About The Role What if your deep mathematical training could directly shape how AI reasons about the hardest problems in mathematics? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the exact boundary where human mathematical intuition meets machine-verifiable logic. This is a fully remote, flexible contract role for mathematicians who are passionate about formal verification and excited to push the limits of what proof assistants can do.

Organization: Alignerr

Type: Hourly Contract

Location: Remote

Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness

Analyze domain-specific and general proofs, identifying gaps, hidden assumptions, and formalizable sub-structures

Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail

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

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

Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models

Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, or otherwise

Reveal deeper patterns and generalizations implicit in the original mathematics through your formalizations Who You Are Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science,



or a closely related field

Solid foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete mathematics

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

Able to translate informal mathematical arguments into clean, structured formal proofs

Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics A mathematically mature problem-solver who finds satisfaction in expressing elegant human arguments in a form a machine can verify 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 AI evaluation systems

Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us Work on cutting-edge AI projects alongside leading research labs and AI teams

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

Freelance autonomy with the structure of meaningful, intellectually challenging work

Contribute directly to the development of AI systems that can reason about advanced mathematics

Work at the true frontier of formal verification — on problems that push the limits of what machines can understand

Potential for ongoing work and contract extension as new projects launch

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