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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

(p.109) Chapter β‎ How to Explain Number Theory at a Dinner Party
Mathematics without Apologies

Michael Harris

Princeton University Press

This chapter continues the discussion began in Chapter α‎. It presents the second 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 equations of degree 3 (or 4) in one variable or degree 2 in two variables. He says that if we are willing to allow square roots into our arithmetic, we can consider the quadratic equation a problem whose solution has been long understood (in some cases by the ancient Babylonians). Equations of degree 3 and 4, such as x3 − 2x2 + 14x + 9 and x4 + 5x3 + 11x2 + 17x − 29, were first solved in Renaissance Italy to great acclaim; the solutions are given by formulas involving cube roots and fourth roots.

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

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