I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics.… — 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
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