We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
Carl Friedrich GaussRead
I protest against the use of infinite magnitude ..., which is never permissible in mathematics.
Interpretation
What this quote means
Gauss argues against the acceptance of infinite values in mathematics, suggesting they are not usable or acceptable.
In this quote, Carl Friedrich Gauss expresses his strong disapproval of the concept of infinite magnitudes in mathematics. He implies that utilizing infinite values leads to contradictions and inaccuracies, which are not acceptable within the precise field of mathematics. Gauss's stance reflects his belief in the importance of rigorous standards in mathematical practice, advocating for clarity and finite values in mathematical discourse.
Themes
InfinityMathematicsGaussPrecisionMagnitude
In practice
Example use cases
In a lecture on mathematical foundations, one might quote Gauss to emphasize the need for rigorous definitions.
More from Carl Friedrich Gauss
All quotes βMathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
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To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.
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The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
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When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.
Carl Friedrich GaussRead
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