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.
John Von NeumannRead
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
John Von NeumannRead
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 NeumannRead
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 NeumannRead
Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.
John Von NeumannRead
Similar quotes
I was taught over and over again that the accumulation of random mutations led to evolutionary change - led to new species. I believed it until I looked for evidence.
Lynn MargulisRead
The actual organization of behavior goes on the level of the individual nerve cells and their connections, and we have a hundred billion nerve cells, probably a hundred trillion connections. It's just mind-boggling to think of all the different ways in which they're arranged in a baby's head.
Steven PinkerRead
I have lived much of my life among molecules. They are good company. I tell my students to try to know molecules, so well that when they have some question involving molecules, they can ask themselves, What would I do if I were that molecule? I tell them, Try to feel like a molecule; and if you work hard, who knows? Some day you may get to feel like a big molecule!
George WaldRead
The Three Laws of Robotics: 1: A robot may not injure a human being or, through inaction, allow a human being to come to harm; 2: A robot must obey the orders given it by human beings except where such orders would conflict with the First Law; 3: A robot must protect its own existence as long as such protection does not conflict with the First or Second Law; The Zeroth Law: A robot may not harm humanity, or, by inaction, allow humanity to come to harm.
Isaac AsimovRead
Astronomy is perhaps the science whose discoveries owe least to chance, in which human understanding appears in its whole magnitude, and through which man can best learn how small he is.
Georg C. LichtenbergRead
Science, at bottom, is really anti-intellectual. It always distrusts pure reason, and demands the production of objective fact.
H. L. MenckenRead