In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and… — David Hilbert Copy Share Image
[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity. — David Hilbert Copy Share Image
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next… — David Hilbert Copy Share Image
How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler… — David Hilbert Copy Share Image
Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a… — David Hilbert Copy Share Image
If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven? — David Hilbert Copy Share Image
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of… — David Hilbert Copy Share Image
A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first… — David Hilbert Copy Share Image
Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples… — David Hilbert Copy Share Image
Is mathematics doomed to suffer the same fate as other sciences that have split into separate branches?... Mathematics is, in my opinion, an indivisible… — David Hilbert Copy Share Image
One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs — David Hilbert Copy Share Image
I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. — David Hilbert Copy Share Image
I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight… — David Hilbert Copy Share Image
No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other… — David Hilbert Copy Share Image
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated… — David Hilbert Copy Share Image
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