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.
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

Work arrangement
Yes