# LLMs with in-context learning for Algorithmic Theoretical Physics

arXiv: https://arxiv.org/abs/2605.08212 · HTML: https://mlsanity.com/paper/2605.08212/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 18 of 18)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Context Length Alone Hurts LLM Performance Despite Perfect Retrieval](https://mlsanity.com/paper/2510.05381/) (2025)
- [Long-Context LLMs Meet RAG: Overcoming Challenges for Long Inputs in RAG](https://mlsanity.com/paper/2410.05983/) (2024)
- [MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning](https://mlsanity.com/paper/2402.17231/) (2024)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics](https://mlsanity.com/paper/2510.12787/) (2025)
- [Fewer is More: Boosting LLM Reasoning with Reinforced Context Pruning](https://mlsanity.com/paper/2312.08901/) (2023)
- [AgentMath: Empowering Mathematical Reasoning for Large Language Models via Tool-Augmented Agent](https://mlsanity.com/paper/2512.20745/) (2025)
- [Can Theoretical Physics Research Benefit from Language Agents?](https://mlsanity.com/paper/2506.06214/) (2025)
- [Test-time Scaling Techniques in Theoretical Physics -- A Comparison of Methods on the TPBench Dataset](https://mlsanity.com/paper/2506.20729/) (2025)
- [What Makes In-context Learning Effective for Mathematical Reasoning: A Theoretical Analysis](https://mlsanity.com/paper/2412.12157/) (2024)
- [Reliable Proof Generation with LLMs via Analogical Retrieval and Symbolic Verification: A Case Study in Euclidean Geometry](https://mlsanity.com/paper/2505.14479/) (2025)
- [Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrieval](https://mlsanity.com/paper/2411.16454/) (2024)
- [SymCode: A Neurosymbolic Approach to Mathematical Reasoning via Verifiable Code Generation](https://mlsanity.com/paper/2510.25975/) (2025)
- [O-Forge: An LLM + Computer Algebra Framework for Asymptotic Analysis](https://mlsanity.com/paper/2510.12350/) (2025)
- [Process In-Context Learning: Enhancing Mathematical Reasoning via Dynamic Demonstration Insertion](https://mlsanity.com/paper/2601.11979/) (2026)

## Built on by (most cited first, 2 of 2)

- [AI's Capability in Assisting Scientific Research in Physics, Astrophysics, and Cosmology I: Literature Review](https://mlsanity.com/paper/2607.25672/) (2026)
- [AI's Capability in Assisting Scientific Research in Physics, Astrophysics, and Cosmology II: Project Planning and Proposal Evaluation](https://mlsanity.com/paper/2607.25881/) (2026)

## Abstract (arXiv)

There is an increasing number of algorithmic computations in theoretical physics. These, while conceptually simple, can nevertheless be time-consuming and contain subtleties that should not be overlooked. Given the recent improvement of Large Language Models (LLM), it is natural to investigate whether LLMs equipped with a computer algebra system (CAS) runtime and sufficiently informative context can reliably carry out these algorithmic tasks. In this work, we interface Claude with Maple, and apply this framework to cosmological perturbations in modified theories of gravity. We demonstrate the current capabilities of this approach, the typical failures, and how the same can be improved. We find that a frontier LLM supplied with worked examples is able to solve most test problems.