Lean Engineer, Formal Mathematics (Lean 4, Mathlib, Theorem Proving)

The role in one line

A formal mathematician writes and reviews Lean 4 proofs to help AI models produce machine-verified mathematics with correct formal semantics.

Written by Training Turk from the public listing; it may be incomplete or out of date. Read the full posting on Mercor.

Skills this role asks for

What the interview is likely to probe

1. 1.Formalization fidelity assessment

   The core challenge is ensuring formal statements capture mathematical intent; evaluators must spot subtle mismatches between informal and formal versions that would mislead AI training

   Expect something like: “A textbook lemma states conditions that seem equivalent informally but differ under formal interpretation in Lean. How would you determine which formalization is appropriate, and when would you flag this ambiguity?”

2. 2.AI proof failure diagnosis

   AI-generated proofs may type-check but prove something different from intended; engineers need to understand why specific proofs fail conceptually, not just technically

   Expect something like: “The model produced a Lean proof that compiles without error but proves a generalization of what the original textbook result claimed. How would you categorize this as success, partial success, or failure?”

3. 3.Mathlib navigation mastery

   Correct Lean proofs require selecting the right existing lemmas; evaluators demonstrate whether they know the library deeply enough to write proofs efficiently

   Expect something like: “You're formalizing a polynomial identity that requires specific lemmas about field operations. Multiple paths through mathlib could work. How would you choose which lemma sequence to use, and when would you contribute a new lemma?”

4. 4.Multi-domain proof expertise

   The role spans algebra, analysis, and combinatorics; evaluators need sufficient breadth to recognize when an AI proof works in one domain but assumes unjustified structure from another

   Expect something like: “You're evaluating a proof about finite group properties that uses techniques valid for vector spaces. The proof type-checks but is flawed conceptually. What signals that structural confusion, and how would you explain it?”

5. 5.Standard establishment

   As proof standards evolve, engineers must articulate why one proof style is preferable over another; this shapes AI training and code consistency

   Expect something like: “You and a colleague disagree on whether a particular proof should use classic tactics or constructive techniques for a given lemma. How would you document this choice to help train models on consistent practices?”

Exercise you may get

Given 3-4 informal mathematical statements across different domains and corresponding AI-generated Lean proofs, identify which formal statements faithfully capture the originals, explain specific proof errors or successes, and suggest improvements.

How to prepare

• Review recent mathlib contributions and the decision-making behind different formalization approaches
• Study how AI benchmarks for formal mathematics (miniF2F, ProofNet, PutnamBench) define proof quality and fidelity
• Explore examples where informal and formal versions of a theorem diverge subtly to understand common pitfalls
• Practice explaining why specific mathlib lemmas or proof styles are preferred for clarity and maintainability

Facts

Pay

$90–110/hr

Commitment

part-time

Hours

20 per week

Work arrangement

remote · Remote

Domain

Life, Physical, and Social Science

Posted

9/30/2026

Open slots

38