David Hilbert Quotes

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

Modern mathematics, that most astounding of intellectual creations, has projected the mind's eye through infinite time and the mind's hand into boundless space.

I began to realize that an intuitive understanding and consciousness was more significant than abstract thinking and intellectual logical analysis. Intuition is a very powerful thing, more powerful than intellect, in my opinion. That's had a big impact on my work.

A concept is stronger than a fact.

The power of mathematics is often to change one thing into another, to change geometry into language.

I don't care much for equations myself. This is partly because it is difficult for me to write them down, but mainly because I don't have an intuitive feeling for equations.

I enjoyed mathematics from a very young age. At the beginning of college, I had this illusion, which was kind of silly in retrospect, that if I just understood math and physics and philosophy, I could figure out everything else from first principles.

Pure mathematics is, in its way, the poetry of logical ideas.

Logicians may reason about abstractions. But the great mass of men must have images.

The essence of mathematics lies precisely in its freedom.

I can see that, without being excited, mathematics can look pointless and cold.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

I just . . . knew, the way you know how to breathe or to pull your hand back from a hot stove.

As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.

Generalization is always a new influx of divinity into the mind. Hence the thrill that attends it.

Still more astonishing is that world of rigorous fantasy which we call mathematics.

Our account does not rob the mathematicians of their science... In point of fact they do not need the infinite and do not use it.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

Numbers are intellectual witnesses that belong only to mankind.

The Geometer has the special privilege to carry out, by abstraction, all constructions by means of the intellect.

There are things so deep and complex that only intuition can reach it in our stage of development as human beings.

In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.

To a mathematician the eleventh means only a single unit: to the bushman who cannot count further than his ten fingers it is an incalculable myriad.

If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.