John von Neumann Quotes about Mathematics

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

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 Neumann

Science, Trying, Mathematics

John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.628, World Scientific

The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.

John von Neumann

Thinking, Depth, Mathematics

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, Physics, Mathematics

John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.453, World Scientific