MAA Writing Awards
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.
Read the Article (Note this is a large file: 6,415 KB)
About the Author: (From the Prizes and Awards booklet, MathFest 2010)