About The Role
What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems — especially Lean — to tackle problems that sit beyond the reach of automated tools.
This is a fully remote, flexible contract role at the intersection of mathematics and computer science. You'll work on genuinely hard problems, translating rigorous human arguments into machine-verifiable formalizations that help map the frontier of what proof assistants can express, capture, and automate.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: Flexible, task-based
What You'll Do
Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
Analyze proofs across mathematical domains — 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 AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
Develop clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Sample Work You Might Do
Formalize classical proofs and compare machine-verifiable structures against textbook arguments
Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
Write Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Required
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 comparable formal proof systems — Lean strongly preferred
Genuine enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
Ability to translate dense, informal mathematical arguments into clean, structured formal proofs
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
Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
The Ideal Candidate
You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can understand. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You don't just do mathematics — you think carefully about how mathematics is done.
Why Join Us
Work on cutting-edge AI research 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
Contribute directly to advancing the reliability and reasoning capabilities of next-generation AI
Potential for ongoing work and contract extension as new projects launch