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
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.
Interpretation
What this quote means
The quote highlights the significance of understanding prime numbers and their factors in mathematics.
Carl Friedrich Gauss emphasizes the fundamental role that prime numbers and composite numbers play in arithmetic. The ability to distinguish between these two types of numbers, as well as to factor composite numbers into their prime constituents, is not only crucial for theoretical mathematics but also has practical applications in various fields, including cryptography and number theory.
Themes
Prime NumbersComposite NumbersArithmeticMathematicsFactoring
In practice
Example use cases
During a mathematics lecture, I quoted Gauss to demonstrate the importance of primes.
More from Carl Friedrich Gauss
All quotes →I 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.
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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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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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