I protest against the use of infinite magnitude ..., which is never permissible in mathematics.
Carl Friedrich GaussRead
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.
Interpretation
What this quote means
This quote emphasizes the distinction between human-created concepts and the objective reality of space.
Gauss highlights the idea that while numbers and mathematical concepts are inventions of the human mind, space itself is an objective reality that exists independently of our perceptions. This suggests that our understanding of the universe is limited by our mental frameworks, and we must remain humble in recognizing that we cannot fully define or control the properties of space solely through our intellect.
Themes
HumilityRealitySpaceNumberKnowledge
In practice
Example use cases
In a lecture about the philosophy of mathematics, this quote could illustrate the limits of human understanding.
More from Carl Friedrich Gauss
All quotes →Mathematics 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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Life stands before me like an eternal spring with new and brilliant clothes.
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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.
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