Applied Formal Methods Researcher (Lean 4)

Miami

* Location: Remote About the job At Alignerr, we partner with the world's leading AI research teams and labs to build and train cutting-edge AI models. Write and formalize advanced mathematical proofs in Lean for cutting-edge AI research. Ideal for mathematicians passionate about formal verification and pushing the limits of modern proof assistants. **Organization** : Alignerr **Position** : Applied Formal Methods Researcher (Lean 4) **Type** : Hourly Contract **Compensation** : $70--$150 /hour **Location** : Remote **Commitment** : 10--40 hours/week **Role Overview** - We are seeking mathematicians with deep training in rigorous proof construction and hands-on experience with formal proof languages, especially Lean. This role sits at the intersection of mathematics and computer science, focusing on translating human-written mathematical arguments into precise, machine-verifiable formalizations.- You will work on proofs that often lie beyond the current capabilities of automated provers, helping us map the frontier of what formal verification can express, capture, and automate. **What You'll Do:** - Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness.- Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures.- Construct formalizations that test 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 highly 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.- Sample Work You Might Do: - Formalize classical proofs and compare machine-verifiable structures against textbook arguments.- Investigate where automated provers break down, and articulate why (complexity, missing lemmas, insufficient libraries, etc.).- Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics. **Requirements:** - Master's degree (or higher) in Mathematics, Logic, Theoretical Computer Science, or a closely related field.- Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math.- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems, with Lean strongly preferred.- Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.- Ability to translate informal arguments into clean, structured formal proofs. **Preferred** * Prior experience with data annotation, data quality, or evaluation systems- Familiarity with type theory, Curry-Howard correspondence, and proof automation tools.- Experience with large-scale formalization projects (e.g., mathlib).- Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding.- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies. Ideal Candidate - A mathematically mature problem-solver who enjoys working at the frontier of formal verification; someone who finds satisfaction in taking a dense, elegant human argument and expressing it in a form that a machine can understand. You appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge. Why Join Us: - Competitive pay and flexible remote work.- Collaborate with a team working on cutting-edge AI projects.- Exposure to advanced LLMs and how they're trained.- Freelance perks: autonomy, flexibility, and global collaboration.- Potential for contract extension. Application Process (Takes 15-20 min) - Submit your resume- Complete a short screening- Project matching and onboarding PS: Our team reviews applications daily. Please complete your AI interview and application steps to be considered for this opportunity.