Formal Verification Scientist (Lean 4 & Mathlib)

About The Role
What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for Formal Verification Scientists to translate advanced mathematics into machine-verifiable Lean 4 proofs — working at the intersection of rigorous mathematics and cutting-edge AI research.
This is a fully remote, flexible contract role built for mathematicians who live for 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, correct, and well-structured Lean 4 formalizations
Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — to identify gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test and map the frontier of what modern proof assistants can express and automate
Investigate where automated provers break down and articulate the underlying reasons — missing lemmas, complexity barriers, insufficient libraries
Develop reproducible, readable proof scripts aligned with mathematical best practices and Lean/Mathlib idioms
Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Who You Are
Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Possess a strong foundation in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics
Have hands-on experience with Lean (Lean 3 or Lean 4), with Lean 4 strongly preferred; experience with Coq, Isabelle/HOL, or Agda also welcomed
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, informal arguments into structured formal proofs with clarity and precision
Self-motivated, detail-oriented, and comfortable working independently in an asynchronous environment
Nice to Have
Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
Experience contributing to or working within 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, evaluation systems, or formal data quality workflows
Strong written communication skills for documenting formalization decisions, edge cases, and reasoning strategies
Why This Role
You're not just writing proofs — you're helping define the boundary of what machines can know. This work sits at one of the most intellectually demanding and consequential frontiers in AI research: teaching AI systems to reason about mathematics with the same rigor that mathematicians demand of themselves.
If you find deep satisfaction in taking an elegant human argument and expressing it in a form a machine can verify — and you're energized by the places where that translation breaks down — this is the role for you.
Why Join Us
Work on cutting-edge AI research projects alongside world-leading research labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, technically rich work
Direct impact on how next-generation AI systems understand and reason about mathematics
Potential for ongoing work and contract extension as new projects launch

Work arrangement
Yes