Research Mathematician — Formalization & AI

Company Description: Millennium Research is dedicated to advancing the frontier of mathematics through the application of artificial intelligence. The organization focuses on machine-verified mathematics, developing systems to fundamentally change how mathematical reasoning models approach high-level problems. Team members collaborate across formal methods, competition-level mathematics, and modern AI to build tools that deepen theoretical understanding and enable new discoveries. Millennium Research offers a highly technical, research-focused environment for professionals interested in the intersection of advanced mathematics and machine learning. Role Description: This is an on-site contract role for a Research Mathematician (Formalization) based in New York, NY, well suited to a mathematics specialist who wants their subject-matter depth to be the core of the work. You'll turn published mathematics into machine-verified formal artifacts and help shape the data and evaluation behind our agentic AI for mathematics. The work centers on combinatorics (including Ramsey and extremal theory), number theory, and discrete mathematics , with adjacent areas as the corpus grows. Day-to-day, you'll read theorems and definitions translate them faithfully into Lean 4 / mathlib, judge whether a formal statement genuinely captures the mathematical content of its source (compiling is not the same as meaning the same thing), write and verify Lean proofs of competition-level (Putnam, IMO) and research-level results, and work with the team to turn hard mathematics into rigorous signal our systems can learn from. You'll help keep methods, verdicts, and results reproducible and well documented. Qualifications Strong background in one or more of combinatorics (Ramsey theory, extremal/enumerative combinatorics), number theory (analytic or additive), or discrete mathematics ; comfort reading current research or graduate-level material in these areas. Real mathematical maturity — the ability to read a theorem from a paper and know precisely what it claims, including where a hypothesis is load-bearing or a quantifier order matters. A competition background (Putnam, IMO, or similar) is a significant plus. Hands-on experience with a proof assistant, Lean 4 strongly preferred (Coq, Isabelle, or Agda also welcome); alternatively, a strong pure-mathematics background with the ability to become productive in Lean quickly. Familiarity with Python is helpful; exposure to LLM or agentic tooling (tool use, evaluations) is a plus for the AI-systems side, but this is a mathematics-first role. Bachelor's, Master's, or PhD (completed or in progress) in Mathematics or a closely related field, or equivalent demonstrated ability. Ability to work collaboratively in a research-oriented environment and communicate mathematical reasoning clearly and precisely. Contributions to mathlib, or a background in autoformalization / formal methods, is highly beneficial.