Researcher - Lean 4 & Formal Proof Systems
Alignerr · Dallas, TX
- Hybrid
- Contract
- $50,000 / year
- Dallas, TX
Job highlights
- Translate math proofs into Lean 4 formalizations.
- Analyze and formalize complex mathematical arguments.
- Test limits of proof assistant technologies.
- Collaborate on AI verification pipelines.
- Remote, flexible contract for researchers.
About the role
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
- Lean 4
- Formal Proof Systems
- Mathematics
- Logic
- Theoretical Computer Science
- Formal Verification
- Proof Assistants
- Mechanized Mathematics
- AI Training
- Research
Skills & topics
- Researcher
- Lean 4
- Formal Proof Systems
- Mathematics
- Logic
- Theoretical Computer Science
- Formal Verification
- Proof Assistants
- AI Training
- Remote Contract
How to get hired
- Tailor your resume: Highlight your Master's or higher degree in Math, Logic, or CS, and specific experience with Lean 4, Coq, or Agda.
- Showcase formalization skills: Emphasize your ability to translate informal proofs into structured, machine-verifiable formal proofs.
- Demonstrate passion: Clearly express your enthusiasm for formal verification, proof assistants, and mechanized mathematics in your application.
- Prepare for technical questions: Be ready to discuss your experience with proof systems and how you'd approach formalizing complex arguments.
Technical preparation
Master Lean 4 syntax and proof tactics.,Practice translating informal math to Lean.,Familiarize with proof assistant idioms.,Study formalization of algebra or logic.
Behavioral questions
Describe a complex proof you formalized.,How do you ensure proof correctness?,Explain a proof assistant limitation.,How do you handle intellectual challenges?
Frequently asked questions
- What are the primary responsibilities for a Researcher - Lean 4 & Formal Proof Systems at Alignerr?
- As a Researcher at Alignerr, your primary responsibility will be translating informal mathematical proofs into Lean 4 formal proofs. This includes analyzing existing proofs, constructing new formalizations, and investigating the limitations of proof assistants, all contributing to AI training.
- What qualifications are essential for the Researcher - Lean 4 & Formal Proof Systems role at Alignerr?
- An essential qualification for this role is a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a related field, coupled with hands-on experience in Lean 4, Coq, or similar proof systems. A strong foundation in rigorous proof writing is also critical.
- Is the Researcher - Lean 4 & Formal Proof Systems position at Alignerr remote?
- Yes, the Researcher - Lean 4 & Formal Proof Systems position at Alignerr is a fully remote role, offering flexibility in where and when you work, as long as you can commit 10–40 hours per week.
- What is the preferred proof system for the Researcher - Lean 4 & Formal Proof Systems job at Alignerr?
- While experience with systems like Coq, Isabelle/HOL, and Agda is valuable, hands-on experience with Lean 4 is strongly preferred for the Researcher - Lean 4 & Formal Proof Systems role at Alignerr.
- How does Alignerr utilize formal proofs in AI training with this Researcher role?
- Alignerr utilizes formal proofs by having Researchers translate complex mathematical arguments into machine-verifiable Lean 4 proofs. This work directly trains AI systems to understand and reason about formal mathematical logic.
- What kind of mathematical backgrounds are suitable for the Researcher - Lean 4 & Formal Proof Systems position?
- The Researcher position at Alignerr is ideal for individuals with strong backgrounds in areas like algebra, analysis, topology, logic, or discrete mathematics, who can apply rigorous proof writing skills to formal systems.
- Can I apply for the Researcher - Lean 4 & Formal Proof Systems role if I have Lean 3 experience but not Lean 4?
- While Lean 4 experience is strongly preferred, significant experience with Lean 3 and a demonstrated ability to learn and adapt to new proof systems like Lean 4 would be considered. Your application should highlight your foundational skills and enthusiasm for Lean 4.