Applied Formal Methods Researcher (Lean 4)

About The Role
What if your deep mathematical training could directly shape how AI understands and constructs formal proofs? We're looking for mathematicians with hands-on experience in formal verification to work at one of the most exciting intersections in modern AI research — mechanized mathematics.
You'll translate rigorous human-written arguments into machine-verifiable Lean 4 proofs, explore the boundaries of what automated provers can and cannot do, and help build the datasets that train the next generation of AI reasoning systems.
This is a fully remote, flexible contract role designed for mathematicians who love precision, structure, and the intellectual challenge of formal verification.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on correctness and readability
Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
Construct formalizations that probe and test the limits of existing proof assistants, particularly where automation breaks down
Investigate why automated provers fail on specific problems — whether due to complexity, missing lemmas, or insufficient libraries — and document your findings clearly
Collaborate with AI researchers to refine strategies for improving formal verification pipelines
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Develop highly reproducible proof scripts aligned with mathematical best practices and Lean idioms
Create Lean proofs that expose deeper patterns or generalizations implicit in the original mathematics
Who You Are
Holder of a 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), with Lean 4 strongly preferred — experience with Coq, Isabelle/HOL, or Agda also considered
Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, informal mathematical arguments into precise, machine-checkable formal proofs
Self-directed and comfortable working independently in an asynchronous, remote environment
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, evaluation systems, or AI training workflows
Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
The Ideal Candidate
You're a mathematically mature problem-solver who thrives at the frontier of formal verification. You find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify. You appreciate precision and structural beauty — and you're energized by the challenge of resolving gaps that automated tools cannot yet bridge.
Why Join Us
Work directly on cutting-edge AI research projects alongside leading AI labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy: set your own pace within a 10–40 hour weekly range
Gain rare exposure to how advanced AI reasoning systems are built and trained
Contribute to research that is actively pushing the frontier of what machines can prove
Potential for ongoing work and contract extension as new projects launch

Work arrangement
Yes