About The Role What if your deep mathematical training could directly shape how AI reasons, proves, and understands the most rigorous ideas in human knowledge? We're looking for Applied Formal Methods Researchers to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs — working at the precise boundary of what automated reasoning can and cannot yet do. This is a fully remote, versátil contract role built for mathematicians who love precision, structural elegance, and the challenge of pushing proof assistants to their limits.

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 gaps, hidden assumptions, and formalizable sub-structures

Construct formalizations that deliberately test the boundaries of existing proof assistants, especially where tools struggle or fail

Collaborate with AI researchers to design and refine formal verification strategies and pipelines

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

Provide expert guidance on proof decomposition, lemma selection, and structuring techniques

Investigate where automated provers break down and clearly articulate why — complexity, missing lemmas, library gaps, and beyond

Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments Who You Are Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Strong foundation in rigorous proof writing 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 a comparable proof assistant — Lean 4 strongly preferred

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

Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics 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 significant manual scaffolding

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

Strong communication skills for explaining formalization decisions, edge cases, and proof strategies The Ideal Candidate You're a mathematically mature problem-solver who finds deep satisfaction in taking a dense, 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. You're excited to work on problems that sit at the very frontier of what formal mathematics can express and automate.

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

Fully remote and flexible — work when and where it suits you, on your own schedule

Freelance autonomy with meaningful, intellectually stimulating work

Contribute to a field that is actively redefining the boundaries of mathematical knowledge and AI capability

Potential for ongoing work and contract extension as new projects launch

📌 Applied Formal Methods Researcher (Lean 4) (Ciudad de México)
🏢 Alignerr
📍 Ciudad de México