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Sir William Rowan Hamilton

Thomas L. Hankins
Johns Hopkins University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Patricia R. Allaire
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Originally published in 1980, Thomas L. Hankins' Sir William Rowan Hamilton has been reissued in paperback by the Johns Hopkins University Press. Reviewers at the time of publication were enthusiastically positive, and it is not our intention here to review the work, but rather to re-view it. Although 25 years old, Hankins' Hamilton remains as important a contribution to history of mathematics as when it was first published.

There are three major secondary sources of information about Hamilton (1805-1865): Robert P. Graves' 3-volume Life of Sir William Rowan Hamilton (1882, 1885, 1889), Hankins' volume, and (slightly) more recently, Seán O' Donnell's William Rowan Hamilton: Portrait of a Prodigy (1983). Although Graves does include biographical material, his work consists mainly of selections from Hamilton's poetry, correspondence and other papers, and is thus closer to being a primary source. O'Donnell is emphatic that his work is not a competitor to Hankins', describing his own volume as "an attempt... to further an understanding of the individual rather than what he did."

But it should not be inferred that Hankins ignores Hamilton the man. We see not only Hamilton's work in optics, dynamics, and mathematics but also his philosophy, his poetry, and his professional and personal life. All these are intertwined and interpreted in the context of Victorian science in Ireland. The ten-page bibliographical essay is far richer than an itemized bibliography could ever be.

Mathematicians are most interested in Hamilton's creation (discovery, perhaps?) of quaternions. Once he represented complex numbers as number couples and interpreted them geometrically using perpendicular axes in a plane, the next logical step seemed to be number triples interpreted geometrically using three mutually perpendicular axes in space. Hankins describes in full mathematical detail Hamilton's long and fruitless quest for triples having the properties he desired. It is enthralling to watch each attempt and to see how Hamilton's effort to fix what was "wrong" brought him ever closer to that final step — quaternions. Quaternions, which fulfill all field properties save commutativity under multiplication, were a crucial factor (arguably the crucial factor) in freeing algebra from its ties to arithmetic.

The questions to ask about Hankins' Hamilton 25 years after its original publication are, "Has it been supplanted?" and "Is it worth the challenging read?" The answers are emphatically "No " and "Yes!" respectively.

Pat Allaire ( is Associate Professor of Mathematics and Computer Science at Queensborough Community College, CUNY and serves as secretary of the Canadian Society for History and Philosophy of Mathematics.

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