David Hilbert: Completion

David Hilbert was German prominent mathematician. Explore interesting quotes on completion.
David Hilbert: 60   quotes 18   likes

“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

Mathematics , Nature , Knowledge , Science

“A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts.”

David Hilbert Mathematical Problems

Mathematical Problems (1900)
Context: A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

Mathematics , Problem , Effort

“A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.”

David Hilbert Mathematical Problems

Eine mathematische Theorie ist nicht eher als vollkommen anzusehen, als bis du sie so klar gemacht hast, daß du sie dem ersten Manne erklären könntest, den du auf der Straße triffst.
Mathematical Problems (1900)
Context: An old French mathematician said: A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street. This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

Mathematics

“Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.”

David Hilbert

Quoted in Hilbert's Die Grundlagen der Mathematik (1927)

God , Mathematics , Understanding , Science