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 human-written mathematics into precise, machine-verifiable Lean 4 formalizations --- helping map the very frontier of what modern proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role built for mathematicians who are passionate about formal verification and eager to push the limits of mechanized mathematics.

* 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 a focus on clarity, correctness, and mathematical rigor
* Analyze proofs across domains --- identifying hidden assumptions, gaps, and formalizable sub-structures
* Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
* Investigate where automated provers break down and articulate why --- complexity, missing lemmas, library gaps, and beyond
* Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
* Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
* Formalize classical proofs and compare machine-verifiable structures against textbook arguments
* Create Lean proofs that surface 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 writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
* Have 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 arguments into precise, 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 manual scaffolding
* Prior experience with data annotation, data quality, or AI evaluation workflows
* Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

**Why This Role** You're not just writing proofs --- you're working at the intersection of mathematics and artificial intelligence, helping determine what formal reasoning can and cannot yet do. This is rare, meaningful work that only a small number of people in the world are positioned to do well.

**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, high-impact work
* Contribute directly to how AI systems learn to reason about mathematics
* Potential for ongoing work and contract extension as new projects launch