George Pólya:The only student of mine I was ever intimidated by. He was so quick.There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof.After that I was afraid of von Neumann.(他是唯一的令我感到自己的教师地位受到威胁的学生,他实在是太敏锐了.有一次我在苏黎世为研究生们作演讲,当时冯诺依曼也在听课,我提出了一个悬而未决的问题,过了5分钟冯诺依曼举起了手,当我叫他的时候他径直走到了讲台前,写下了此问题的证明,自此之后我对冯诺依曼感到畏惧。)Eugene Wigner(诺贝尔物理学奖获得者):他很有幽默感,因他这种讲故事和笑话的能力很受人即使是陌生人的喜爱,他可以在必要的时候变得简单快乐,但绝不轻浮愚蠢。冯诺依曼这种非凡的大脑需要理解大部分像我们一样的人不想去理解的甚至不奢求理解的东西。这个事实影响了冯诺依曼的道德判断,只有在科学上的错误和不和谐的地方会让他感到愤怒或者遗憾,在任何人犯了科学上面的错误时,他都会毫不犹豫地纠正别人的错误。Herman Goldstine:他的一个非凡的能力就是绝对精准的记忆力,据我所知,冯诺依曼有能力看过一本书或者一篇文章后一字不错地背诵出来,更甚,他同样能够在多年以后不带丝毫犹豫地做到。他还可以将其实时翻译成英文背诵出来,而且速度丝毫不减。有一次我为了测试他的能力,问他《双城记》是怎么开头的,片刻,他开始背诵第一章节,直到可能10或者15分钟后我让他停下来。Miklós Rédei:It seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician who ever lived.(如果论谁是在科学领域之间因为数学工作而辗转,而每做一份工作都能在其领域应用数学并产生长远的影响的,冯诺依曼可以说是有史以来最具有影响力的数学家。)