“A ring of polynomials in any number of variables over a ring of coeffcients that has an identity element and a finite basis, itself has a finite basis.”
As quoted in Morris Kline, Mathematical Thought From Ancient to Modern Times (1972) p. 1153.
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Emmy Noether 7
German mathematician 1882–1935Related quotes
“We've all got the disease - the disease of being finite. Death is the basis of all horror.”
on mortality
The Four Cardinal Virtues: Prudence, Justice, Fortitude, Temperance (1965)
First On The Moon : A Voyage with Neil Armstrong, Michael Collins, Edwin E Aldrin, Jr. (1970) edited by Gene Farmer and Dora Jane Hamblin, p. 113, states of this: "Like many a quote which gets printed once and therefore enshrined in the libraries of all newspapers and magazines, this particular one was erroneous. Neil recalled having heard the quote, and he even recalled having repeated it once. He did not subscribe to its thesis, however, and he only quoted it so that he could disagree with it."
Misattributed
“I. Thesis. Finite elements of Space and Time. Antithesis.”
Continuity.
Antimonies
Gesammelte Mathematische Werke (1876)
“The world's nature is a harmonious compound of infinite and finite elements”
The Life of Pythagoras (1919)
Context: Fragment 1. (Stob.21.7; Diog.#.8.85) The world's nature is a harmonious compound of infinite and finite elements; similar is the totality of the world in itself, and of all it contains.
b. All beings are necessarily finite or infinite, or simultaneously finite and infinite; but they could not all be infinite only.
“There may be oodles of possible humans, but it is a finite number.”
Source: Flashforward (1999), Chapter 16 (p. 167)
Letter to Gustac Enestrom, as quoted in Georg Cantor : His Mathematics and Philosophy of the Infinite (1990) by Joseph Warren Dauben ~ ISBN 0691024472