Researcher - Lean 4 & Formal Proof Systems

Alignerr; Sheffield (TX); Remote; USD 55,000 - 96,000; Part time

Benefits offered by this job

Fully remote

Flexible hours

Contract extension potential

Job summary

Alignerr is seeking a Researcher to translate informal mathematical proofs into machine-verifiable Lean 4 formalizations for AI training. You will analyze proofs across multiple domains and collaborate with AI researchers to build robust verification pipelines.

We value deep mathematical training, proficiency with Lean 3/4 or other proof assistants, and the ability to craft clean, reproducible proof scripts. This is a fully remote, hourly contract with flexible hours.

Qualifications

• Master's degree or higher in a relevant field.
• Strong proof-writing and mathematical reasoning.
• Experience with Lean or other proof assistants.
• Ability to translate informal arguments into formal proofs.

Responsibilities

• Translate informal mathematical proofs into precise Lean 4 formalizations.
• Analyze proofs across algebra, analysis, topology, logic, and discrete math.
• Construct formalizations to test limits of proof assistants where automation breaks down.
• Develop clean, readable, and reproducible Lean scripts.
• Collaborate with AI researchers to design formal verification pipelines.
• Provide guidance on proof decomposition and lemma selection.
• Investigate failure modes of automated provers and workarounds.
• Create Lean proofs that reveal deeper patterns in the original math.

Skills

Proof writing

Formal verification

Mathematical reasoning

Communication

Education

Master's degree or higher in Mathematics, Logic, or Theoretical CS

Tools

Lean 3/4

Coq

Isabelle/HOL

Agda

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 about formal proof? We're looking for mathematicians and formal verification researchers to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs - working at the very frontier of what automated reasoning can express and automate.

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

What You'll Do

• Translate informal, human-written mathematical proofs into precise, machine-verifiable Lean 4 formalizations
• Analyse proofs across domains - algebra, analysis, topology, logic, discrete mathematics - identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that test and expose the limits of existing proof assistants, especially where automation breaks down
• Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Collaborate with AI researchers to design, refine, and evaluate formal verification pipelines
• Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
• Investigate failure modes of automated provers - articulating why they struggle (complexity, missing lemmas, library gaps) and how to work around them
• Create Lean proofs that surface deeper patterns and 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 core mathematical areas
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable system - Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal arguments into clean, structured formal proofs with precision and clarity
• Find genuine satisfaction in resolving gaps that automated tools cannot yet bridge

Nice to Have

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

Why Join Us

• Work on cutting-edge AI research projects alongside leading labs and research teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute directly to advancing the capabilities of AI in formal reasoning and mathematics
• Potential for ongoing work and contract extension as new projects launch