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Researcher - Lean 4 & Formal Proof Systems

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<strong>Researcher — Lean 4 & Formal Proof Systems (AI Training)<br><br></strong><strong>About The Role<br><br></strong>What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification experts to translate sophisticated proofs into Lean 4 — working at the exact boundary where human mathematical intuition meets machine-verifiable logic.<br><br>This is a rare opportunity to contribute to cutting-edge AI research by helping build training data that pushes proof assistants beyond their current limits. If you find satisfaction in taking a dense, elegant argument and expressing it with machine-level precision, this role was made for you.<br><br><ul><li>Organization: Alignerr</li><li>Type: Hourly Contract</li><li>Location: Remote</li><li>Commitment: 10–40 hours/week (flexible)<br><br></li></ul><strong>What You'll Do<br><br></strong><ul><li>Translate informal mathematical proofs into rigorous, machine-verifiable Lean 4 formalizations</li><li>Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures</li><li>Construct formalizations that probe the limits of existing proof assistants, especially where automation fails</li><li>Collaborate with AI researchers to design and refine formal verification strategies</li><li>Develop clean, readable, reproducible proof scripts aligned with mathematical best practices</li><li>Provide expert guidance on proof decomposition, lemma selection, and structuring techniques</li><li>Investigate and articulate where automated provers break down — and why</li><li>Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics<br><br></li></ul><strong>Who You Are<br><br></strong><ul><li>Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field</li><li>Possess a strong foundation in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics</li><li>Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistants — Lean strongly preferred</li><li>Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics</li><li>Able to translate informal mathematical arguments into clean, structured formal proofs independently<br><br></li></ul><strong>Nice to Have<br><br></strong><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 in contexts where automated reasoning fails or requires extensive manual scaffolding</li><li>Prior experience with data annotation, data quality evaluation, or AI training pipelines</li><li>Strong communication skills for articulating formalization decisions, edge cases, and proof strategies<br><br></li></ul><strong>Why Join Us<br><br></strong><ul><li>Work at the frontier of formal verification and AI research — problems here are genuinely unsolved</li><li>Fully remote and flexible — structure your hours around your life</li><li>Freelance autonomy with the substance of impactful, intellectually demanding work</li><li>Collaborate with researchers at leading AI labs on projects that matter</li><li>Contribute directly to advancing what AI systems can reason about and verify</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...

2. HOW DO YOU USE THE DIFFERENT COMMUNICATION TOOLS IN DIFFERENT SITUATIONS?

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...

6. HOW DO YOU MANAGE THE CALENDAR AND THE PROGRAM? WHICH APPLICATIONS / SYSTEM DO YOU USE?

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?...

7. HOW DO YOU ORGANIZE FILES, LINKS, AND TABS ON YOUR COMPUTER?

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

8. HOW TO PRIORITIZE WORK?

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...

9. HOW DO YOU PREPARE FOR A MEETING AND PREPARE A MEETING? WHAT DO YOU SEE HAPPENING DURING THE MEETING?

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...

10. HOW DO YOU USE TECHNOLOGY ON A DAILY BASIS, IN YOUR WORK AND FOR YOUR PLEASURE?

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...