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
A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.
Interpretation
What this quote means
The quote reflects on the complexity of discovering profound truths through simple reasoning, revealing the challenges in understanding deep concepts.
Carl Friedrich Gauss highlights the paradox of knowledge acquisition, where important truths may appear simple and accessible, yet are often challenging to demonstrate. This indicates that while initial intuitive insights can lead to discoveries, the formal proofs of these truths can be convoluted and require significant effort, showcasing the intricate relationship between simplicity and depth in intellectual pursuits.
Themes
SimplicityTruthKnowledgeDiscoveryInductionComplexity
In practice
Example use cases
In a lecture about scientific methodologies, one might use this quote to illustrate the contrast between simple ideas and complex proofs.
More from Carl Friedrich Gauss
All quotes βI protest against the use of infinite magnitude ..., which is never permissible in mathematics.
Carl Friedrich GaussRead
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.
Carl Friedrich GaussRead
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.
Carl Friedrich GaussRead
Life stands before me like an eternal spring with new and brilliant clothes.
Carl Friedrich GaussRead
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