Researcher - Lean 4 & Formal Proof Systems
Alignerr, Sheffield, England, United Kingdom
3 days ago – Be among the first 25 applicants
This range is provided by Alignerr. Your actual pay will be based on your skills and experience – talk with your recruiter to learn more.
Base pay range
$70.00/hr - $150.00/hr
* Location: Remote
At Alignerr, we partner with the world’s leading AI research teams and labs to build and train cutting‑edge AI models.
Write and formalize advanced mathematical proofs in Lean for cutting‑edge AI research. Ideal for mathematicians passionate about formal verification and pushing the limits of modern proof assistants.
Organization: Alignerr
Position: Researcher - Lean 4 & Formal Proof Systems
Type: Hourly Contract
Compensation: $70–$150 /hour
Location: Remote
Commitment: 10–40 hours/week
Role Overview: We are seeking mathematicians with deep training in rigorous proof construction and hands‑on experience with formal proof languages, especially Lean. This role sits at the intersection of mathematics and computer science, focusing on translating human‑written mathematical arguments into precise, machine‑verifiable formalizations.
What You’ll Do:
* Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness.
* Analyze generic and domain‑specific proofs, identifying gaps, hidden assumptions, and formalizable sub‑structures.
* Construct formalizations that test the limits of existing proof assistants, especially where 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.
* Formalize classical proofs and investigate where automated provers break down, articulating reasons like complexity or missing lemmas.
* Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.
Requirements:
* Master’s degree (or higher) in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
* Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math.
* Hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems, with Lean strongly preferred.
* Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.
* Ability to translate informal arguments into clean, structured formal proofs.
Preferred:
* Prior experience with data annotation, data quality, or evaluation systems.
* Familiarity with type theory, Curry–Howard correspondence, and proof automation tools.
* Experience with large‑scale formalization projects (e.g., mathlib).
* Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding.
* Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies.
Why Join Us:
* Competitive pay and flexible remote work.
* Collaborate with a team working on cutting‑edge AI projects.
* Exposure to advanced LLMs and how they’re trained.
* Freelance perks: autonomy, flexibility, and global collaboration.
* Potential for contract extension.
Application Process (takes 15‑20 minutes):
* Submit your resume.
* Complete a short screening.
* Project matching and onboarding.
PS: Our team reviews applications daily. Please complete your AI interview and application steps to be considered for this opportunity.
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