About this opportunity
Alignerr Corp. lists this Researcher - Lean 4 & Formal Proof Systems opportunity in sheffield, Alabama. Review the employer’s description below for duties, qualifications and application requirements.
Job description
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 proof? We're looking for mathematicians and formal verification researchers to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — working at the very frontier of what automated reasoning can express and automate.
This is a fully remote, flexible contract role designed for researchers who love rigour, structural elegance, and the challenge of pushing proof assistants to their limits.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal, human-written mathematical proofs into precise, machine-verifiable Lean 4 formalizations
Analyse proofs across domains — algebra, analysis, topology, logic, discrete mathematics — identifying hidden assumptions, gaps, and formalizable sub-structures
Construct formalizations that test and expose the limits of existing proof assistants, especially where automation breaks down
Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices and Lean idioms
Collaborate with AI researchers to design, refine, and evaluate formal verification pipelines
Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
Investigate failure modes of automated provers — articulating why they struggle (complexity, missing lemmas, library gaps) and how to work around them
Create Lean proofs that surface deeper patterns and 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
Have a strong foundation in rigorous proof writing across core mathematical areas
Have hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable system — Lean 4 strongly preferred
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, informal arguments into clean, structured formal proofs with precision and clarity
Find genuine satisfaction in resolving gaps that automated tools cannot yet bridge
Nice to Have
Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
Experience with large-scale formalization projects such as Mathlib
Exposure to theorem provers where automated reasoning frequently requires manual scaffolding
Prior experience with data annotation, evaluation systems, or AI training workflows
Strong communication skills for explaining formalization decisions, edge cases, and proof strategies
Why Join Us
Work on cutting‑edge AI research projects alongside leading labs and research teams
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually stimulating work
Contribute directly to advancing the capabilities of AI in formal reasoning and mathematics
Potential for ongoing work and contract extension as new projects launch
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Who can apply
Review the original listing for work authorization, qualifications and employer requirements.