**Role & seniority: ** Formal Verification Scientist (contract), Senior/advanced individual contributor (requires independent proof formalization)

**Stack/tools: ** Lean 4 (preferred; Lean 3 acceptable), proof assistants such as Coq / Isabelle/HOL / Agda; possible familiarity with Mathlib; proof automation tooling (unspecified)

**Top 3 responsibilities: **

Translate informal mathematical arguments into machine-verifiable Lean 4 proofs (clear, correct, reproducible scripts)
Analyze existing proofs to find hidden assumptions, gaps, and formalizable components, then refactor into lemmas/structures
Investigate and document why automation fails (missing lemmas/libraries/complexity barriers) and collaborate on improving verification pipelines
Must-have skills:
- Master’s+ in Mathematics/Logic/TCS or related field
- Strong rigorous proof-writing background across areas (e.g., algebra, analysis, topology, logic, discrete math)
- Ability to independently formalize proofs with Lean idioms and maintain correctness/clarity
- Comfortable with asynchronous work and managing time in a flexible contract setting
Nice-to-haves:
- Type theory / Curry–Howard / proof automation experience
- Contributions to large-scale formalizations (e.g., Mathlib)
- Experience with theorem proving workflows where automation often fails
- Prior data annotation/evaluation exposure for AI (data quality/AI evaluation pipeline

Full Description

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for Formal Verification Scientists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — helping push the boundaries of what automated reasoning can express, capture, and learn from.

This is a fully remote, flexible contract role built for mathematicians who live and breathe rigorous proof construction. If you find satisfaction in taking a dense, elegant argument and expressing it with machine-level precision, this role was made for you.

Organization: Alignerr

Type: Hourly Contract

Location: Remote

Commitment: 10–40 hours/week

What You'll Do

Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures Construct formalizations that test the limits of existing proof assistants, especially where automation breaks down Investigate why automated provers struggle — complexity barriers, missing lemmas, insufficient libraries — and document those findings clearly Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines Develop highly readable proof scripts aligned with mathematical best practices and Lean idioms Create proofs that reveal deeper patterns or generalizations implicit in the original mathematics Provide expert guidance on proof decomposition, lemma selection, and structuring techniques

Who You Are

Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field Deeply grounded in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics Experienced with Lean (Lean 3 or Lean 4), with Lean 4 strongly preferred — or comparable systems such as Coq, Isabelle/HOL, or Agda Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to translate informal mathematical arguments into precise, well-structured formal proofs independently Comfortable working asynchronously and managing your own time across flexible hours

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 manual scaffolding Prior experience with data annotation, data quality, or AI evaluation workflows Strong written communication skills for explaining formalization decisions, edge cases, and proof strategies

Why Join Us

Work on some of the most intellectually demanding problems in AI research alongside world-leading labs Fully remote and flexible — structure your work around your life, not the other way around Freelance autonomy with the substance of genuinely meaningful, high-impact work Contribute directly to advancing the frontier of formal verification and AI mathematical reasoning Potential for ongoing work and contract extension as new projects launch

Formal Verification Scientist (Lean 4 & Mathlib)

Full Description