Researcher – Lean 4 & Formal Proof Systems (AI Training)
About The Role
What if your deep mathematical training could directly shape how AI reasons about proofs — and push the boundary of what machines can formally verify? We're looking for mathematicians and formal methods researchers to translate sophisticated mathematical arguments into Lean 4, working at the cutting edge of AI research and mechanized mathematics.
This is a fully remote, flexible contract role for people who find beauty in rigor — and satisfaction in making a machine understand what a human mind sees instantly.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems)
Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test the limits of existing proof assistants, especially where automation breaks down
Collaborate with researchers to design, refine, and evaluate formal verification strategies
Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
Provide guidance on proof decomposition, lemma selection, and structuring techniques
Investigate where automated provers fail — and articulate precisely why
Who You Are
Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Strong foundation in rigorous proof construction across one or more core mathematical domains
Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable proof assistant — Lean strongly preferred
Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to take a dense, informal argument and express it in a form a machine can verify — without losing what makes the proof elegant
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 requires manual scaffolding
Prior experience with data annotation, data quality, or evaluation systems
Strong communication skills for explaining formalization decisions, edge cases, and proof strategies
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, technically demanding work
Contribute directly to advancing the capabilities of formal verification and AI reasoning
Potential for ongoing work and contract extension as new projects launch