## Reviews of John Herivel's books

John Herivel wrote three books on the history of mathematics, two of which have been reviewed by a large number of reviewers. Below we give short extracts from a number of these reviews, attempting to give the flavour of the review in these extracts. Herivel also published

*Herivelismus and the German Military Enigma*(M & M Baldwin, 2008) which described his codebreaking work at Bletchley Park during the Second World War deciphering the German Enigma machine cipher. We choose not to quote from reviews of this recent book.**The Background to Newton's Principia. A study of Newton's dynamical researches in the years 1664-84 (1965), by John Herivel.**

**1.1. Review by: Robert Kargon.**

*Isis***57**(3) (1966), 403-404.

The appearance of John Herivel's welcome effort, The Background to Newton's Principia, is in itself a commentary upon the increasing maturity of the history of science as a scholarly discipline. It may seem shocking to historians in other areas that Herivel's book is the first extended and systematic look at Newton's dynamical manuscripts; to historians of science, the book may serve as a pathfinder. As Derek Whiteside has pointed out, it is only recently that Newtonian scholar- ship has turned to a careful examination of his vast manuscript remains. Perhaps now, after Herivel, we will have an increasing number of studies in depth on other areas of Newton's achievement: optics, mathematics, chemistry. ... as Herivel demonstrates, the key to an understanding of the seventeenth century's greatest scientist lies in the manuscript record. In his preface, Herivel promises the reader " some sort of connected account of the growth of Newton's dynamical thought prior to the composition of the Principia," through an interpretation and ordering of the documentary evidence. The format of the book especially lends itself to this task; it is a format increasingly being adopted in many areas of historical study. ... This book will be basic reading for further study of Newton's dynamical thought.

**1.2. Review by: Morris Kline.**

*Mathematical Reviews*, MR0234794**(38 #3108)**.

This book offers the history of Newton's development of those dynamical concepts which he incorporated in Book I of his classic*Principia*. The author describes what Newton learned from the work of Galileo, Descartes and Huygens, but the main contribution of the book is an examination of all of Newton's manuscripts on the basic concepts of dynamics, manuscripts that are now housed in the Portsmouth collection of the Cambridge University Library. ... Beyond the interesting account of how Newton gradually sharpened his own ideas, the author shows that Newton derived the formula for centrifugal force before Huygens did and that Newton did ultimately appreciate that centripetal rather than centrifugal force is the real force. He also weighs the available information on whether Newton appreciated the law of universal gravitation of mutual attraction, as opposed to a one-way force exerted, for example, by the sun on the earth, before Hooke enunciated the universal law of mutual attraction. ... the book is a very positive contribution to the history of dynamics at least insofar as Newton's thinking during the period 1664-1684 is concerned.

**1.3. Review by: Richard S Westfall.**

*Science, New Series***152**(3724) (1966), 915.

A good decade of research on the Portsmouth manuscripts by various scholars has made it possible for Herivel to publish ... all of the sources that bear on the development of Newton's dynamics until the composition of the 'Principia'. The past few years have witnessed the publication of several Newtonian manuscripts ... Herivel's volume can legitimately take its place beside them. ... Some aspects of the work are more difficult to appreciate. When Herivel is not concerned with editing and analysing individual documents, that is to say when he undertakes to explore in a connected essay the very topic promised in the title, the quality of the volume declines markedly. Indeed I can only say that Herivel's approach to dynamics in the 17th century lacks historical perspective. ... Perhaps the discussion is nowhere more disappointing than when Herivel takes up the subject of force. The volume is devoted to the development of Newton's dynamics, and the concept of force was the very heart of his contribution to the science. Herivel does not discuss the concept of force before Newton. He does not seriously examine the difficulties in Newton's concept, difficulties that one might expect to find illuminated by the record of their development. Much of the discussion appears to assume that the concept of force was the common property of the entire 17th century.

**1.4. Review by: E J Aiton.**

*The British Journal for the History of Science***3**(3) (1967), 298-299.

