Researcher - Lean 4 & Formal Proof Systems
Alignerr • Remote
Education
Any
Type
Pay Rate
$185/task
Listed
Today
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About this Role
What You'll Do
- Translate informal mathematical proofs into Lean 4 (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 entirely
- Collaborate with AI 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 expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- 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, and more
- Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
About the Role
What if your deep mathematical training could directly shape how the world's most advanced AI systems reason about proof? We're looking for mathematicians with serious formal verification chops to help us map the frontier of what machines can understand, verify, and learn from — working on proofs that push the limits of modern proof assistants like Lean 4. This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof and formal systems. If you find genuine satisfaction in translating a dense, elegant argument into something a machine can verify — and in resolving the gaps that automated tools cannot yet bridge — this role was designed for you.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: 10–40 hours/week
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 areas such as algebra, analysis, topology, logic, or discrete mathematics
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal proof system — Lean 4 strongly preferred
- Are genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Can translate informal mathematical arguments into clean, structured, machine-verifiable proofs
- Enjoy working at the frontier — where the tools haven't caught up yet and human judgment still matters
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience contributing to large-scale formalization projects such as Mathlib
- Exposure to theorem provers where automated reasoning frequently fails or requires extensive manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training data quality
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work directly with teams building cutting-edge AI at leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually demanding work
- Contribute to a research frontier that will define how AI reasons about mathematics for years to come
- Potential for ongoing work and contract extension as new projects launch
Requirements
- Fluent proficiency in English (Written & Verbal)
- Reliable high-speed internet connection
- Bachelor's degree or equivalent professional experience
- Demonstrated expertise in Mathematics
Compensation Analysis
What if your deep mathematical training could directly shape how the world's most advanced AI systems reason about proof? We're looking for mathematicians with serious formal verification chops to help us map the frontier of what machines can understand, verify, and learn from — working on proofs that push the limits of modern proof assistants like
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Frequently Asked Questions
What is the assessment actually like?
Notoriously strict. Alignerr uses TestGorilla for role-specific timed tests — a blank coding environment for engineers, rigorous grammar and fact-checking for writers. There is almost no hand-holding. The critical catch: this is essentially a one-shot process. Fail or abandon the assessment, and you are typically locked out of that role permanently with no option to retake.
How quickly can I start earning after I pass?
Not immediately. Even after passing the assessment and completing identity verification (via Persona) and billing setup (via Deel), you may sit in a waiting pool for weeks or months. You only start earning when a project matching your specific skills launches and you are officially assigned. Do not plan around Alignerr income until you are actively on a project.
Is there a community?
Yes — and it is one of Alignerr's genuine strengths. Once assigned to a project, you are added to Slack channels where you can ask questions, get rubric clarifications from admins, and talk to other AI trainers. This is rare in AI training and makes a real difference when guidelines are ambiguous or change mid-project.
Is this traditional consulting?
Not exactly. You act as a "Teacher" for advanced AI. Instead of client deliverables, you are given complex scenarios to evaluate. You grade the AI's logic, correct its hallucinations, and provide expert-level reasoning. Your job is to train the model to think like you do.
Why is the pay so high?
This role requires deep, verified expertise. General knowledge isn't enough; the model is specifically being trained on "edge cases"—the rare, difficult, or highly technical nuances that only a senior professional would know.
What is the workload like?
This is cognitive, deep work. Unlike simple data labeling, you might spend 45-60 minutes on a single task, researching citations or verifying complex calculations. Quality is prioritized over speed.
What is the barrier to entry?
Alignerr is known for difficult technical assessments. You must pass a timed test in your specific domain (e.g., Python, Physics, or Language) before you are eligible for any paid projects.