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Georg Cantor
(3 Mar 1845 - 6 Jan 1918)
German mathematician.
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Science Quotes by Georg Cantor (8 quotes)
A set is a Many that allows itself to be thought of as a One.
— Georg Cantor
Quoted in Carol Schumacher, Chapter Zero: Fundamental Notions of Abstract Mathematics (1996), 23.
In arithmetic, purely arithmetic methods are far superior to analytical ones.
— Georg Cantor
From doctoral dissertation, 'De aequationibus secundi gradus indeterminatis' (On indeterminate equations of the second degree, 1867), 26, Theses summary, I. As translated from the original Latin: “In arithmetica methodi mere arithmeticae analyticis longe praestant.” ChatGTP explains: “Arithmetic methods refer to those based on the properties and operations of numbers, often involving direct computation or algebraic manipulation. Analytic methods, on the other hand, often involve the use of calculus and continuous functions, focusing more on the properties of functions and continuity.”
In mathematics the art of asking questions is more valuable than solving problems.
— Georg Cantor
From doctoral dissertation, 'De aequationibus secundi gradus indeterminatis' (On indeterminate equations of the second degree, 1867), 26, Theses summary, III. As translated from the original Latin, “In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.” Other translations include: “In mathematics, the art of posing a problem is more important than solving it,” or “In mathematics the art of proposing a question must be held of higher value than solving it.”
Mathematics is perfectly free in its development and is subject only to the obvious consideration, that its concepts must be free from contradictions in themselves, as well as definitely and orderly related by means of definitions to the previously existing and established concepts.
— Georg Cantor
In Grundlagen einer allgemeinen Manigfaltigkeitslehre (1883), Sect. 8.
The essence of mathematics lies in its freedom.
— Georg Cantor
In Mathematische Annalen, Bd. 21, 564.
The essence of mathematics lies precisely in its freedom.
— Georg Cantor
Gesammelte Abhandlungen (1932), 182, trans. Ivor Grattan-Guinness. Also, givened as: 'The essence of mathematics lies in its freedom,' in Mathematische Annalen, 21, 564. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 12.
The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.
— Georg Cantor
Gesammelte Abhandlungen (1932),395, trans. Ivor Grattan-Guinness.
Whether space and time possess an absolute reality cannot be decided because of the very nature of the controversy.
— Georg Cantor
From doctoral dissertation, 'De aequationibus secundi gradus indeterminatis' (On indeterminate equations of the second degree, 1867), 26, Theses summary, II. A.I. translation from the original Latin: “Num spatii ac temporis realitas absoluta sit, propter ipsam controversiae naturam dijudicari non potest.”
Quotes by others about Georg Cantor (1)
No one shall expel us from the paradise which Cantor has created for us.
Expressing the importance of Cantor's set theory in the development of mathematics.
Expressing the importance of Cantor's set theory in the development of mathematics.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 33.
See also:
- 3 Mar - short biography, births, deaths and events on date of Cantor's birth.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
