Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Seattle (WA); À distance; USD 83 000 - 165 000; Temps partiel

Résumé du poste

Alignerr seeks a Researcher to translate dense mathematical arguments into Lean 4 for AI training and formal verification research. This fully remote contract role emphasizes rigorous formalization of proofs across domains.

You will collaborate with AI researchers to test and push the limits of proof systems, produce readable proof scripts, and contribute to building and improving verification pipelines in a frontier area of mathematics and AI.

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Strong proof-writing and formalization abilities.
• Experience translating informal mathematics to Lean 4 or other proof systems.

Responsabilités

• Translate informal proofs into Lean 4 (and related proof systems) with clarity, structure, and correctness.
• Analyze proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
• Develop formalizations that test and extend the limits of proof assistants.
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with mathematical best practices.

Connaissances

Formal verification

Proof writing

Lean 4

Mathematics

Analytical thinking

Formation

Master's degree or higher (Mathematics/Logic/CS)

Outils

Lean 4

Coq

Isabelle/HOL

Agda

Description du poste

Researcher - Lean 4 & Formal Proof Systems (AI Training)

What if your deep mathematical training could directly shape how AI reasons about formal proofs - pushing the boundaries of what machines can understand and verify? We're looking for mathematicians and formal verification experts to translate sophisticated mathematical arguments into Lean 4, working at the intersection of pure mathematics and cutting-edge AI research.

About The Role

This is a fully remote, flexible contract role. If you find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify - this role was built for you.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10-40 hours/week

What You'll Do

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with a focus on clarity, structure, and correctness
• Analyze proofs across domains, identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend 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 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
• Investigate where automated provers break down and articulate precisely why - complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that reveal deeper patterns or 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 areas such as algebra, analysis, topology, logic, or discrete mathematics
• Bring hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable system - Lean 4 strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, well-structured formal proofs
• Mathematically mature and energized by working at the frontier of what formal systems can express

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience contributing to large-scale formalization projects such as Mathlib
• Exposure to theorem provers where automated reasoning frequently fails or requires substantial manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies clearly

Why Join Us

• Work on genuinely frontier problems - proofs that lie beyond the current capabilities of automated systems
• Fully remote and flexible - structure your work around your life, not the other way around
• Collaborate with teams working alongside the world's leading AI research labs
• Freelance autonomy with the depth and intellectual rigor of serious mathematical research
• Contribute to work that is actively shaping how AI understands and reasons about mathematics
• Potential for ongoing contract extension as new projects launch