Why Did Lagrange "Prove" the Parallel Postulate?
Author: Grabiner, Judith V.
Source: American Mathematical Monthly, Volume 116, Number 1, January 2009 , pp. 3-18(16)
Publisher: Mathematical Association of America
Abstract:In 1806, Joseph-Louis Lagrange read a memoir "proving" Euclid's parallel postulate to the Institut de France in Paris. The memoir still exists in manuscript, and we'll look at what it says. We ask why he tried to prove the postulate, and why he attacked the problem in the way that he did. We also look at how the ideas in this manuscript are related to such things as Lagrange's philosophy of mathematics, artists' ideas about space, Newtonian mechanics, and Leibniz's Principle of Sufficient Reason. Finally, we reflect on how this episode changes our views about eighteenth-century attitudes toward geometry, space, and the nature of science.
Document Type: Research Article
Publication date: January 2009
- American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. AMM readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels.
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