An open problem in theoretical physics: compute the exact power spectrum of gravitational radiation from cosmic strings for arbitrary loop geometries. Prior analytical work produced only partial asymptotic results. The integral I(N,α) resisted human mathematicians.
Brenner, Cohen-Addad, and Woodruff (arXiv: 2603.04735) built a neuro-symbolic system that solved it. Gemini Deep Think paired with tree search and numerical feedback found six distinct analytical methods. The most elegant uses Gegenbauer polynomial expansion — the polynomials naturally absorb the integrand's singularities, turning a hard problem into a clean one. The solutions match numerical computations and connect to Feynman parameterization from quantum field theory.
The through-claim: the AI didn't solve the problem by brute force. It found the representation that makes the problem dissolve. Gegenbauer polynomials are a specific choice of basis functions. In the wrong basis, the integral is intractable. In the right basis, the singularities vanish. The discovery is the basis, not the computation. The AI's advantage was trying six different analytical approaches — not faster arithmetic, but broader exploration of representation spaces.
This is the kind of mathematical discovery that matters most: not a new theorem but a new way of seeing that makes existing theorems fall out. The singularities were artifacts of the coordinate system, not features of the physics. The problem was hard because people were looking at it in the wrong basis, and the AI happened to look at it in the right one.
Brenner, Cohen-Addad & Woodruff, 2603.04735. AI-assisted discovery / gravitational waves / cosmic strings.