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Lean 4 Proof Engineer - Mathematical Formalization

June 6, 2026

Lean 4 Proof Engineer — Mathematical Formalization About The Role What if your deep mathematical training could directly shape how the world's most advanced AI systems reason about formal logic and proof? We're looking for Lean 4 Proof Engineers to translate complex, human-written mathematical arguments into precise, machine-verifiable formalizations — pushing the boundary of what modern proof assistants can express and automate. This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof construction and formal verification. <ul><li>Organization: Alignerr</li><li>Type: Hourly Contract</li><li>Location: Remote</li><li>Commitment: 10–40 hours/week </li></ul>What You'll Do <ul><li>Translate informal mathematical proofs into Lean 4 (and related systems) with an emphasis on clarity, structure, and correctness</li><li>Analyze domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures</li><li>Construct formalizations that stress-test the limits of existing proof assistants — especially where automation breaks down</li><li>Collaborate with AI researchers to design, refine, and evaluate formal verification strategies</li><li>Develop readable, reproducible proof scripts aligned with best mathematical practices and proof assistant idioms</li><li>Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models</li><li>Investigate where automated provers fail and articulate why — complexity, missing lemmas, insufficient libraries, and more</li><li>Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics </li></ul>Who You Are <ul><li>Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field</li><li>Have a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete math</li><li>Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred</li><li>Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics</li><li>Can translate dense informal arguments into clean, well-structured formal proofs with precision </li></ul>Nice to Have <ul><li>Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools</li><li>Experience contributing to large-scale formalization projects such as mathlib</li><li>Exposure to theorem provers where automated reasoning frequently fails or requires extensive manual scaffolding</li><li>Prior experience with data annotation, evaluation systems, or AI training workflows</li><li>Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators </li></ul>The Ideal Candidate You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify. You appreciate structural beauty and precision — and you're energized by the challenge of resolving gaps that automated tools can't yet bridge. You're comfortable working independently, asynchronously, and at the frontier of what formal verification can do. Why Join Us <ul><li>Work on cutting-edge AI projects alongside leading research labs</li><li>Fully remote and flexible — work when and where it suits you</li><li>Freelance autonomy with meaningful, intellectually demanding work</li><li>Gain rare exposure to how advanced AI systems are trained to reason formally</li><li>Contribute to work that is actively mapping the frontier of mechanized mathematics</li><li>Potential for ongoing work and contract extension as new projects launch</li></ul>

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Common Interview Questions And Answers

1. HOW DO YOU PLAN YOUR DAY?

This is what this question poses: When do you focus and start working seriously? What are the hours you work optimally? Are you a night owl? A morning bird? Remote teams can be made up of people working on different shifts and around the world, so you won't necessarily be stuck in the 9-5 schedule if it's not for you...

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When you're working on a remote team, there's no way to chat in the hallway between meetings or catch up on the latest project during an office carpool. Therefore, virtual communication will be absolutely essential to get your work done...

3. WHAT IS "WORKING REMOTE" REALLY FOR YOU?

Many people want to work remotely because of the flexibility it allows. You can work anywhere and at any time of the day...

4. WHAT DO YOU NEED IN YOUR PHYSICAL WORKSPACE TO SUCCEED IN YOUR WORK?

With this question, companies are looking to see what equipment they may need to provide you with and to verify how aware you are of what remote working could mean for you physically and logistically...

5. HOW DO YOU PROCESS INFORMATION?

Several years ago, I was working in a team to plan a big event. My supervisor made us all work as a team before the big day. One of our activities has been to find out how each of us processes information...

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Or you may receive even more specific questions, such as: What's on your calendar? Do you plan blocks of time to do certain types of work? Do you have an open calendar that everyone can see?...

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Just like your schedule, how you track files and other information is very important. After all, everything is digital!...

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The day I watched Marie Forleo's film separating the important from the urgent, my life changed. Not all remote jobs start fast, but most of them are...

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Just as communication is essential when working remotely, so is organization. Because you won't have those opportunities in the elevator or a casual conversation in the lunchroom, you should take advantage of the little time you have in a video or phone conference...

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This is a great question because it shows your comfort level with technology, which is very important for a remote worker because you will be working with technology over time...