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
If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.
Interpretation
What this quote means
Gauss suggests that deep reflection on mathematical concepts can lead to significant discoveries.
In this quote, Carl Friedrich Gauss expresses the idea that if others devoted the same level of thought and persistence to understanding mathematical truths as he has, they too would arrive at revolutionary discoveries. This underscores the importance of deep thinking and reflection in the pursuit of knowledge and innovation in the field of mathematics.
Themes
MathematicsDiscoveryReflectionKnowledgeTruth
In practice
Example use cases
In a lecture about mathematical innovation, one might quote Gauss to emphasize the importance of deep thinking.
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.
Carl Friedrich GaussRead
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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