Jump to ContentJump to Main Navigation
Circles DisturbedThe Interplay of Mathematics and Narrative$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 25 June 2022

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

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

Federica La Nave

Princeton University Press

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

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.