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John von Neumann

John von Neumann Books

Mathematician

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“When we talk mathematics, we may be discussing a secondary language, built on the primary language truly used by the central nervous system. Thus the outward forms of our mathematics are not absolutely relevant from the point of view of evaluating what the mathematical or logical language truly used by the central nervous system is. However, the above remarks about reliability and logical and arithmetical depth prove that whatever the system is, it cannot fail to differ considerably from what we consciously and explicitly consider as mathematics.”

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Book:The Computer and the Brain
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“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.”

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Author:John von Neumann
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“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.”

PeopleShouldLittlesHas BeensEndsMatterNumbersBuildingMembersComputerRaisesCome UpTeaClockThe End Of The DayHallsSugarUnfairStaffSuppliesSupervision
Author:John von Neumann
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“The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work-that is, correctly to describe phenomena from a reasonably wide area.”

TryingScienceCertainModelsEvidenceAreasAccountsMathematicsWideExpectedObservationMathematicalInterpretationJustificationConstructsMathematical Models
Book:The Neumann Compendium
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“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.”

ThinkingFirstsStillsDifficultTeachingModernDevelopmentAchievementImportanceMathematicsMathMathematicalAnalysisLogicalCalculusOverestimateInceptionMathematical Analysis
Book:The Neumann Compendium
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“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.”

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Book:The Neumann Compendium
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