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, in James R. Newman The World of MathematicsThe 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.
“Method in the Physical Sciences”, in The Unity of Knowledge (1955), ed. L. G. Leary (Doubleday & Co., New York), p. 157- John von Neumann (Wikipedia)
John “Johnny” von Neumann (/vɒn ˈnɔɪmən/; Hungarian: Neumann János Lajos, pronounced [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest coverage of any mathematician of his time and was said to be “the last representative of the great mathematicians who were equally at home in both pure and applied mathematics”. He integrated pure and applied sciences.
- Von Neumann was the first to establish a rigorous mathematical framework for quantum mechanics, known as the Dirac–von Neumann axioms, in his influential 1932 work Mathematical Foundations of Quantum Mechanics.
- Von Neumann’s closest friend in the United States was the mathematician Stanisław Ulam.
Young man, in mathematics you don’t understand things. You just get used to them.
John von Neumann
