Older listing: position may have been filled
This listing is no longer actively promoted, but you're still welcome to apply. Platforms often reopen roles or keep applications on file.
Researcher - Lean 4 & Formal Proof Systems
Alignerr • USA
Education
Not stated
Type
Hourly
Pay Rate
$170–$200/hr
Listed
Today
Apply opens Alignerr in a new tab.
Check Listing → ⚡ Boost your chances - Optimize your resume with Rezi.aiAbout this role
From the Alignerr listing
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
Why this 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
Skills and categories
Explore other opportunities in related specializations:
Related jobs
Browse All Jobs from Alignerr
Discover more opportunities on Alignerr that match your skills and interests.
View All Alignerr Jobs →Verified Reviews
Community Reviews
Share your experience with Alignerr
Help other candidates make better decisions by leaving a review.
Sign in to leave a reviewLeave your review
Common questions
How hard is the Alignerr assessment?
Hard, and unforgiving. Alignerr uses TestGorilla for timed, role-specific tests: a blank coding environment for engineers, strict grammar and fact-checking for writers. Treat it as one shot. Failing or abandoning it typically locks you out of that role permanently, with no retake.
How soon can I start earning on Alignerr after passing the assessment?
Not right away. After passing, you still complete identity verification through Persona and billing setup through Deel, then wait in a pool for weeks or months. You only start earning once a project matching your specific skills launches and assigns you. Don't count on Alignerr income until you're actively placed on a project.
Why do these AI training roles pay so much?
Because general knowledge isn't what's being tested. The model already knows the basics; what it needs is expertise on edge cases, the rare, difficult, highly technical judgment calls only a senior professional in the field would make correctly.
What does the day-to-day workload look like for elite-expert AI training roles?
Slow and deep, not fast and repetitive. A single task can take 45-60 minutes of researching citations or verifying complex calculations. Quality is what's being measured here, not throughput.
What does Mathematics work look like for a Researcher - Lean 4 & Formal Proof Systems?
Tasks here are scoped to Mathematics, not generic labeling. As a Researcher - Lean 4 & Formal Proof Systems, expect to draw on real domain judgment (evaluating outputs, correcting errors, or providing expert reasoning specific to Mathematics) rather than following a one-size-fits-all rubric. If you don't have hands-on Mathematics background, this is likely not the right listing to start with.
What specific skills does this listing call for?
Data Annotation and Entry Level are named directly in the listing. If you don't have hands-on experience with these, expect the screening process to test for them directly rather than accepting adjacent experience as a substitute.
How much does this specific role pay?
This listing is posted at $170–$200/hr, an hourly rate. The range reflects experience level and negotiated terms, not a placeholder, so where you land in it depends on your background and the assessment. Pay can change between when we last checked the listing and when you apply, so confirm the current number on the platform's own application page before committing time.
What happens when I click Apply on this listing?
You'll be taken to Alignerr's external site to complete your application there. This listing links through a referral, but the process is identical to applying directly; the link just routes you correctly. Create an account on their site and follow their onboarding steps.
Can I apply from outside the United States?
This specific role is open only to people based in the United States. If you are somewhere else, applying is unlikely to lead to an offer even if you pass the assessment, because the restriction is usually about where the work can legally be contracted rather than your skills. Read the full description for any tax-residency or right-to-work caveats before you apply.
What is the barrier to entry for Alignerr?
A difficult, timed technical assessment in your specific domain, like Python, physics, or language. Passing it is required before you're eligible for any paid projects.