Unveiling the Mathematical Reasoning in DeepSeek Models: A Comparative Study of Large Language Models

With the rapid evolution of Artificial Intelligence (AI), Large Language Models (LLMs) have reshaped the frontiers of various fields, spanning healthcare, public health, engineering, science, agriculture, education, arts, humanities, and mathematical reasoning. Among these advancements, DeepSeek models have emerged as noteworthy contenders, demonstrating promising capabilities that set them apart from their peers. While previous studies have conducted comparative analyses of LLMs, few have delivered a comprehensive evaluation of mathematical reasoning across a broad spectrum of LLMs. In this work, we aim to bridge this gap by conducting an in-depth comparative study, focusing on the strengths and limitations of DeepSeek models in relation to their leading counterparts. In particular, our study systematically evaluates the mathematical reasoning performance of two DeepSeek models alongside five prominent LLMs across three independent benchmark datasets. The findings reveal several key insights: 1). DeepSeek-R1 consistently achieved the highest accuracy on two of the three datasets, demonstrating strong mathematical reasoning capabilities. 2). The distilled variant of LLMs significantly underperformed compared to its peers, highlighting potential drawbacks in using distillation techniques. 3). In terms of response time, Gemini 2.0 Flash demonstrated the fastest processing speed, outperforming other models in efficiency, which is a crucial factor for real-time applications. Beyond these quantitative assessments, we delve into how architecture, training, and optimization impact LLMs' mathematical reasoning. Moreover, our study goes beyond mere performance comparison by identifying key areas for future advancements in LLM-driven mathematical reasoning. This research enhances our understanding of LLMs' mathematical reasoning and lays the groundwork for future advancements