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.
Wilson, Nancy
Wilkes, M. V.
Waerden, Bartel Leendert van der
Verburgt, Lukas M.
Pycior, Helena M.
Concepts
Algebra
Mathematics
Philosophy of mathematics
Arithmetic
Science and culture
Algebraic geometry
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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