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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. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

Carl Friedrich Gauss#1

MathematicsHistoryNumber theoryBeauty

About this quote

What does it mean?
Factoring numbers is a crucial and beautiful problem that has attracted great effort throughout history.
In plain terms
Number factoring is important and elegant.
What can you take from it?
Studying fundamental problems drives mathematical progress.

Where it applies

  • cryptography
  • academic research

Putting it to work

  • learn factoring algorithms
  • apply to security

Questions to consider

  • Why is factoring so valued?
  • How does elegance relate to usefulness?

Another view

Not all mathematical problems have practical impact.

More from Carl Friedrich Gauss

  1. The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it. But when a person …

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  2. It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhau…

    Permalink to quote #3
  3. 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 …

    Permalink to quote #4

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