Document Type
Article
Program
Mathematics (Pitzer)
Publication Date
1-2009
Keywords
Joseph-Louis Lagrange, Euclidean geometry, Parallel postulate
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.
Rights Information
© 2009 Mathematical Association of America. All Rights Reserved.
Recommended Citation
Grabiner, Judith V. "Why Did Lagrange "Prove" the Parallel Postulate?" The American Mathematical Monthly 116.1 (January 2009): 3-18.
Comments
Please note that this paper won the Lester R. Ford Award in 2010.