Mathematics is the music of reason.

数学是理性的音乐。

In mathematics, the art of proposing a question must be held of higher value than solving it.

在数学中，提出问题的艺术必须比解决问题更有价值。

The essence of mathematics lies in its freedom.

数学的本质在于它的自由。

A mathematician is a device for turning coffee into theorems.

数学家是将咖啡转化为定理的装置。

The best way to learn mathematics is to do mathematics.

学习数学的最好方法就是做数学。

Topology is the study of the properties of a figure that are unchanged by any deformation.

拓扑学是对图形在任何变形下保持不变的性质的研究。

The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...'

在科学中最令人兴奋的短语，预示着新发现的，不是“我找到了！”而是“这很有趣...”

In mathematics, you don't understand things. You just get used to them.

在数学中，你并不理解事物。你只是习惯了它们。

The beauty of mathematics is that it is one of the few areas of human endeavor where absolute truth can be known.

数学之美在于它是人类少数几个可以知晓绝对真理的领域之一。

Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.

数学不是一门演绎科学——那是陈词滥调。当你试图证明一个定理时，你不仅仅是列出假设然后开始推理。你所做的是反复试验、实验和猜测。