John von Neumann 约翰·冯·诺依曼
Truth is much too complicated to allow anything but approximations.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
If one has really technically penetrated a subject, things that previously seemed in complete contrast might be purely mathematical transformations of each other.
如果一个人真的在技术上深入研究了一门学科, 以前看起来完全相反的事物, 可能是彼此之间纯粹的数学转换.
Young man, in mathematics you don’t understand things. You just get used to them.
年轻人, 你是不懂数学的. 你只是习惯了它们.
It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.
抱怨人们自私和奸诈是愚蠢的, 就像抱怨磁场不会增加, 除非电场有旋度一样. 两者都是自然法则.
Computers are like humans – they do everything except think.
The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.
数学的所有学科显然对我们任何人来说都太宽泛了。 我认为自高斯以来，没有任何数学家完全且全面的掌握所有科目; 甚至希尔伯特也没有, 而且除了问题的深度之外，我们所有人了解的宽度都比希尔伯特小得多。
All stable processes we shall predict. All unstable processes we shall control.
The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory – and away from the algorithm of differential equations which dominates mathematical physics.
You wake me up early in the morning to tell me I am right? Please wait until I am wrong.
Alan Turing 阿兰·图灵
We can only see a short distance ahead, but we can see plenty there that needs to be done.
Science is a differential equation. Religion is a boundary condition.
Sometimes it’s the very people who no one imagines anything of who do the things no one can imagine.
Those who can imagine anything, can create the impossible.
A computer would deserve to be called intelligent if it could deceive a human into believing that it was human