Applied Formal Methods Researcher (Lean 4)

Job summary

Translate informal mathematical arguments into clear, correct, reproducible Lean 4 formalizations, and analyze proofs for assumptions, gaps, and formalizable structures. Investigate the limits and failure modes of automated provers, and collaborate with researchers to improve formal verification strategies and pipelines.

Job details

About The Role What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for mathematicians and formal methods experts to work at the cutting edge of AI research — translating rigorous mathematical arguments into machine-verifiable Lean 4 formalizations, and helping map the frontier of what automated reasoning can actually do. This is a fully remote, flexible contract role designed for mathematicians who find beauty in precision and satisfaction in making a machine understand what a human mind can see. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into clean, correct, and readable Lean 4 formalizations Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures Construct formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down Investigate and articulate why automated provers fail — whether due to complexity, missing lemmas, or library gaps Collaborate with researchers to design and evaluate strategies for improving formal verification pipelines Develop reproducible proof scripts aligned with mathematical best practices and proof assistant idioms Provide expert guidance on proof decomposition, lemma selection, and formal modelling strategies Formalize classical results and compare machine-verifiable structures against textbook arguments Uncover deeper patterns or generalizations implicit in the original mathematics Who You Are Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field Has a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics Has hands-on experience with Lean (Lean 3 or Lean 4), with Lean 4 strongly preferred Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to take a dense, informal argument and express it in a form that a machine can verify — cleanly and correctly Mathematically mature, precision-driven, and genuinely excited by hard problems Nice to Have Experience with Coq, Isabelle/HOL, Agda, or comparable proof systems 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 extensive manual scaffolding Prior experience with data annotation, evaluation systems, or AI training workflows Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us Work on cutting-edge AI projects alongside leading AI research labs Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, intellectually rigorous work Contribute directly to how AI systems learn to reason about advanced mathematics Potential for ongoing work and contract extension as new projects launch Be part of a global collaboration at the intersection of mathematics, formal methods, and artificial intelligence

What you’ll do

Translate informal mathematical arguments into clear, correct, reproducible Lean 4 formalizations, and analyze proofs for assumptions, gaps, and formalizable structures. Investigate the limits and failure modes of automated provers, and collaborate with researchers to improve formal verification strategies and pipelines.

Requirements

Requires a master's degree or higher in mathematics, logic, theoretical computer science, or a related field, along with rigorous proof-writing ability and hands-on experience with Lean, preferably Lean 4. Candidates should be mathematically mature, precise, and enthusiastic about formal verification; experience with other proof systems or large-scale formalization projects is an advantage.

Benefits

• Fully Remote And Flexible Work
• Freelance Autonomy
• Work On Cutting-Edge AI Projects
• Potential For Ongoing Work And Contract Extension

Listed skills

• Lean · Preferred
• Flexible · Preferred
• enthusiastic · Preferred
• precision · Preferred
• Training · Preferred
• analysis · Preferred
• Collaboration · Preferred
• Communication · Preferred
• Communication Skills · Preferred
• future · Preferred
• Organization · Preferred
• Strong Communication · Preferred

Other relevant skills

Identified from the job description. Confirm important requirements above.

• Lean 4
• Formal Proof Writing
• Mathematical Proof Formalization
• Formal Verification
• Proof Assistants
• Mathematical Reasoning
• Proof Decomposition
• Lemma Selection
• Formal Modeling
• Proof Automation
• Type Theory
• Curry-Howard Correspondence
• Mathlib
• Coq
• Isabelle/HOL
• Agda

Job areas

• Science & Research
• Technology
• Software
• Education

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