Mathematical Physicist (PhD)

What you'll do

Of Mercor's CritPt panels this is the most proof-driven one: the listing says the standard of proof here sits closer to mathematics than to physics. If your papers are more theorem than estimate, this is the panel that uses that.

The work is for CritPt, a public benchmark of research-level physics problems built to test whether frontier AI models can reason like a working physicist rather than solve textbook exercises. The benchmark paper is arXiv:2509.26574, and Mercor suggests reading it before you apply. Depending on where your publications fit, you create problems, solve them, review finished work or audit it; Mercor agrees the exact assignment once you are matched to an area. Everything you hand in has to be complete enough for another specialist to follow and verify independently, so written reasoning is part of every task.

Who qualifies

Four research areas, matched narrowly. You need papers on one of these phenomena, not mathematical physics in general, and published work on an adjacent topic is the most common reason Mercor declines strong applicants:

• Special functions: hypergeometric identities, quadratic transformations and analytic continuation in a series index
• Integrable systems: the half-wave maps equation, Lax pairs, Haldane-Shastry and Calogero-Moser systems
• Permutation combinatorics for random tensor network entanglement: Cayley distance, non-crossing partitions, Weingarten calculus
• Conformal geometry: the Fefferman-Graham ambient metric and obstruction tensors

A PhD in mathematical physics, theoretical physics or mathematics is a hard requirement. Postdocs, research scientists and junior faculty are the strongest fit, and senior PhD students with a strong first-author record may apply. Mercor asks for three to five representative papers with arXiv IDs or DOIs, ideally from the last five years and first-authored, and checks every one against the public record. You work in LaTeX, Python, SymPy and Jupyter, and need English at B2 or above. Mathematicians are explicitly eligible.

What it pays

$80–110 per hour, Mercor's published figure and the same band across its CritPt physics panels. The listing does not state weekly hours or payment terms.

Worth knowing

Good:

• Proof-level work that rewards careful mathematical writing
• Open to mathematicians as well as physicists
• No country restriction published

Less good:

• Only four areas, so most mathematical physicists will not match
• Every listed paper is checked
• Hours and payment schedule not on the listing

About this listing

Posted by Mercor as a remote hourly contract, confirmed open on 27 September 2026 and flagged as a new opportunity. Another CritPt panel: Condensed Matter Physicist (PhD). See Mercor.