"In mathematics, as in any scientific research, we find two tendencies... [T]he tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material in a systematic and orderly manner. On the other hand, the tendency toward intuitive understanding fosters a more immediate grasp of the objects... a live rapport with them... which stresses the concrete meaning of their relations. ...[I]ntuitive understanding plays a major role in geometry. ...[S]uch concrete intuition is of great value not only for the research worker, but... for anyone who wishes to study and appreciate the results of research in geometry."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Academics from GermanyAgnosticsMathematicians from GermanyPhysicists from GermanyLogicians from Germany
Original Language: English
Available Languages (1)
Sources
Preface
https://en.wikiquote.org/wiki/David_Hilbert
Revision History
No revisions have been submitted for this quote.
Categories
David Hilbert
1862 – 1943
deutscher Mathematiker
46 quotes on TrueQuotesView all quotes by David Hilbert →
Related Quotes
"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis b…"
"One of the supreme achievements of purely intellectual human activity."
"If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in exist…"
""Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of …"
"One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it."
"The art of doing mathematics consists in finding that special case which contains all the germs of generality."
"Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country."
"Wir dürfen nicht denen glauben, die heute mit philosophischer Miene und überlegenem Tone den Kulturuntergang propheze…"
"Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics."
"But he (Galileo) was not an idiot,... Only an idiot could believe that scientific truth needs martyrdom — that may be…"