There is no point in being precise if you do not even know what you are talking about. John von Neumann More Quotes by John von Neumann More Quotes From John von Neumann The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking. John von Neumann teaching math thinking By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful. John von Neumann desire discovery years You don't have to be responsible for the world that you're in. John von Neumann being-responsible responsible world Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics. Physicist: I'm afraid I don't understand the method of characteristics. Neumann: In mathematics you don't understand things. You just get used to them. John von Neumann understanding simple science It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe. John von Neumann effort understanding running Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number - there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method. John von Neumann arithmetic sin numbers Life is a process which may be abstracted from other media. John von Neumann media life-is may The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level. John von Neumann levels peculiar facts You wake me up early in the morning to tell me I am right? Please wait until I am wrong. John von Neumann up-early waiting morning If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other. John von Neumann mathematical transformation might 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. John von Neumann algorithms mathematics physics I am a little troubled about the tea service in the electronic computer building. Apparently the members of your staff consume several times as much supplies as the same number of people do in Fuld Hall and they have been especially unfair in the matter of sugar.... I should like to raise the question whether it would not be better for the computer people to come up to Fuld Hall at the end of the day at 5 o'clock and have their tea here under proper supervision. John von Neumann tea numbers people Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Godel's achievement. John von Neumann logic achievement space Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. John von Neumann powerful humorous witty I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is ... governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas. John von Neumann It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years. John von Neumann achieve technology limits sound
