Alignerr
Researcher - Lean 4 & Formal Proof Systems
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Researcher – Lean 4 & Formal Proof Systems (AI Training)
About the Role
What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs — advancing the frontier of mechanized mathematics for millions of future users?
We're looking for mathematicians and formal verification specialists to write and formalize advanced mathematical proofs in Lean 4 for cutting-edge AI research. This role sits at the intersection of mathematics and computer science, translating rigorous human arguments into precise, machine-verifiable formalizations that push the limits of what proof assistants can express and automate.
This is a fully remote, flexible contract role designed for researchers who love structure, precision, and working at the cutting edge of what's formally possible.
Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week
What You’ll Do
- Translate informal mathematical proofs into Lean 4 (and related proof systems), emphasising clarity, structure, and correctness
- Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalisable sub-structures
- Construct formalisations that test the limits of existing proof assistants — particularly where automated tools struggle or fail
- Collaborate with researchers to design, refine and evaluate strategies for improving formal verification pipelines
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Formalise classical proofs and compare machine-verifiable structures against textbook arguments
- Investigate and articulate where automated provers break down — due to complexity, missing lemmas, insufficient libraries, or other factors
- Create Lean 4 proofs that reveal deeper patterns or generalisations implicit in the original mathematics
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Who You Are
** requirements:**
- Hold a Master’s degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Have 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 preferred) or comparable systems like Coq, Isabelle/HOL, or Agda
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanised mathematics
- Ability to translate informal arguments into clear, structured formal proofs with precision and care
- Mathematically mature problem-solver who finds satisfaction in expressing dense, elegant human arguments in a form a machine can verify
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Nice to have:
- Familiarity with type theory and the Curry-Howard correspondence
- Experience with large-scale formalisation 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 evaluation systems
- Strong communication skills for explaining formalisation decisions, edge cases, and reasoning strategies
Why Join Us
- Work on cutting-edge AI projects alongside leading research labs and teams
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, high-impact technical work
- Contribute directly to advancing the capabilities of AI at the frontier of formal mathematics
- Potential for ongoing work and contract extension as new projects launch
- Collaborate with a global community of researchers tackling some of the hardest problems in formal verification
“It took my CV and asked me questions relevant to understanding what kind of jobs to suggest for me. Suggestions were almost perfect. Jobs were exactly what I’ve been looking for.”
Jessica, London
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