Claude has done it: Anthropic's AI model has computed a nine-loop amplitude in N=4 super-Yang-Mills theory – a problem from theoretical particle physics that physicists long considered too computationally demanding. The breakthrough was documented by Anthropic in a guest post by physicist and science writer Matt von Hippel.
The essentials
- Claude solved an open problem in amplitude theory – a subfield of theoretical particle physics
- Computing a nine-loop amplitude in Yang-Mills theory was considered the limit of what academic resources could achieve
- Von Hippel posed a challenge to AI companies to crack exactly this problem – shortly after, it was solved
- The result shows: AI can not only find mathematical ideas, but also tackle computationally hard problems
What the challenge was about
Matt von Hippel, a former particle physicist now science journalist, posed a concrete task to AI companies: Solve a problem from my former research field using the tools academics have. His challenge was clear – either N=8 supergravity to seven loops or N=4 super Yang-Mills to nine loops.
Why these problems? Because they sit at the boundary of what researchers can handle with available computers and time. It's not that nobody knows how to do it in principle – it's that the computational burden is enormous. Von Hippel wanted to see whether a more intelligent system – an AI – could use the same resources more efficiently.
"I wanted to see if those researchers were wrong: if a smarter, artificial researcher could use the same computers, and solve the problem anyway."
That's how von Hippel framed it. He wasn't looking for new mathematical ideas (those are hard to evaluate), but for genuine computational power under pressure.
What amplitude theory is – and why it matters
Amplitude theory is a subfield of theoretical particle physics. Physicists use so-called scattering amplitudes – mathematical formulas – to predict how elementary particles interact with each other. With these amplitudes, they can calculate how likely certain reactions are. This is central to verifying experiments like at the Large Hadron Collider: Do measured results match predictions?
The more precise the calculations, the better the predictions. But: The more precise, the more complex the mathematics – and eventually even specialized supercomputers hit their limits.
What this means for AI capabilities
Claude's success sends a signal beyond physics. It shows that AI isn't just making progress on "soft" tasks like writing or brainstorming, but also on hard-structured, computationally intensive problems. This differs from previous AI successes in mathematics, which often relied on conceptual breakthroughs.
The question von Hippel posed to himself was deliberately chosen: Can AI push past a computational boundary that isn't rooted in lack of creativity, but in sheer effort? The answer appears to be yes.
What this means for German research and industry
This breakthrough has implications for companies and institutes working on optimization problems, materials science, or complex simulations. If AI models like Claude can tackle computationally hard problems under academic resource constraints, it could open new paths for research efficiency – in chemistry, physics, or engineering sciences. At the same time, it raises questions: What other "impossible" problems might suddenly become solvable? And how do requirements for specialized research teams change?
Sources
Editorially owned by Ideal Syka. Sources and method: Newsroom & method. Tips and corrections: ai@i6eal.de.
