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Claude Solves Nine-Loop Amplitude in N=4 SYM Theory

TL;DR

Anthropic's Claude solved a nine-loop scattering amplitude in N=4 super Yang-Mills theory, a frontier computational physics problem that a field expert publicly challenged AI companies to crack, completing it roughly one month after the challenge was issued.

What happened

  • Physicist and science writer Matt von Hippel publicly challenged AI companies to solve one of two open problems in theoretical particle physics: N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops.
  • The challenge was explicit: use only the compute budget an academic researcher has access to, not a supercomputer center.
  • Anthropic accepted the N=4 super Yang-Mills target, and Claude solved it in roughly one month after the challenge was posted.
  • The nine-loop result is a significant step beyond the current frontier: most scattering amplitude calculations stop at two or three loops, with five loops representing the most precise prediction in mainstream particle physics.
  • Von Hippel framed the test as a check on whether AI could beat a computational ceiling, not just find a clever new idea, making the result harder to dismiss as a lucky shortcut.

Why it matters

  • Scattering amplitudes underpin predictions tested at the Large Hadron Collider; more precise loop calculations could reveal mismatches pointing to new physics, including dark matter candidates.
  • The result directly challenges the "LLMs are near their ceiling" camp: this was a problem where the barrier was compute and engineering discipline, not conceptual novelty.
  • N=4 super Yang-Mills is the community's primary stress-test sandbox for new amplitude techniques, so a nine-loop result validates methods that researchers will carry into harder, more realistic theories.
  • Completing a months-long expert calculation in weeks on academic-scale hardware suggests AI could compress the research timeline in theoretical physics broadly, not just in this toy model.
  • The challenge was issued by a domain expert who explicitly said he wanted to see something he knew was hard, raising the credibility bar above typical AI benchmark claims.

What to watch next

  • Whether Anthropic or the physics community publishes a peer-reviewed paper with the nine-loop result, which would allow independent verification and establish it as a citable scientific contribution.
  • Whether the companion challenge, N=8 supergravity to seven loops, is attempted next, which would test whether the approach generalizes across different toy-model theories.
  • How the amplitudeology community responds: adoption of AI-assisted loop calculations as a standard workflow would be a stronger signal than the result alone.

Originally published on Present of AI, a daily source-linked AI news timeline. Read the full timeline or browse the open dataset.