“The payment for writing a book review is getting to keep the book? … But what if it is a bad book?” My 11-year-old learned several truths about academic publishing while I was reading this 937-page brick of a volume. Fortunately for both of us, though, Helmholtz is emphatically not a “bad book.” Rather, David Cahan (University of Nebraska–Lincoln) has prepared the work of a career, collecting what must be nearly every known detail about the life of the German scientist and intellectual, Hermann von Helmholtz (1821–1894). He seemingly effortlessly weaves together Helmholtz’s family life, education, academic positions, organizational and political involvements, roles in establishing and administrating institutions, and efforts to popularize recent developments in science. Helmholtz was also an accomplished theorist who is known for stating the law of conservation of energy, testing accepted conclusions in the laboratory, doing pioneering work on vision and sound — partly utilizing instruments he invented himself — explaining non-Euclidean geometry, discovering equations useful for hydrodynamics and thermodynamics, and joining in debates over increasing tensions in classical physics, coming down on the side supporting the existence of the ether.
While I wholeheartedly recommend this book for anyone who wants to know more about Helmholtz and the staggeringly large number of 19th-century intellectual giants with whom he interacted, I do caution that mathematical readers may not find Helmholtz’s mathematics discussed in as much depth as they desire. Of course, Helmholtz was a polymath who was active in multiple disciplines, and there is only so much space for each one, even in a book of this length. Additionally, a significant portion of his mathematical contributions happened in the 1840s and 1850s, so most of the coverage of them appears in the opening chapters of Part II of Cahan’s biography. Toward the end of Part II, about two-fifths of Chapter 15, which explores Helmholtz’s activities in the late 1860s while he was angling to succeed Julius Plücker at the University of Bonn, traces the publication and reception of two papers on the foundations of geometry, as well as Helmholtz’s disputes with William Stanley Jevons and others about alternative systems of geometry. Cahan credits Helmholtz with educating English and German readers on the principles of non-Euclidean geometry and provides a thorough outline of his 1876 published lecture, “The Origin and Meaning of Geometrical Axioms.” Sofia Kovalevskaia also appears briefly at the beginning of this chapter.
The main thing I wished for in reading this book was a chronology to use for reference since the timelines for different aspects of Helmholtz’s life necessarily overlapped. As far as I could tell, Cahan’s use of evidence — which is drawn from a dazzling array of published and manuscript primary sources — is appropriate, sufficient, representative, and faithful. By weaving together the many threads of Helmholtz’s career, he demonstrates an interest in current trends in biography-writing, although I did not see much use of the approaches to historical interpretation often utilized in that scholarship. Similarly, the conclusions tend to be straightforward instead of ground-breaking. Indeed, Cahan sees his contribution as overcoming earlier hagiographic treatments of Helmholtz. His writing style is readable, accessible, and informative, and the copyediting and layout are professional.
Helmholtz was well worth the time required to read it.
Amy Ackerberg-Hastings is an independent scholar who trained in the history of technology and science at Iowa State University and whose interests include mathematical and scientific contexts in 18th- and 19th-century Europe, particularly in relation to university education, Euclidean geometry, scientific instruments, and women as creators and consumers of knowledge.