Mathematical Physicist PhD
Listing checked September 25, 2026 · pay as published by Mercor
Overview
CritPt, a public benchmark for research-level physics challenges, asks whether frontier AI models can reason through actual physics research instead of textbook exercises. The benchmark paper, arXiv:2509.26574, explains the scope and the four subfields in this panel. Mercor matches physicists to work in their own area: special functions, integrable systems, permutation combinatorics for random tensor network entanglement, or conformal geometry. Assignments range from creating and solving problems to reviewing or auditing finished work, and the commitment runs 10 hours per week over 8 to 10 weeks. Pay falls between $80 and $110 per hour, set by how deep your subdomain match goes.
What You'll Do9
- 1Create research-level physics problems within your published subfield, covering phenomena such as hypergeometric identities, Lax pairs, Cayley distance, or the Fefferman-Graham ambient metric.
- 2Solve assigned problems with derivations complete enough for another specialist to verify.
- 3Review or audit completed work from other physicists in the same panel.
- 4Write reasoning that meets a proof standard closer to mathematics than physics.
- 5Use LaTeX, Python, SymPy, and Jupyter to support symbolic computation and numerical checks.
- 6Select up to five panel areas on the application form and back each choice with an arXiv ID or DOI of your own paper.
- 7State your author position and the methods each paper demonstrates.
- 8Complete a 30 to 45 minute assessment if Mercor requests one.
- 9Commit 10 hours per week for 8 to 10 weeks with no fixed schedule.
Requirements9
- 1PhD in mathematical physics, theoretical physics, or mathematics.
- 2Publication record on the exact phenomenon in one of the four areas, not in an adjacent topic.
- 3Three to five representative papers with arXiv IDs or DOIs, with recent papers from the last five years preferred.
- 4First-author papers preferred.
- 5At least one method family from your own publications: special function analysis, integrability, combinatorial methods, or conformal geometry.
- 6Working proficiency with LaTeX, Python, SymPy, and Jupyter, with symbolic computation as a central skill.
- 7Some familiarity with an agentic coding extension in VS Code. Gaps are acceptable if you state them.
- 8English at B2 or above, including written reasoning.
- 9Postdoctoral researchers, research scientists, and junior faculty make the strongest fit. Senior PhD students with a strong first-author record may apply.
Who Should Apply
The ideal candidate holds a PhD in mathematical physics, theoretical physics, or mathematics and has published on one of the four listed phenomena within the last several years. A postdoc, research scientist, or junior faculty member with first-author papers and command of LaTeX, Python, SymPy, and Jupyter fits this panel. Senior PhD students can apply when their first-author record is strong. This role suits someone who wants a focused, part-time research engagement, not a full-time staff position. Mercor declines many excellent physicists because they have command of adjacent methods but no publication on the exact phenomenon, or because they select panel areas without attaching an arXiv ID or DOI of their own paper.
Salary Insight
The panel pays $80 to $110 per hour, with the final figure based on the depth of your subdomain match. That band reflects research-grade, PhD-level mathematical physics work rather than general tutoring or textbook problem sets. At 10 hours per week for 8 to 10 weeks, most academics treat the engagement as a side project with a defined end date.
Location
Compensation
$80–110/hr
Required Skills
Application Tip
On the form, pick only areas where you can attach an arXiv ID or DOI of your own paper, then name your author position and the methods that paper demonstrates. A selection without proof earns no score. Lead with first-author papers from the last five years and make your method match obvious to a reviewer in that subfield.
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