Applied Formal Methods Researcher (Lean 4)

About The Role

What if your deep mathematical intuition could directly shape how AI reasons, proves, and understands the world's hardest problems? We're looking for Applied Formal Methods Researchers to translate rigorous human mathematics into machine-verifiable Lean 4 proofs — working at the precise boundary where human mathematical genius meets the limits of automated reasoning. This is a fully remote, flexible contract role designed for mathematicians who are passionate about formal verification and hungry to push proof assistants further than they've ever gone.

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 formalizations in Lean 4
• Identify gaps, hidden assumptions, and formalizable sub-structures within complex mathematical arguments
• Construct Lean proofs that probe and expose the current limits of automated proof assistants
• Collaborate with researchers to design and refine formal verification strategies and pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Advise on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where and why automated provers break down — and document those findings rigorously
• Formalize classical results and compare machine-verifiable structures against established textbook arguments

Who You Are

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the trajectory of mechanized mathematics
• Able to translate dense, informal arguments into clean, precise formal proofs with minimal ambiguity

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
• Experience contributing to large-scale formalization projects such as Mathlib
• Exposure to theorem provers where automated reasoning frequently fails or requires significant manual scaffolding
• Prior involvement in data annotation, evaluation, or quality assessment workflows
• Strong communication skills for articulating formalization decisions, edge cases, and proof strategies

The 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 fully verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving the gaps that automated tools cannot yet bridge. You're drawn to frontiers — and this is one of the most exciting in modern mathematics.

Why Join Us

• Work directly on cutting-edge AI research projects alongside world-leading labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high-impact technical work
• Gain exposure to how advanced AI models are trained on formal mathematical reasoning
• Contribute to work that is actively advancing the frontier of mechanized mathematics
• Potential for ongoing engagement and contract extension as new projects launch