Remote Lean 4 Formal Proof Researcher

Alignerr Corp.; Sheffield (TX); Remote; USD 96,000 - 152,000; Part time

Job summary

Aligner r Corp. is seeking a researcher to translate informal mathematical proofs into Lean 4 formalizations for AI training. You will analyze proofs across algebra, analysis, topology, logic, and discrete math, identifying gaps and formalizable sub-structures.

The role emphasizes precision, readability, and reproducibility of Lean scripts. The position is fully remote, flexible, and hourly, with 10–40 hours per week.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing across core mathematical areas.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems (Lean 4 strongly preferred).
• Deep enthusiasm for formal verification, proof assistants, and mechanized mathematics.

Responsibilities

• Translate informal, human-written proofs into precise, machine-verifiable Lean 4 formalizations.
• Analyse proofs across domains—algebra, analysis, topology, logic, discrete mathematics—identifying hidden assumptions and gaps.
• Construct formalizations to test limits of proof assistants where automation breaks down.
• Develop readable, reproducible Lean proof scripts aligned with best practices and Lean idioms.
• Collaborate with AI researchers to design and evaluate formal verification pipelines.
• Provide guidance on proof decomposition, lemma selection, and structuring strategies for formal models.
• Investigate failure modes of automated provers and how to work around them.
• Create Lean proofs that surface deeper patterns and generalizations in the original mathematics.

Skills

Rigorous proof writing

Formal reasoning

Strong communication

Education

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

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Mathlib

Job description

Aligner r Corp. is seeking a researcher to translate informal mathematical proofs into Lean 4 formalizations for AI training. You will analyze proofs across algebra, analysis, topology, logic, and discrete math, identifying gaps and formalizable sub-structures.

The role emphasizes precision, readability, and reproducibility of Lean scripts. The position is fully remote, flexible, and hourly, with 10–40 hours per week.