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Mathematics without ApologiesPortrait of a Problematic Vocation$
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Michael Harris

Print publication date: 2017

Print ISBN-13: 9780691175836

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175836.001.0001

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How to Explain Number Theory at a Dinner Party

How to Explain Number Theory at a Dinner Party

Chapter:
Chapter β‎.5 How to Explain Number Theory at a Dinner Party
Source:
Mathematics without Apologies
Author(s):

Michael Harris

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175836.003.0009

This chapter discusses transcendental numbers. The first transcendental number was exhibited by Joseph Liouville in 1844; it was a number λ‎ he concocted for just that purpose, but it answers the question,“Are there any transcendental numbers? ”, and therefore certainly qualifies as a number. The statement that Liouville “exhibited” the number means that he wrote down a description and used this description to show that there is no polynomial f for which f(λ‎) = 0. If all transcendental numbers were as artificial as Liouville's λ‎, transcendence would never have grown into a mathematical theory. Methods were soon developed, however, to show that some familiar numbers are transcendental.

Keywords:   mathematicians, number theory, transcendental numbers, Joseph Liouville

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