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Circles DisturbedThe Interplay of Mathematics and Narrative$
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Apostolos Doxiadis and Barry Mazur

Print publication date: 2012

Print ISBN-13: 9780691149042

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691149042.001.0001

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Deductive Narrative and the Epistemological Function of Belief in Mathematics

Deductive Narrative and the Epistemological Function of Belief in Mathematics

On Bombelli and Imaginary Numbers

Chapter:
(p.79) Chapter 3 Deductive Narrative and the Epistemological Function of Belief in Mathematics
Source:
Circles Disturbed
Author(s):

Federica La Nave

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691149042.003.0003

This chapter explores the epistemological function of belief in mathematical thinking by considering Rafael Bombelli's contribution to the creation of imaginary numbers. The discussion focuses on Bombelli's L'Algebra, which he wrote in 1550 in five books, three of them published in 1572. Over that period, Bombelli completely changed his mind about the solvability of the so-called irreducible case of cubic equations—that is, the case in which the solution of the cubic equation contains square roots of negative numbers—and about the nature of the numbers involved in such a solution. The chapter explains the evolution in Bombelli's thinking in those years: he initially believed that the irreducible case was insolvable and that the roots of negative numbers were unacceptable, but eventually made a complete turnaround. Bombelli's pursuit reflected his concept of algebra as a discipline that was no less speculative than geometry.

Keywords:   belief, Rafael Bombelli, imaginary numbers, L'Algebra, cubic equations, square roots, negative numbers, algebra, geometry

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