纯粹数学与应用数学

李俨先生对中国古代算学成就的整理，不仅奠定了中国数学史研究的基础，也为人们理解纯粹数学与应用数学、数学与科学、基础研究与应用研究的关系提供了线索。

His work established the foundation of history study of Chinese mathematics . His work also provided us guiding information to understand the relationship between pure mathematics and applied mathematics .

小波分析是从傅立叶分析方法演变出来的，是傅立叶分析的扩充与发展，体现了继傅立叶分析之后纯粹数学与应用数学的又一完美结合。

Wavelet analysis , which evolved from Fourier transform and actually extended and developed it , embodied another perfect combination between the pure mathematical and the applied mathematical behind the Fourier analysis .

同时，分析了数学自身发展中暴露出来的一些问题，主要分析了纯粹数学与应用数学的分离导致数学对服务于科学这一主题的偏离。

It also analyzed the potential problems caused by mathematics itself , which are mainly due to the separation of pure mathematics and applied mathematics , and render to be separated from science and technology .