguments into machine-verifiable Lean 4 proofs — working at the very edge of what automated reasoning can do today. This is a fully remote, flexible contract role designed for people who find genuine satisfaction in the precision and structural elegance of formal mathematics.

No AI background required — just deep mathematical maturity and hands-on experience with proof assistants.

Organization: Alignerr

Type: Hourly Contract

Location: Remote

Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations

Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures

Construct formalizations that probe the limits of existing proof assistants, especially where automation breaks down

Investigate why automated provers struggle — complexity, missing lemmas, insufficient libraries — and document your findings clearly

Collaborate with researchers to design, refine, and evaluate formal verification strategies and pipelines

Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms

Guide proof decomposition, lemma selection, and structuring decisions for complex formal models

Formalize classical proofs and compare machine-verifiable structures against textbook arguments

Surface deeper patterns or generalizations implicit in the original mathematics Who You Are Holds a 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 mathematics

Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred

Genuinely enthusiastic about formal verification, proof assistants, and mechanized mathematics

Able to translate dense informal arguments into clean, precise formal proofs

Comfortable working independently in an asynchronous, remote environment 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 where automated reasoning frequently fails or requires manual scaffolding

Prior experience with data annotation, data quality, or evaluation workflows

Robust communication skills for articulating formalization decisions, edge cases, and reasoning strategies The Ideal Candidate You're a mathematically mature problem-solver who thrives at the frontier of formal verification. You find deep satisfaction in taking an elegant human argument and expressing it in a form a machine can verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge.

Why Join Us Work on cutting-edge AI projects alongside leading research labs

Fully remote and flexible — work when and where it suits you

Freelance autonomy with the structure of meaningful, intellectually stimulating work

Gain direct exposure to how advanced AI models are trained on formal mathematical reasoning

Contribute to work that is genuinely pushing the boundaries of mechanized mathematics

Potential for ongoing work and contract extension as new projects launch

📌 Applied Formal Methods Researcher (Lean 4) (Montreal)
🏢 Alignerr
📍 Montreal