“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.”

Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum tum veterum tum recentiorum industriam ac sagacitatem occupavisse, tam notum est, ut de hac re copiose loqui superfluum foret. … [P]raetereaque scientiae dignitas requirere videtur, ut omnia subsidia ad solutionem problematis tam elegantis ac celebris sedulo excolantur.
Disquisitiones Arithmeticae (1801): Article 329

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors…" by Carl Friedrich Gauss?
Carl Friedrich Gauss photo
Carl Friedrich Gauss 50
German mathematician and physical scientist 1777–1855

Related quotes

David Hilbert photo
Marcus du Sautoy photo
Bill Gates photo

“The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.”

Source: The Road Ahead (1995), p. 265 in hardcover edition, corrected in paperback

Henry John Stephen Smith photo
Augustus De Morgan photo
Elinor Ostrom photo
Mike Rosen photo
Lucio Russo photo

“Euclid … manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.”

Lucio Russo (1944) Italian historian and scientist

2.4, "Discrete Mathematics and the Notion of Infinity", p. 45
The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (2004)

Joseph Louis Lagrange photo

Related topics