About The Role
What if your deepest mathematical knowledge could directly shape how AI reasons about truth, proof, and logic? We're looking for Formal Verification Scientists to translate advanced human-written mathematics into machine-verifiable Lean proofs — helping map the frontier of what AI can understand, verify, and automate.
About The Role
This is a fully remote, flexible contract role for mathematicians who live and breathe rigorous proof and want to work at the cutting edge of formal verification and AI research.
- 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 clarity, correctness, and mathematical elegance
- Analyze proofs across domains — algebra, analysis, topology, logic, and beyond — identifying gaps, hidden assumptions, and formalizable sub-structures
- Push the boundaries of existing proof assistants by constructing formalizations where automated tools struggle or fail
- Investigate where automated provers break down and articulate precisely why — missing lemmas, library gaps, complexity barriers
- Develop highly readable, reproducible proof scripts aligned with Mathlib conventions and best practices
- Collaborate with AI researchers to design and refine formal verification pipelines
- Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
- Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
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
- Genuinely excited by formal verification, proof assistants, and the future of mechanized mathematics
- Able to bridge the gap between informal mathematical intuition and precise formal structure
- Thrive working independently on deep, intellectually demanding problems
Nice to Have
- Experience with large-scale formalization projects such as Mathlib
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Exposure to theorem provers in settings where automated reasoning frequently requires manual scaffolding
- Prior experience with data annotation, evaluation systems, or proof quality assessment
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
Why This Role
This isn't routine annotation work. You'll be operating at the true frontier — taking dense, elegant mathematical arguments and expressing them in forms a machine can verify. Every proof you formalize contributes directly to how the next generation of AI systems understands and reasons about mathematics.
- Work on research-grade problems that matter at the intersection of mathematics and AI
- Fully remote and flexible — structure your own schedule around deep work
- Freelance autonomy with the intellectual depth of a research environment
- Collaborate with world-class AI research teams and labs
- Potential for ongoing work and contract extension as projects evolve
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Formal Verification Scientist (Lean 4 & Mathlib) in Glasgow employer: Alignerr Corp.
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