Arguments on motivation in the rise and decline of a mathematical theory; the ''Construction of equations'', 1637 - ca. 1750
type: Item
instance of: scholarly article
title: Arguments on motivation in the rise and decline of a mathematical theory; the ''Construction of equations'', 1637 - ca. 1750
zbMATH Open document ID: 0552.01005
DOI: 10.1007/BF00328124
published in: Archive for History of Exact Sciences
publication date: 1984-01-01T00:00:00Z
review text: Die folgende originale Einleitung des Autors gibt anhand des Beispiels der Konstruktion gewisser Gleichungen eine Darstellung der Motive für den geschichtlichen Aufstieg und Abstieg mathematischer Theorien: ''Between 1650 and 1750 the 'construction of equations' was a recognized area of mathematical research and a standard subject in books on algebra. The equations were polynomial equations in one unknown; 'constructing' such an equation meant performing a geometrical construction yielding line segments with lengths equal to the roots of the equation. - The subject is now forgotten; it fell into oblivion shortly after 1750. But in the seventeenth century it was considered a crucial technique within analytic geometry, and it was developed by top-ranking mathematicians. In the present study I shall describe the rise and decline of the subject. I shall devote particular attention to the arguments which various mathematicians used to motivate their studies about the construction of equations or to argue against the work of others. From these arguments it will appear that the rise and decline of the construction of equations fits into a general line of development in mathematics in the period, namely the receding of the geometrical conception of mathematical entities and operations, and the emergence of an analytic style in which the main interest focused on formulas and the manipulations performed on them. A discussion of the arguments on motivation will also shed light on the particular process of decline that occurred in the case of the construction of equations, and thus it may contribute to the understanding of processes of development of separate sectors of science. The story of the construction of equations provides an interesting test case for ideas about 'degenerating' research programs which have been put forward by Lakatos and other philosophers and historians of science.''
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 01A50
zbMATH DE Number: 3878877
zbMATH Keywords: polynomial equations in one unknown
zbMATH Keywords: geometrical conception of mathematical entities
zbMATH Keywords: analytic style
author: Henk Bos
reviewed by: Karl Strubecker
MaRDI profile type: Publication
cites work: On the representation of curves in Descartes' geometrie
cites work: Q3236661
cites work: The death of a mathematical theory. A study in the sociology of knowledge
cites work: Towards a Theory of Mathematical Research Programmes (I)
cites work: Q4149431
cites work: Q5680066
cites work: Q3849856
full work available at URL: https://doi.org/10.1007/bf00328124
OpenAlex ID: W1995456499
description: scientific article; zbMATH DE number 3878877