“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.”
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)
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Lucio Russo 9
Italian historian and scientist 1944Related quotes

Quoted in Hilbert's Die Grundlagen der Mathematik (1927)

Report on the Theory of Numbers (1859) Part I, p. 49.
The Collected Mathematical Papers of Henry John Stephen Smith (1894) Vol. 1
Source: Business Systems Planning and Business Information Control Study: A comparison, 1982, p. 31

Source: A Mathematical Theory of Systems Engineering (1967), p. 3.

Mathematics Magazine, Vol. 23-24. (1949), p. 161
Context: Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. Then, in the alleged proof, be alert for inexplicit assumptions. Euclid's notorious oversights drove this lesson home.
“Only by a study of the development of mathematics can its contemporary significance be understood.”
100 Years of Mathematics: a Personal Viewpoint (1981)
Context: The professional mathematician can scarcely avoid specialization and needs to transcend his private interests and take a wide synoptic view of the whole landscape of contemporary mathematics. His scientific colleagues are continually seeking enlightenment on the relevance of mathematical abstractions. The undergraduate needs a guidebook to the topography of the immense and expanding world of mathematics. There seems to be only one way to satisfy these varied interests... a concise historical account of the main currents... Only by a study of the development of mathematics can its contemporary significance be understood.
100 Years of Mathematics: a Personal Viewpoint (1981)

Editor's Introduction, The Teaching of Elementary Mathematics https://books.google.com/books?id=NKoAAAAAMAAJ (1906) by David Eugene Smith