What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians who love rigorous proof and formal verification to help us map the frontier of what machine-verifiable mathematics can express - and push it further.
This is a fully remote, flexible contract role working with leading AI research labs. If you've spent years building intuition for proof structure, love the challenge of translating human arguments into formal systems, and have hands-on experience with Lean or similar proof assistants, this role was made for you.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: Flexible - work on your own schedule
What You'll Do
Translate informal mathematical proofs into Lean (Lean 3 or Lean 4) with an emphasis on clarity, structure, and correctness
Analyze complex proofs across domains, identifying hidden assumptions, gaps, and formalizable sub-structures
Construct formalizations that test and extend the limits of existing proof assistants - especially where automated tools struggle or fail
Collaborate with researchers to design and refine strategies for improving formal verification pipelines
Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
Advise on proof decomposition, lemma selection, and structuring techniques for formal models
Who You Are
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 (strongly preferred), Coq, Isabelle/HOL, Agda, or comparable formal proof systems
Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, elegant mathematical arguments into clean, structured formal proofs
Thrive working independently on intellectually demanding, open-ended problems
Nice to Have
Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
Experience with large-scale formalization projects (e.g., mathlib)
Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
Ability to clearly articulate formalization decisions, edge cases, and reasoning strategies
Sample Work You Might Do
Formalize classical theorems and compare machine-verifiable structures against textbook arguments
Investigate where automated provers break down and articulate exactly why - missing lemmas, library gaps, complexity limits
Write Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
Why Join Us
Work on genuinely frontier problems at the intersection of mathematics and AI
Fully remote and asynchronous - work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually stimulating work
Collaborate with leading AI labs and researchers pushing the boundaries of machine reasoning
Potential for ongoing work and contract extension as new projects launch
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