Joint PM/CO Grad Colloquium

Eric Boulter, Department of Pure Mathematics, University of Waterloo

"The Parallel Postulate: a 2000-year controversy"

Euclid's book The Elements was groundbreaking in its logical formulation of synthetic geometry, and it is profoundly influential to this day, as it is widely considered to be the most published non-religious book in human history. One small piece of this work bothered two thousand years worth of mathematicians: were all five postulates necessary for the logical structure of the book? In this talk we will introduce The Elements and the infamous parallel postulate, discuss its many failed proofs, and the 19th-century resolution of the mystery which led to the field of non-Euclidean geometry. We will end with a brief tour of non-Euclidean geometries, and a discussion of which the "real" geometry is. (Warning: a vague recollection of high school geometry may be required.) 

MC 5501