Researcher - Lean 4 & Formal Proof Systems
Alignerr · Dallas, TX
- Hybrid
- Contract
- $60,000 / year
- Dallas, TX
Job highlights
- Translate mathematical proofs into Lean 4.
- Analyze proofs and identify gaps.
- Formalize proofs to test proof assistants.
- Collaborate on verification pipelines.
- Develop readable, reproducible proof scripts.
About the role
Researcher - Lean 4 & Formal Proof Systems (AI Training)
About The Role
What if your deepest mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — pushing the boundaries of what proof assistants can express, capture, and automate.
This is a fully remote, flexible contract role built for researchers who thrive on rigor, precision, and intellectual challenge. If you find satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify, this role was made for you.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness
- Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop 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
- Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond
- Create Lean proofs that reveal deeper patterns or 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
- Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete math
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal mathematical arguments into clean, structured formal proofs independently
- Naturally precise, patient, and driven by structural elegance and logical completeness
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 fails or requires 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 research labs and top AI teams
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually stimulating work
- Operate at the true frontier of formal verification and mechanized mathematics
- Contribute directly to how next-generation AI systems reason about mathematics and logic
- Potential for ongoing work and contract extension as new projects launch
Key skills/competency
- Formal Proof Systems
- Lean 4
- AI Training
- Mathematics
- Logic
- Theoretical Computer Science
- Formal Verification
- Proof Assistants
- Mechanized Mathematics
- Theorem Provers
Skills & topics
- Researcher
- Lean 4
- Formal Proof Systems
- AI Training
- Mathematics
- Logic
- Formal Verification
- Proof Assistants
- Theorem Provers
- Remote
- Contract
- Mathlib
- Coq
- Agda
- Isabelle/HOL
How to get hired
- Tailor your resume: Highlight experience with Lean 4, formal verification, and advanced mathematics degrees.
- Showcase formal proofs: Include links to your Lean 4 projects, GitHub, or publications demonstrating rigorous proof writing.
- Understand the tools: Research Lean 4, proof assistants, and their applications in AI training.
- Prepare for technical questions: Be ready to discuss your approach to translating informal math into formal proofs.
- Emphasize remote work skills: Demonstrate your ability to work independently and communicate effectively asynchronously.
Technical preparation
Master Lean 4 syntax and proof construction.,Practice translating informal proofs into formal ones.,Familiarize with proof assistant idioms and best practices.,Study formal verification challenges and automation limits.
Behavioral questions
Describe a complex proof you formalized.,How do you ensure logical completeness?,Discuss challenges in proof assistant automation.,How do you handle ambiguity in mathematical arguments?
Frequently asked questions
- What is Alignerr looking for in a Researcher for Lean 4 & Formal Proof Systems?
- Alignerr seeks individuals with a Master's degree or higher in Mathematics, Logic, or Theoretical Computer Science. Candidates should have strong proof writing skills and hands-on experience with Lean 4 or similar proof systems, and a passion for formal verification and its role in AI training.
- Is this role specific to Lean 4, or are other proof systems accepted for the Researcher position at Alignerr?
- While Lean 4 experience is strongly preferred, Alignerr also considers candidates with experience in Coq, Isabelle/HOL, Agda, or comparable systems. The ability to translate informal mathematical arguments into formal proofs is key, with a preference for Lean 4 expertise.
- What kind of mathematical backgrounds are most suitable for the Researcher - Formal Proof Systems role at Alignerr?
- The role is ideal for those with a strong foundation in rigorous proof writing across various mathematical domains such as algebra, analysis, topology, logic, or discrete mathematics. A Master's degree or higher in a related field is required.
- How does the AI Training aspect of the Researcher role at Alignerr work?
- The Researcher will translate complex mathematical arguments into machine-verifiable Lean 4 proofs. This work directly contributes to how AI systems understand and reason about formal proofs, essentially training AI in mathematical logic and verification.
- What are the benefits of working as a remote contractor for Alignerr as a Researcher?
- Alignerr offers a fully remote and flexible contract role, allowing you to work 10-40 hours per week from anywhere. You'll collaborate with leading research labs on cutting-edge AI projects at the forefront of formal verification.
- What is the expected commitment for the Researcher - Lean 4 & Formal Proof Systems position?
- The commitment for this hourly contract role is flexible, ranging from 10 to 40 hours per week, allowing you to balance it with other research or academic pursuits.
- How important is experience with large-scale formalization projects like Mathlib for this Alignerr role?
- Experience with large-scale formalization projects such as Mathlib is considered a 'Nice to Have' rather than a strict requirement. It demonstrates a capacity for handling complex formalization tasks, which is beneficial for the Researcher role.