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

arXiv: https://arxiv.org/abs/2603.04735 · HTML: https://mlsanity.com/paper/2603.04735/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 9 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 2 of 2)

- [An AI system to help scientists write expert-level empirical software](https://mlsanity.com/paper/2509.06503/) (2025)
- [Early science acceleration experiments with GPT-5](https://mlsanity.com/paper/2511.16072/) (2025)

## Built on by (most cited first, 8 of 8)

- [Artificial Intelligence and the Structure of Mathematics](https://mlsanity.com/paper/2604.06107/) (2026)
- [Stargazer: A Scalable Model-Fitting Benchmark Environment for AI Agents under Astrophysical Constraints](https://mlsanity.com/paper/2604.15664/) (2026)
- [Agentic Publication Protocol: An Attempt to Modernize Scientific Publication](https://mlsanity.com/paper/2606.27386/) (2026)
- [The Agentification of Scientific Research: A Physicist's Perspective](https://mlsanity.com/paper/2604.14718/) (2026)
- [k-server-bench: Automating Potential Discovery for the k-Server Conjecture](https://mlsanity.com/paper/2604.07240/) (2026)
- [Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery](https://mlsanity.com/paper/2604.21187/) (2026)
- [How Good Are Frontier Models at Physics? Expert Re-Grading Reveals Broken Evaluations and Near-Saturation of Leading Benchmarks](https://mlsanity.com/paper/2609.13009/) (2026)
- [The Future of AI-assisted Physics: Discovering, Verifying and Organizing Results via Formalization](https://mlsanity.com/paper/2610.14059/) (2026)

## Abstract (arXiv)

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,α) for arbitrary loop geometries, directly improving upon recent AI-assisted attempts citeBCE+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 Cl(3/2) to naturally absorb the integrand's singularities. The methods lead to an asymptotic result for I(N,α) 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.