John von Neumann Quotes

Long intervals frequently elapse between the discovery of new principles in science and their practical application... Those intellectual qualifications, which give birth to new principles or to new methods, are of quite a different order from those which are necessary for their practical application.

I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler-such penetrating minds as Descartes and Pascal-were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

Psychoanalysts seem to be long on information and short on application.

I have found a very great number of exceedingly beautiful theorems.

I enjoyed like nothing else working in pure math, discovering new formulas.

Science, which cuts its way through the muddy pond of daily life without mingling with it, casts its wealth to right and left, but the puny boatmen do not know how to fish for it.

Mathematical discoveries, like springtime violets in the woods, have their season which no man can hasten or retard.

Scientific theory and its application to the growing needs of mankind advance hand in hand.

Mathematicians aren't motivated by money and material gain, or even by practical applications of their work. For us it's the glory of solving one of the great unsolved problems that have outwitted previous generations of mathematicians. …. Despite all the things we've discovered over the last 7 millennia, there are still many things we don't understand.

The deep things in science are not found because they are useful; they are found because it was possible to find them..

It is a profound and necessary truth that the deep things in science are not found because they are useful; they were found because it was possible to find them.

You have to spend some energy and effort to see the beauty of math.

So, we've gone from covered wagons to going to the moon in just under 100 years. For all the centuries and thousands of years before us, people walked or rode horses, cows, camels or whatever. This so-called modern era, from the late 19th century through now, has been the period of the most amazing development, discovery, innovation and acceleration of change that humans have ever experienced. And it hasn't slowed down yet.

In mathematical science, more than in all others, it happens that truths which are at one period the most abstract, and apparently the most remote from all useful application, become in the next age the bases of profound physical inquiries, and in the succeeding one, perhaps, by proper simplification and reduction to tables, furnish their ready and daily aid to the artist and the sailor.

Science is the most exciting and sustained enterprise of discovery in the history of our species. It is the great adventure of our time. We live today in an era of discovery that far outshadows the discoveries of the New World five hundred years ago.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.

It seems that there's a constant humbling - I don't know if that's the right word - because things are disproved all the time with new discoveries, at least that's the way it feels sometimes in the layman's world. Like, people will make proclamations of something to be true, and then 50 years later that's proven wrong because there's something else.

The amount of scientific information we've discovered in the last twenty years is more than all the discoveries up to that point, from the beginning of language.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

Mathematics is the surest way to immortality. If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten

Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.

Well, in the first place, it leads to great anxiety as to whether it's going to be correct or not ... I expect that's the dominating feeling. It gets to be rather a fever... At age 60, when asked about his feelings on discovering the Dirac equation.

About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.