Article ID: CBB994897235

Duncan F. Gregory, William Walton and the Development of British Algebra: ‘Algebraical Geometry’, ‘Geometrical Algebra’, Abstraction (2016)

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This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.

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Authors & Contributors
Becher, Harvey W.
Bachelard, S.
Wilson, Nancy
Hankins, Thomas L.
Pycior, Helena M.
Bloor, David
Journals
Historia Mathematica
Actes du ... Congrès International d'Histoire des Sciences
Studies in History and Philosophy of Science
Sciences et Techniques en Perspective
Revue d'Histoire des Sciences
Notes and Records: The Royal Society Journal of the History of Science
Publishers
Vandenhoeck & Ruprecht
American Mathematical Society
Concepts
Algebra
Mathematics
Arithmetic
Philosophy of mathematics
Algebraic geometry
Number theory; number concept
People
Peacock, George
Hamilton, William Rowan
Babbage, Charles
Gregory, Duncan Farquharson
Herschel, John Frederick William
Woodhouse, Robert
Time Periods
19th century
20th century, early
18th century
Places
British Isles
Great Britain
Institutions
Cambridge University
Analytical Society
University of Chicago
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