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Job description
About The Role
What if your deepest mathematical knowledge could directly shape how AI reasons about formal proof — permanently expanding the boundary of what machines can verify and understand?
We're looking for mathematicians with serious formal verification experience to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs. This isn't routine formalization work. You'll be operating at the frontier — tackling proofs that push or exceed the current limits of automated proof assistants, and helping leading AI research teams understand exactly where those limits lie and why.
This is a fully remote, flexible contract role built for mathematicians who think precisely, work independently, and care deeply about the structure underlying rigorous argument.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations
Analyze proofs across domains — algebra, analysis, topology, logic, discrete mathematics — identifying hidden assumptions, gaps, and formalizable sub-structures
Construct formalizations that stress-test the limits of current proof assistants, and clearly articulate where and why they struggle
Collaborate with AI researchers to design and refine formal verification pipelines and evaluation strategies
Develop reproducible, well-structured proof scripts aligned with mathematical best practices and Lean idioms
Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
Formalize classical results and compare machine-verifiable structures against textbook arguments to surface deeper patterns and generalizations
Who You Are
Holder of a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Deeply trained in rigorous proof construction across core mathematical areas
Experienced with Lean (Lean 3 or Lean 4), with Lean 4 strongly preferred — or with comparable systems such as Coq, Isabelle/HOL, or Agda
Genuinely passionate about formal verification, proof assistants, and mechanized mathematics
Able to take a dense, informal mathematical argument and render it in a form a machine can understand — without losing mathematical meaning
Self-directed and comfortable working asynchronously at a high level of precision
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 structured data quality workflows
Strong ability to communicate formalization decisions, edge cases, and reasoning strategies clearly in writing
The Ideal Candidate
You’re a mathematically mature problem‑solver who finds genuine satisfaction in taking an elegant human argument and expressing it in a form that a machine can verify. You appreciate structural precision, notice the gaps that automated tools miss, and are energized — not frustrated — by the places where formal verification is still an open problem. You work well independently, document your reasoning carefully, and enjoy contributing to something at the actual edge of what’s possible.
Why Join Us
Work directly on cutting‑edge AI research projects alongside world‑leading research labs
Fully remote and flexible — structure your hours around deep work, on your schedule
Freelance autonomy with access to some of the most intellectually challenging mathematical problems in AI today
Exposure to advanced LLMs and insight into how formal reasoning capabilities are built and evaluated
Potential for ongoing work and contract extension as new projects launch
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Worksite address
sheffield, TX, 79781, US
Who can apply
Review the original listing for work authorization, qualifications and employer requirements.