Although the documents in the Portsmouth Collection had been catalogued when Rouse Ball wrote his classic Essay on Newton's Principia, it is only recently that the extent and importance of this source material have been recognized. In The Background to Newton's Principia, John Herivel presents a study of the development of Newton's dynamical thought based firmly on the manuscripts. The work is divided into two parts; the second part, occupying more than half the volume, is devoted to the publication of the manuscripts, in some cases for the first time. In each case the text is followed by two sets of notes, one textual, the other explanatory, and where the original is in Latin, a translation is provided. Herivel's study of Newton's dynamical thought, set out in the first part of the work, takes the form of an extended commentary on the manuscripts, including an attempt to determine the order and dates of composition. The manuscripts themselves fall into two sets; the first set contains Newton's early dynamical researches, a field largely neglected by Rouse Ball but explored in detail by Herivel, while the second set, written mainly in 1684 and 1685, concerns the more familiar story of the composition of the Principia.**Joseph Fourier: The Man and the Physicist (1975), by John Herivel.**

**2.1. Review by: Eugene Frankel.**

*American Scientist***64**(3) (1976), 351.

Herivel presents a much-needed full-length account of Fourier's turbulent life, a shorter description of Fourier's contributions as a theoretical physicist, and English translations of 28 letters written by Fourier to colleagues at various times in his career. Herivel deliberately chooses not to discuss Fourier's influence on mathematics, leaving that for the mathematicians and the historians of the subject. "Fourier the man" is clearly the better half of the book. Herivel has done a great deal of extremely thorough background and biographical research and has un earthed important details concerning the major events in Fourier's life: his early education, various activities (including two arrests, one by the Left and one by the Right) during the Revolution, his secretaryship of the Cairo Institute during and after Napoleon's Egyptian campaign, his prefecture at Is re for eleven years under the Emperor, his return to Paris in 1815, and his election as secretary to the Academy of Sciences in 1822. ... If Fourier can indeed be classified as a physicist - and I feel he more appropriately belongs with the applied mathematicians like Laplace, Poisson, and Cauchy than with physicists such as Fresnel and Ampere-some discussion of the important developments in early 19th-century French physics would seem appropriate. In any event, Fourier's obvious debt to rational mechanics in general and to Lagrange's analytical mechanics in particular should have at least been mentioned. These lacunae, along with Herivel's obsession with details and dense prose style, made this section far less successful than the biographical one.

**2.2. Review by: Thomas L Hankins.**

*Science, New Series***189**(4199) (1975), 279.

It is a matter of great good fortune that Fourier's famous 'Analytical Theory of Heat' reached the light of day. Now recognized as a masterpiece of mathematical analysis and theoretical physics, it was not highly admired by the leading mathematicians at the Academy of Sciences, Laplace, Lagrange, Poisson, and Biot. They seemed to be unable to recognize Fourier's merit and worked to delay, if not actually to prevent, the publication of his work. As if this were not obstacle enough, the guillotine almost took Fourier before he even began his research. He survived because his great administrative skills were in demand and because he was able to change sides deftly as the Revolution oscillated between terror and reaction. Even so, he was in prison twice during the Terror and twice afterward. He would almost certainly have been guillotined if Robespierre had kept his head for a few more days. ... The drama of this story comes out well in Herivel's straightforward reporting of it. By careful scholarship he has made it much more complete than any previous account, and he has resolved some of the ambiguities in Fourier's own recollections. Fourier always seemed to be explaining his actions after the tide of battle had turned, and it was frequently necessary for him to colour the facts a bit. ... Herivel has chosen to divide his biography into two parts: Fourier the man and Fourier the physicist. The two parts are not very well matched. The reader who has enjoyed the biographical section may find himself in difficulty when he comes to the section on Fourier's scientific work, particularly if he is not already familiar with the 'Analytical Theory of Heat'. Herivel has wished to avoid duplicating the work on Fourier's mathematics done by Ivor Grattan-Guinness and others, and has therefore limited his treatment to Fourier the physicist. But since the physics and mathematics are so closely related the exclusion of mathematics produces some awkwardness.

