Applied Formal Methods Researcher; Lean

Position: Applied Formal Methods Researcher (Lean 4)
About

The Role
What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for mathematicians and formal methods experts to work at the cutting edge of AI research — translating rigorous mathematical arguments into machine-verifiable Lean 4 formalizations, and helping map the frontier of what automated reasoning can actually do.

About

The Role
What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for mathematicians and formal methods experts to work at the cutting edge of AI research — translating rigorous mathematical arguments into machine-verifiable Lean 4 formalizations, and helping map the frontier of what automated reasoning can actually do.

This is a fully remote, flexible contract role designed for mathematicians who find beauty in precision and satisfaction in making a machine understand what a human mind can see.

Organization:
Alignerr

Type:
Hourly Contract

Location:

Remote

Commitment: 10–40 hours/week

What You'll Do

Translate informal mathematical proofs into clean, correct, and readable Lean 4 formalizations

Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures

Construct formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down

Investigate and articulate why automated provers fail — whether due to complexity, missing lemmas, or library gaps

Collaborate with researchers to design and evaluate strategies for improving formal verification pipelines

Develop reproducible proof scripts aligned with mathematical best practices and proof assistant idioms

Provide expert guidance on proof decomposition, lemma selection, and formal modelling strategies

Formalize classical results and compare machine-verifiable structures against textbook arguments

Uncover deeper patterns or generalizations implicit in the original mathematics

Who You Are

Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Has a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics

Has hands‑on experience with Lean (Lean 3 or Lean
4), with Lean 4 strongly preferred

Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics

Able to take a dense, informal argument and express it in a form that a machine can verify — cleanly and correctly

Mathematically mature, precision‑driven, and genuinely excited by hard problems

Nice to Have

Experience with Coq, Isabelle/HOL, Agda, or comparable proof systems

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 workflows

Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

Work on cutting-edge AI projects alongside leading AI research labs

Fully remote and flexible — work when and where it suits you

Freelance autonomy with the structure of meaningful, intellectually rigorous work

Contribute directly to how AI systems learn to reason about advanced mathematics

Potential for ongoing work and contract extension as new projects launch

Be part of a global collaboration at the intersection of mathematics, formal methods, and artificial intelligence