Large Language Models (LLMs) have shown impressive abilities in various tasks, but can they truly *understand* math, or are they just sophisticated pattern matchers? New research delves into this question by examining how LLMs learn mathematical concepts, exploring whether they grasp the underlying structure of problems or merely rely on superficial cues. The study uses a novel method called NTKEval, inspired by the Neural Tangent Kernel, to assess how an LLM's probability distribution changes when trained on different types of math data. The findings reveal intriguing differences between in-context learning and instruction-tuning. In-context learning, where the model is given examples before tackling a problem, shows evidence of genuine understanding. LLMs perform better when presented with examples sharing the same underlying mathematical skill, suggesting they recognize deep structures. However, instruction-tuning, where the model is fine-tuned on specific instructions and data, tells a different story. Here, LLMs exhibit similar performance improvements regardless of the training data, hinting that they might be focusing on format rather than true mathematical reasoning. This research highlights the complexities of evaluating mathematical understanding in LLMs and suggests that while they can learn to perform well on math problems, the nature of their understanding differs depending on the learning method. The insights gained from this study are crucial for developing more effective and transparent AI assistants for scientific discovery, paving the way for LLMs that can truly reason mathematically, not just mimic human calculations.