**2.3. Review by: Richard Olson.**

*Isis***67**(4) (1976), 651-652.

This, the second English-language biography of Fourier in three years, provides a valuable and interesting contribution to our understanding of one of the greatest mathematical physicists of modern times. Focusing on biographical detail and on the physical side of Fourier's work, it complements rather than duplicates Ivor Grattan-Guinness' 'Joseph Fourier: 1768-1830' (1972), which emphasized Fourier's mathematical work and provided only a brief and relatively uncritical biography. In addition, as one of a series of recent biographies of French exact scientists born in the eighteenth century, it enriches our knowledge of a remarkably fruitful period for French mathematics and physics. John Herivel maintains the high standards of scholarship and literacy which characterize such work as Thomas Hankins' 'Jean D'Alembert: Science and Enlightenment' (1970), Charles C Gillispie's 'Lazare Carnot: Savant' (1971), and C Stewart Gillmor's 'Coulomb and the Evolution of Physics and Engineering in Eighteenth Century France' (1971), but his book shares and even intensifies the disturbing tendency of these works to separate and compartmentalize rather than to integrate the lives and various aspects of the activity of their subjects. In his introduction Herivel explicitly justifies his decision to forego attempting "that fully integrated biographico-scientific study of which historians of science sometimes dream" and to "make a clean division into two parts, Part I on Fourier the Man, and Part II on Fourier the Physicist." One of his reasons is that Fourier began his major work on heat only around 1804, after an exciting if not terribly significant series of careers as mathematics teacher, minor revolutionary, political prisoner, student of Egyptian culture, and civil administrator under both Napoleon and Louis XVIII. Thus, there seems a natural separation of Fourier's life into an early non-physicist portion and a later physicist portion. Furthermore, Herivel has self-consciously chosen to de-emphasize a third Fourier - "Fourier the mathematician," who could unite the earlier and later man-because he has been thoroughly discussed by others (presumably by Grattan-Guinness). ... Herivel's biographical sections are admirable. They portray a man much more complex and interesting than that paragon of all virtues portrayed by Grattan-Guinness and Cousin; a man who may not simply have been forced into political service but who was both academically and politically ambitious, a man who understandably made enemies ... as well as friends.

**2.4. Review by: L Bucciarelli.**

*The British Journal for the History of Science***10**(3) (1977), 270-271.

When the name Joseph Fourier is mentioned, one is more likely to think of series, of transforms or of equations describing the propagation of heat in solids, than of a young man caught up in the complexities of a revolution, of a companion to Napoleon on an ill-fated excursion to Egypt, or of an excellent administrator serving the Emperor in a rural setting away from Paris. In the eyes of posterity, the names of those responsible for significant work in science have customarily come to be little more than labels identifying the evolution and fate of their productions. Rarely has the scientist as a person received full attention, and more rarely still in a form that integrates his life and technical work. In 'Joseph Fourier, the man and the physicist', John Herivel has attempted to reconstruct a more complete Fourier; to render account of his subject's rich and varied life experiences as well as his scientific achievements. Yet this is no grand synthesis, for the author chooses to disconnect the man from the physicist, presenting the reader with essentially two books in one. ... Though this is not the definitive biography (the author forewarns the reader that this is not his intent), and although the dissection of the subject into two parts abandons to the reader the task of moulding a coherent vision of Joseph Fourier, John Herivel has produced an accurate, richly detailed and reasonably complete study of one of France's finest physicists.**Joseph Fourier: face aux objections contre sa théorie de la chaleur (1980), by John Herivel.**

**3.1. Review by: Louis Charbonneau.**

*Mathematical Reviews*, MR0636934**(83f:01017)**.

The author documents Fourier's reaction to the criticism by some members of the Parisian scientific community of his first memoir on heat propagation, presented to the Paris Academy of Science in 1807, and his later memoir of 1812. The documents include eight letters of Fourier, and ten manuscripts by Fourier, Laplace, Biot, and Poisson that help to clarify the contents of the letters.