You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
John Von NeumannRead
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.
Interpretation
What this quote means
The calculus is a foundational achievement in modern mathematics, crucial for logical analysis and technical advancement.
John Von Neumann emphasizes the significance of calculus as a cornerstone achievement that marks the beginning of modern mathematics. He argues that its development is pivotal not only for the evolution of mathematical thought but also for its role in enhancing precision in reasoning and technical applications in various fields.
Themes
CalculusMathematicsExact ThinkingAnalysisModern Mathematics
In practice
Example use cases
In a lecture about the evolution of mathematics, one could quote this to highlight the importance of calculus.
More from John Von Neumann
All quotes →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.
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Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
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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.
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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.
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Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.
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