David Hilbert Quotes

Mathematical discoveries, small or great are never born of spontaneous generation.

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

The time was not yet ripe for the growth of mathematical science among us, and any development that might have taken place in that direction was rudely stopped by the civil war.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years.

The advancement and perfection of mathematics are intimately connected with the prosperity of the State.

The beauty of mathematics only shows itself to more patient followers.

I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.

The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.

The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon.

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.

With an absurd oversimplification, the "invention" of calculus [method in mathematics] is sometimes ascribed to two men, Newton and Leibniz.

I've been a workaholic for many years, but at the same time, I do it because I love it.

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

We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

Some of the greatest advances in mathematics have been due to the invention of symbols, which it afterwards became necessary to explain; from the minus sign proceeded the whole theory of negative quantities.

In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts.

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.

It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or other of his journey sit down and invent a definite integral or two towards the increase of the common stock.

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.

On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.

Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself

I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.

Scientific apparatus offers a window to knowledge, but as they grow more elaborate, scientists spend ever more time washing the windows.