Book Review: Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics, 1869–1926, Volume 50, Number 6

Among historians of mathematics Thomas Hawkins has long been regarded as the leading authority on the early history of Lie groups. After decades of work on this fascinating theme, he has synthesized the fruits of his labors in this 564-page Essay in the History of Mathematics, a landmark study that represents the culmination of his contributions to the field. In recognition of these accomplishments , the AMS recently named Hawkins its first recipient of the prestigious Whiteman Prize for exceptional scholarly writing on the history of mathematics (see the citation and Hawkins's response in Notices 48 (2001), 416–7). Having followed his work for many years, I would like to take this opportunity to congratulate the recipient and to commend the AMS committee that nominated him for this award; Hawkins richly deserves this high distinction. The committee's citation also somewhat relieves me from the strain of finding appropriate superlatives to describe the present book, which requires no further personal endorsement. Hawkins's " essay " sets sharp temporal boundaries spanning the period from 1869, when Lie's earliest work appeared, up to Weyl's classic papers from 1925 to 1926, along with a clearly stated goal. In the preface he calls his book " both more and less than a [comprehensive] history of the theory of Lie groups ". Less, because it deals primarily with the origins of the theory and those parts of it pertaining to the structure of Lie groups and Lie algebras. More, because he has a broader agenda in mind that goes beyond the challenge of weaving together the threads of this complicated story. Historians, at least traditionally, are supposed to be good storytellers, but serious history usually has a larger purpose in mind. Crudely put, historians try to understand the past by explaining why certain things happened the way they did. Hawkins set himself the challenge of trying to understand what motivated the principal actors who contributed to what eventually became known as the theory of Lie groups. He wants to tell us not just what happened but why, by showing how the relevant mathematical developments were influenced by the specific contexts in which this work was un-dertaken. What makes his book such impressive reading is that he never loses sight of this goal, despite all the obstacles involved, including the David E. Rowe is professor of the history of mathematics and natural sciences at Mainz University. His email …