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Why Did Lagrange 'Prove' the Parallel Postulate?

Award: Lester R. Ford

Year of Award: 2010

Publication Information: The American Mathematical Monthly, vol. 116, no. 1, January 2009, pp. 3-18.

Summary: Grabiner's exploration of understandings and beliefs concerning Euclidean geometry and the parallel postulate focuses on the questions of what Lagrange's proof was and why he took this approach, and why the problem was so important to him. In her discussion of these questions, the author explains that Lagrange was following Leibniz' -- principle of sufficient reason. One part of it says that something is true unless there is ample reason for it not being so. This insight leads to an exploration of the understanding of the nature of geometry and space in the seventeenth and eighteenth centuries, with mathematics, physics, philosophy, and art all being important to the story.

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About the Author: (From the Prizes and Awards booklet, MathFest 2010) 

Judith V. Grabiner is the Flora Sanborn Pitzer Professor of Mathematics at Pitzer College, one of the Claremont Colleges in California. She is the author of The Origins of Cauchy’s Rigorous Calculus (MIT Press,) The Calculus as Algebra: J. -L. Lagrange, 1736-1813 (Garland Press,) and a forthcoming book from the Mathematical Association of America, A Historian Looks Back: The Calculus as Algebra and Selected Writings. She also is the author of a Teaching Company DVD course called "Mathematics, Philosophy, and the 'Real World.'" Besides writing many articles about the history of mathematics and history of science, and receiving several Lester R. Ford and Carl B. Allendoerfer awards from the Mathematical Association of America, she won the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching in 2003.

MSC Codes: 
97A30
Author(s): 
Judith Grabiner (Pitzer College)
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Publication Date: 
Wednesday, August 11, 2010
Publish Page: 
Summary: 
Grabiner's exploration of understandings and beliefs concerning Euclidean geometry and the parallel postulate focuses on the questions of what Lagrange's proof was and why he took this approach, and why the problem was so important to him. In her discussion of these questions, the author explains that Lagrange was following Leibniz' -- principle of sufficient reason. One part of it says that something is true unless there is ample reason for it not being so. This insight leads to an exploration of the understanding of the nature of geometry and space in the seventeenth and eighteenth centuries, with mathematics, physics, philosophy, and art all being important to the story.

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