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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:
(p.259) Chapter γ‎ 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/9780691175836.003.0012

This chapter continues the discussion began in Chapter α‎. It presents the third part of author's response to the question, “What is it you do in number theory, anyway?” Working his way up to the guiding problem of the Birch–Swinnerton–Dyer conjecture, here he deals with congruences, specifically how to count solutions to congruences. The story of congruences is that a problem where the variables can take infinitely many values can be replaced by one in which the variables can take only finitely many values, and it is sometimes enough to solve the latter problem in order to solve the former.

Keywords:   mathematicians, number theory, dinner party, Birch–Swinnerton–Dyer conjecture, congruences

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