Large language models (LLMs) have made significant strides in mathematical reasoning, particularly at the elementary level. However, they continue to face substantial challenges when confronted with complex, advanced mathematical problems. In contrast to humans—who can effectively draw upon prior experiences in solving similar problems and retrieve relevant knowledge and theorems from memory—LLMs often struggle to accurately identify analogous problems and to recall or apply appropriate theorems. To overcome these limitations, we introduce a novel framework for constructing a template-theorems knowledge base, leveraging the capabilities of large language models. Inspired by the associative mechanisms of human cognition, our approach abstracts real-world problems into generalized templates and establishes intricate linkages between these templates and pertinent theorems. This design enables the efficient expansion of a comprehensive knowledge base, even when starting from a limited set of seed examples. Moreover, we develop an efficient retrieval strategy that, given a new problem, systematically extracts and presents the most relevant knowledge from the knowledge base as contextual input to the LLM. Extensive experiments on multiple public mathematical datasets and models demonstrate that our approach consistently surpasses conventional methods. Comprehensive ablation studies further corroborate the effectiveness of both our knowledge base construction and retrieval modules.

Large language models (LLMs) have significantly advanced performance across a spectrum of natural language processing (NLP) tasks. Yet, their application to knowledge graphs (KGs), which describe facts in the form of triplets and allow minimal hallucinations, remains an underexplored frontier. In this paper, we investigate the integration of LLMs with KGs by introducing a specialized KG Language (KGL), where a sentence precisely consists of an entity noun, a relation verb, and ends with another entity noun. Despite KGL's unfamiliar vocabulary to the LLM, we facilitate its learning through a tailored dictionary and illustrative sentences, and enhance context understanding via real-time KG context retrieval and KGL token embedding augmentation. Our results reveal that LLMs can achieve fluency in KGL, drastically reducing errors compared to conventional KG embedding methods on KG completion. Furthermore, our enhanced LLM shows exceptional competence in generating accurate three-word sentences from an initial entity and interpreting new unseen terms out of KGs.