Solving an Open Problem in Theoretical Physics using AI-Assisted Discovery

TL;DR

This paper showcases how AI, specifically a neuro-symbolic system combining large language models and systematic search, can autonomously solve a complex open problem in theoretical physics, producing novel analytical solutions.

Contribution

The authors develop an AI system that autonomously derives exact analytical solutions for a physics problem, surpassing previous partial solutions and demonstrating AI's potential in mathematical discovery.

Findings

AI system derived novel analytical solutions for gravitational wave spectrum

Method expands kernel in Gegenbauer polynomials to handle singularities

Results agree with numerical simulations and connect to quantum field theory

Abstract

This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language model with a systematic Tree Search (TS) framework and automated numerical feedback, that successfully derived novel, exact analytical solutions for the power spectrum of gravitational radiation emitted by cosmic strings. Specifically, the agent evaluated the core integral $I(N,\alpha)$ for arbitrary loop geometries, directly improving upon recent AI-assisted attempts \cite{BCE+25} that only yielded partial asymptotic solutions. To substantiate our methodological claims regarding AI-accelerated discovery and to ensure transparency, we detail system prompts, search constraints, and intermittent feedback loops that guided the model. The agent identified a suite of 6 different analytical methods, the most elegant of which expands the kernel in Gegenbauer polynomials $C_l^{(3/2)}$ to naturally absorb the integrand's singularities. The methods lead to an asymptotic result for $I(N,\alpha)$ at large $N$ that both agrees with numerical results and also connects to the continuous Feynman parameterization of Quantum Field Theory. We detail both the algorithmic methodology that enabled this discovery and the resulting mathematical derivations.