新买了一本数论（An Introduction to Number Theory, by Graham Everest & Thomas Ward, GTM232, Springer-Verlag 2005），现在补课已经晚了，只是想偶尔看看，欣赏纯数学的美妙。

作者在前言里提出数学教育的三点认识：

1）数学是个好故事，它的定理不是孤立的，而是文化的一部分。（The first is that mathematics is a good story. Theorems are not discovered in isolation, but happen as part of a culture, and they are generally motivated by paradigms.）

2）学生有不同的偏好和潜力，所以需要通过不同的方法来讲述同样的问题。（The second belief is that mathematics students (and indeed professional mathematicians) come to the subject with different preferences and evolving strengths. Therefore, we have endeavored to present differing approaches to number theory.）

3）即使在最基本的水平上，数论也是活的。（The third belief is that number theory is a living subject, even when studied at an elementary level.）数论的一个显著特点是，两千多年前的问题在今天依然令人们走火入魔，如素数是什么？在哪儿找？素数因子怎么算？

我好奇的还是数论是怎么一点点“浸润”数学的各个领地的——而且是以情意绵绵的秋雨的方式。如果说数学在其他领域基本还只是“用”或“被用”，数论则是自然的生长，有时几乎忘了哪儿是它的根——似乎从任何一点都可以长出来。