
Published online:
24 May 2018
Published in print:
30 May 2017
Online ISBN:
9781400885527
Print ISBN:
9780691175836
Contents
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Third Session: Congruences Third Session: Congruences
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Chapter
γ How to Explain Number Theory at a Dinner Party
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Pages
259–264
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Published:May 2017
Cite
Harris, Michael, 'How to Explain Number Theory at a Dinner Party', Mathematics without Apologies: Portrait of a Problematic Vocation (Princeton, NJ , 2017; online edn, Princeton Scholarship Online, 24 May 2018), https://doi.org/10.23943/princeton/9780691175836.003.0012, accessed 21 Apr. 2025.
Abstract
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
Subject
Logic
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