Applied Formal Methods Researcher (Lean 4)
Alignerr, Boston, MA, United States
About The Role
What if your deep mathematical intuition could directly shape how AI reasons, proves, and understands the world's hardest problems? We're looking for Applied Formal Methods Researchers to translate rigorous human mathematics into machine-verifiable Lean 4 proofs — working at the precise boundary where human mathematical genius meets the limits of automated reasoning.
This is a fully remote, flexible contract role designed for mathematicians who are passionate about formal verification and hungry to push proof assistants further than they've ever gone.
Organization:
Alignerr
Type:
Hourly Contract
Location:
Remote
Commitment:
10–40 hours/week
What You'll Do
Translate informal mathematical proofs into clean, structured, machine-verifiable formalizations in Lean 4
Identify gaps, hidden assumptions, and formalizable sub-structures within complex mathematical arguments
Construct Lean proofs that probe and expose the current limits of automated proof assistants
Collaborate with researchers to design and refine formal verification strategies and pipelines
Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
Advise on proof decomposition, lemma selection, and structuring techniques for formal models
Investigate where and why automated provers break down — and document those findings rigorously
Formalize classical results and compare machine-verifiable structures against established textbook arguments
Who You Are
Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
Have hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
Genuinely enthusiastic about formal verification, proof assistants, and the trajectory of mechanized mathematics
Able to translate dense, informal arguments into clean, precise formal proofs with minimal ambiguity
Nice to Have
Familiarity with type theory, the Curry‑Howard correspondence, and proof automation tooling
Experience contributing to large‑scale formalization projects such as Mathlib
Exposure to theorem provers where automated reasoning frequently fails or requires significant manual scaffolding
Prior involvement in data annotation, evaluation, or quality assessment workflowsStrong communication skills for articulating formalization decisions, edge cases, and proof strategies
The Ideal Candidate
You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can fully verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving the gaps that automated tools cannot yet bridge. You're drawn to frontiers — and this is one of the most exciting in modern mathematics.
Why Join Us
Work directly on cutting‑edge AI research projects alongside world‑leading labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, high‑impact technical work
Gain exposure to how advanced AI models are trained on formal mathematical reasoning
Contribute to work that is actively advancing the frontier of mechanized mathematics
Potential for ongoing engagement and contract extension as new projects launch
#J-18808-Ljbffr
What if your deep mathematical intuition could directly shape how AI reasons, proves, and understands the world's hardest problems? We're looking for Applied Formal Methods Researchers to translate rigorous human mathematics into machine-verifiable Lean 4 proofs — working at the precise boundary where human mathematical genius meets the limits of automated reasoning.
This is a fully remote, flexible contract role designed for mathematicians who are passionate about formal verification and hungry to push proof assistants further than they've ever gone.
Organization:
Alignerr
Type:
Hourly Contract
Location:
Remote
Commitment:
10–40 hours/week
What You'll Do
Translate informal mathematical proofs into clean, structured, machine-verifiable formalizations in Lean 4
Identify gaps, hidden assumptions, and formalizable sub-structures within complex mathematical arguments
Construct Lean proofs that probe and expose the current limits of automated proof assistants
Collaborate with researchers to design and refine formal verification strategies and pipelines
Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
Advise on proof decomposition, lemma selection, and structuring techniques for formal models
Investigate where and why automated provers break down — and document those findings rigorously
Formalize classical results and compare machine-verifiable structures against established textbook arguments
Who You Are
Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
Have hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
Genuinely enthusiastic about formal verification, proof assistants, and the trajectory of mechanized mathematics
Able to translate dense, informal arguments into clean, precise formal proofs with minimal ambiguity
Nice to Have
Familiarity with type theory, the Curry‑Howard correspondence, and proof automation tooling
Experience contributing to large‑scale formalization projects such as Mathlib
Exposure to theorem provers where automated reasoning frequently fails or requires significant manual scaffolding
Prior involvement in data annotation, evaluation, or quality assessment workflowsStrong communication skills for articulating formalization decisions, edge cases, and proof strategies
The Ideal Candidate
You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can fully verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving the gaps that automated tools cannot yet bridge. You're drawn to frontiers — and this is one of the most exciting in modern mathematics.
Why Join Us
Work directly on cutting‑edge AI research projects alongside world‑leading labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, high‑impact technical work
Gain exposure to how advanced AI models are trained on formal mathematical reasoning
Contribute to work that is actively advancing the frontier of mechanized mathematics
Potential for ongoing engagement and contract extension as new projects launch
#J-18808-Ljbffr