Mathematical Physicist (PhD)

About the Role

This panel is built around CritPt, a public benchmark of research-level physics challenges that tests whether frontier AI models can do genuine research reasoning (paper: arXiv:2509.26574). Mercor is engaging mathematical physicists to create, solve, review or audit problems in their own subfield. It is research-grade rather than volume work, and each output must be complete enough for another specialist to verify. Four narrow areas are covered: hypergeometric identities and analytic continuation, integrable systems (half-wave maps, Lax pairs, Haldane-Shastry, Calogero-Moser), permutation combinatorics for random tensor network entanglement, and Fefferman-Graham ambient metric conformal geometry. The standard of proof is closer to mathematics than physics.

What You'll Do

• Create, solve, review or audit research-level problems in the area you are matched to.
• Write complete, verifiable reasoning that a specialist in your subfield can follow.
• Agree the specific assignment with the team after area matching.

Requirements

• PhD in mathematical physics, theoretical physics or mathematics (hard requirement); postdocs, research scientists and junior faculty fit best.
• Verifiable publication record: 3-5 papers with arXiv IDs or DOIs, ideally from the last five years, first-author preferred; every paper is checked.
• Published work on the specific phenomenon in one of the listed areas, not an adjacent one.
• Working proficiency with LaTeX, Python, SymPy and Jupyter; some agentic coding in VS Code is useful.
• English at B2 or above, including clear written reasoning.

Compensation & Logistics

$80-$110 per hour, set by depth of subdomain match. About 10 hours per week over an 8 to 10 week window, starting immediately. Remote and asynchronous with no fixed hours. Application is a form with paper proof per area, then paper verification, then either direct onboarding or a short alignment call; a 30-45 minute assessment is occasional. No location restriction stated.