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Symbols and Things

Kevin Lambert
University of Pittsburgh Press
Publication Date: 
Number of Pages: 
[Reviewed by
Peggy Aldrich Kidwell
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Historians of mathematics and mathematicians are more interested in the statement and transmission of mathematical ideas than in how these ideas were incorporated into physical documents. In this volume, historian of science and mathematics Kevin Lambert seeks to shift this emphasis. He examines the “materiality” of mathematics as represented on paper in nineteenth century Britain, particularly paper associated with university mathematicians. Thus he traces the roots of textbook traditions, starting with classical texts such as Euclid’s Elements and manuals of arithmetic published in eighteenth century Britain for use by practical people to volumes for collegiate instruction such as Augustus de Morgan’s Elements of Arithmetic. Lambert then considers almanacs and problem-solving journals as antecedents of later more specialized journals such as the Cambridge Mathematics Journal. He considers how traditions of exchange fostered by museums shaped works on algebra such as Charles Babbage’s unpublished but widely circulated “Essays on the Philosophy of Analysis” and an article on the history of arithmetic published by George Peacock in The Encyclopedia Metropolitiana.
Lambert also considers how mathematical libraries shaped the intellectual lives of nineteenth century British mathematicians.  These ranged from lending libraries for working class patrons such as George Green and George Boole to the extensive personal library of Augustus de Morgan. The final section of the book focuses on the use of documents in creating mathematical ideas. We read of James Clerk Maxwell’s careful drawings of electromagnetic fields, of William Thomson’s systematic recording of his ideas in notebooks, and of the correspondence of Peter Guthrie Tait and William R. Hamilton on quaternions, particularly as it was assembled and stored by Tait.
Lambert’s decision to focus on paper documents will not surprise most mathematicians and historians of mathematics. Museum people aware of Maxwell’s supervision of the construction of three-dimensional models, of Tait and J.J. Sylvester’s admiration of mechanisms (particularly three-dimensional models of linkages), and of Babbage’s fascination with the construction of computing devices might wish that he took a wider view of “materiality.” On the other hand, at a time when documents written on paper are increasingly giving way to electronic records, it may be well to tell intriguing stories about an age of newly inexpensive paper.
Peggy Aldrich Kidwell is curator of mathematics in the Division of Medicine and Science of the Smithsonian’s National Museum of American History.  Trained in physics and the history of science, she is has written on mathematical objects from blackboards to electronic calculators.