Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Cambridge; Remote; GBP 96,000 - 165,000; Part time

Job summary

Alignerr is seeking a Researcher to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs for AI training. You will work remotely on rigorous formalizations, stretching proof assistants and identifying gaps, with a focus on clarity and correctness.

You will collaborate with researchers, construct reproducible proof scripts, and contribute to formal verification strategies for complex models. This is a flexible hourly contract with 10–40 hours per week.

Qualifications

• Master's degree or higher required or equivalent
• Strong proof-writing skills across algebra, analysis, topology, logic
• Experience with Lean, Coq, Isabelle/HOL or Agda
• Ability to translate informal arguments into machine-verifiable proofs
• Self-directed and able to work independently on open-ended problems
• Excellent written communication for documenting formalization decisions

Responsibilities

• Translate informal proofs into Lean 4 formalizations with clarity and correctness
• Analyze proofs to identify gaps and formalizable sub-structures
• Develop readable, reproducible proof scripts and idioms
• Collaborate to design verification strategies and pipelines
• Guide proof decomposition, lemma selection and structuring approaches
• Formalize classical results and compare to textbook arguments
• Surface patterns and generalizations in the mathematics

Skills

Rigorous proof writing

Independent work

Strong written communication

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or closely related field

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Mathlib familiarity

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 through the hardest proofs in existence? We're looking for mathematicians and formal verification experts to translate sophisticated human-written arguments into machine-verifiable Lean 4 proofs — working at the very edge of what modern proof assistants can do.

This is a fully remote, flexible contract role built for researchers who love rigor, structure, and the intellectual challenge of pushing formal systems to their limits.

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

What You'll Do

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related systems), with a focus on clarity, structure, and correctness
• Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that stress-test proof assistants, especially in areas where automation breaks down or fails entirely
• Investigate why automated provers struggle — missing lemmas, library gaps, complexity limits — and document your findings clearly
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Collaborate with researchers to design and refine formal verification strategies and pipelines
• Provide expert guidance on proof decomposition, lemma selection, and structuring approaches for complex formal models
• Formalize classical results and compare machine-verifiable structures against standard textbook arguments
• Surface deeper patterns and generalizations embedded 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
• Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal proof system — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured, and correct formal proofs
• Self-directed and comfortable working independently on challenging, open-ended problems

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
• Experience contributing to or working within large-scale formalization projects (e.g., Mathlib)
• Exposure to theorem provers in regimes where automated reasoning frequently fails or requires manual scaffolding
• Prior experience with data annotation, data quality, or AI evaluation workflows
• Strong written communication skills for documenting formalization decisions, edge cases, and proof strategies

Why Join Us

• Work on some of the most intellectually demanding problems at the intersection of mathematics and AI
• Fully remote and flexible — structure your work around your life, not the other way around
• Freelance autonomy with access to genuinely cutting-edge AI research projects
• Collaborate with a global team advancing the frontier of formal verification and AI reasoning
• Meaningful, high-signal work — every proof you write contributes directly to how AI models learn to reason
• Potential for ongoing work and contract extension as new projects launch