"Let us then examine the extension of this universe to ascertain whether there exists there an infinitely great. The opinion that the world was infinite was a dominant idea for a long time. Up to Kant and even afterward, few expressed any doubt in the infinitude of the universe. Here too modern science, particularly astronomy, raised the issue anew and endeavored to decide it not by means of inadequate metaphysical speculations, but on grounds which rest on experience and on the application of the laws of nature. There arose weighty objections against the infinitude of the universe. It is Euclidean geometry which leads to infinite space as a necessity. ...Einstein showed that Euclidean geometry must be given up. He considered this cosmological question too from the standpoint of his gravitational theory and demonstrated the possibility of a finite world; and all the results discovered by the astronomers are consistent with this hypothesis of an elliptic universe."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
David Hilbert, "Über das Unendliche" ["On the Infinite"] (1925) address to der Westfälischen Mathematischen Gesellschaft in honour to the memory of Karl Weierstrass, Mathematische Annalen, 95 (1926) pp. 161-190, as quoted by Tobias Dantzig, ' (1930)
https://en.wikiquote.org/wiki/Non-Euclidean_geometry
Revision History
No revisions have been submitted for this quote.
Categories
Non-Euclidean geometry
91 quotes on TrueQuotesView all quotes by Non-Euclidean geometry →
Related Quotes
"The creation of non-Euclidean geometry showed... that mathematics could no longer be regarded as a body of unquestion…"
"Edwin Abbott Abbott"
"In the field of non-Euclidean geometry, Riemann... began by calling attention to a distinction that seems obvious onc…"
"Unlike those of science, the conclusions of mathematics had always regarded as deduced from basic truths. ...the very…"
"What was the effect of non-Euclidean geometry on the future progress of mathematics? ...Mathematics passed from serfd…"
"Even the mathematicians of the late nineteenth century did not take non-Euclidean geometry seriously for physical app…"
"... went considerably beyond Sacherri in deducing propositions under the hypotheses of the acute and obtuse angles. T…"
"It is no wonder that no contradiction was found under the hypothesis of the acute angle, for... the geometry develope…"
"Non-Euclidean geometry was the most weighty intellectual creation of the nineteenth century, or, at worst, might have…"
"Euclid’s Elements"