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Mathematical Physicist (PhD)
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About the Role
CritPt is a public benchmark of research-level physics challenges, built to test whether frontier AI models can carry out genuine physics research reasoning rather than textbook problem solving. The benchmark paper is arXiv:2509.26574 and we recommend reading it before applying. It will tell you quickly whether this work interests you. We are engaging physicists to work on research-level physics problems in their own subfield. Depending on where your publication record fits, that can mean creating problems, solving them, reviewing completed work, or auditing it. We agree the specific assignment with you once you are matched to an area. This is research-grade work rather than volume work. Whatever you produce has to be complete enough for another specialist in your subfield to follow and verify independently, so written reasoning is part of every assignment. In this panel the standard of proof sits closer to mathematics than to physics.
What You'll Do
- Special function analysis: Gaussian hypergeometric functions, parameter differentiation, quadratic transformation identities, analytic continuation in a series index, asymptotic expansions
- Integrability: Lax pair formalism, isospectral flows, Hilbert transform and singular integral operators, hierarchies of conserved charges, numerical quadrature of singular integrals
- Combinatorial: Cayley distance and geodesics in the symmetric group, minimal factorizations of permutations, non-crossing partitions, Weingarten calculus, multipartite entanglement measures
- Geometric: Fefferman-Graham ambient metric construction, Weyl covariance, Schouten and Weyl curvature tensors, order-by-order solution of Ricci-flatness conditions, Poincare-Einstein asymptotic expansions
You're a Good Fit If You
- A PhD in mathematical physics, theoretical physics or mathematics. This is a hard requirement. Postdoctoral researchers, research scientists and junior faculty are the strongest fit. Senior PhD students with a strong first-author record are welcome to apply.
- Published work on the specific phenomenon above, not the adjacent one. This is the single most common reason we decline otherwise excellent physicists. Command of the methods is not enough if you have not published on the phenomenon itself.
- A verifiable publication record. Three to five representative papers with arXiv IDs or DOIs, ideally from the last five years. First author strongly preferred. Every paper you list will be checked against the public record.
- Working proficiency with LaTeX, Python, SymPy and Jupyter. Symbolic computation matters more in this panel than in most. Some familiarity with an agentic coding extension in VS Code is useful. Gaps there are acceptable if you declare them honestly.
- English at B2 or above, including written reasoning. A large part of the value you add is how clearly you set out your argument.
- Application steps
- Apply and complete the attached form. Basic information, education, research experience, your method self-attestation, and up to five of the areas above that you are the best fit for. For each area you select, give an arXiv ID or DOI of your own paper as proof, with your author position and the methods it demonstrates. A selection without proof is not scored.
- We verify your papers and authorship against the public record.
Role Highlights
Pay & Payout
Independent contractor engagement. Apply via the link below - Mercor handles onboarding and pays weekly via Stripe or Wise.
Common Questions
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