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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.311) Chapter δ‎ 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/9780691175836.003.0015

This chapter continues the discussion began in Chapter α‎. It presents the fourth and final part of author's response to the question, “What is it you do in number theory, anyway?” Here he deals with the Birch–Swinnerton–Dyer (BSD) conjecture. The BSD conjecture was the guiding problem for the first part of his career and has the distinction of being one of the seven Clay Millenium Prize Problems, whose solution carries a million dollar price tag. The BSD conjecture is an attempt to discern order in the apparently unpredictable nature of solutions to elliptic curves, following Hasse's theorem, which places strict limits on the numbers of approximate solutions for varying p.

Keywords:   mathematicians, number theory, dinner party, Birch–Swinnerton–Dyer conjecture, order, randomness, elliptic curves

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