Researcher - Lean 4 & Formal Proof Systems

Turn mathematical arguments into verified Lean proofs

Translate advanced informal mathematics into structured Lean 4 formalizations. The work explores what proof assistants can express and verify, including points where automation needs careful mathematical intervention.

Formalization responsibilities

• Analyze general and domain specific arguments for gaps, hidden assumptions and smaller structures that can be formalized.
• Write readable, reproducible proof scripts that follow sound mathematics and proof assistant conventions.
• Develop formalizations that test the capabilities and limitations of existing tools.
• Explain failures caused by complexity, missing lemmas or gaps in available libraries.
• Work with researchers to refine formal verification strategies and guide proof decomposition, lemma choice and structure.
• Formalize classical results and compare their machine checked structure with textbook presentations.
• Identify deeper patterns or possible generalizations visible through the resulting Lean proofs.

Mathematical qualifications

A master's degree or higher in mathematics, logic, theoretical computer science or a closely related field is required. You need a strong foundation in rigorous proof writing across subjects such as algebra, analysis, topology, logic or discrete mathematics.

Hands on experience with Lean 3 or Lean 4, Coq, Isabelle/HOL, Agda or a comparable system is expected. Lean 4 is strongly preferred, and the ability to convert informal reasoning into clear formal proof is central to the role.

The work calls for sustained interest in mechanized mathematics and comfort resolving gaps that automated tools cannot handle independently.

Useful additional experience

• Type theory, the Curry Howard correspondence and proof automation.
• Contributions to substantial formalization efforts such as Mathlib.
• Theorem proving that requires significant manual scaffolding.
• Annotation, AI evaluation or training data quality work.
• Clear explanations of formalization choices, difficult cases and reasoning strategies.

Working arrangement

The role is a fully remote hourly contract, with flexible scheduling for ten to 40 hours weekly. Work is carried out with AI researchers, combining independent formalization with collaborative refinement of proof methods.

Further work or an extension may become available as new projects begin. No compensation amount is stated in the supplied description.