Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.

  • -- Richard Courant 库兰特

数学作为人类思维的一种表达方式,反映了人类积极的意志、沉思的理性和对审美完美的渴望。其基本要素是逻辑与直觉、分析与建构、共性与个性。

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There are a couple of things that I'm sure people don't think are important, but I do. I don't like hair changes unless there's a reason for it. Clothing - I don't like to see an outfit worn more than one time in an hour - you can wear it again a few weeks later.

有几件事我确信人们不认为重要,但我认为重要。我不喜欢头发变了,除非有原因。衣服——我不喜欢看到一件衣服在一个小时内穿了不止一次——你可以在几周后再穿一次。

If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is!

要使数学得到广泛的理解,我们需要强调它的优雅及其应用。有时候,大学似乎想强调这是多么困难!

If the human brain were so simple that we could understand it, we would be so simple that we couldn't.

如果人类的大脑如此简单以至于我们能够理解它,那么我们就会如此简单以至于我们无法理解它。

Trust your hunches. They're usually based on facts filed away just below the conscious level.

相信你的直觉。它们通常是建立在低于意识水平的事实基础上的。

Conscience is our magnetic compass; reason our chart.

良心是我们的罗盘;我们的图表。

The mathematics is not there till we put it there.

数学是不存在的,除非我们把它放在那里。

There is no instinct like that of the heart.

没有一种本能比得上心灵的本能。

The mind of a child is a precious thing.

孩子的头脑是宝贵的。