The tangled origins of the Leibnizian calculus. A case study of a mathematical revolution (Q2898739)

The author of the book under review aims at five goals: NEWLINE{\parindent=7mmNEWLINE\begin{itemize}\item[1)]He would like to give an accurate account of Leibniz's creation and development of the calculus. NEWLINE\item[2)]He would like to understand the results of Leibniz and his contemporaries from their perspective. NEWLINE\item[3)]He attempts to fit some of Th. Kuhn's and Fleck's theses into the history of mathematics. NEWLINE\item[4)]He attempts to show how a particular aspect of 17th century nonmathematical, cultural environment influenced the technical characteristics of Leibniz's mathematics. NEWLINE\item[5)]He tries to give a new interpretation of Leibniz's infamous priority dispute with Newton by combining it with certain aspects of his character.NEWLINENEWLINE\end{itemize}}NEWLINEBrown draws two global conclusions: NEWLINE{\parindent=7mmNEWLINE\begin{itemize}\item[1)]Leibniz benefited from a contemporary nonmathematical intellectual climate. NEWLINE\item[2)]His invention shows that mathematics is a contingent, evolving, perishable, historical product.NEWLINENEWLINE\end{itemize}}NEWLINEAccording to his second goal he criticizes J. E. Hofmann's way of writing Leibniz's results in modern form because Leibniz thought about problems differently than we do. He speaks about different mathematical worlds belonging to different periods of time and emphasizes the difference between their thought styles. In spite of this criticism Brown sometimes does exactly the same saying (p.~40) ``we give the essentials of the argument using the modern algebraic representation of the parabola'' or (p. 90) explaining the transmutation theorem ``In our notation this is\dots'' etc.NEWLINENEWLINENEWLINE NEWLINEReviewer's remark: Unfortunately the book has been carelessly edited. There are many, in fact hundreds of mistakes that continuously distort proper names, titles, especially Latin citations etc.: Grégorie de Sainte Vincent (p.~5), Gregory St. Vincent (p.~149) instead of Grégoire de St. Vincent, Ludwik (!) Fleck allegedly wrote ``Entstehung and Entwicken einer wissenshaftlichen Tatsache: Einführung in die lehr Denkstil and Denkkollective'' (p.~9), exercitiationes (p.~38), Specimen quaetinem (p.~70), trinitatus (p.~74), Hypotheses physica nova (p.~79), Hobbes and Wallace (p.~295: Wallis is meant), etc. Very often English words are lacking, superfluous or erroneously doubled. Publications are attributed to false authors: Hofmann 1974b has been written by E. Knobloch etc.NEWLINENEWLINE Many historical statements are false because the author does not know the relevant original or secondary literature: ``In 1675 he probably did not know that \(d(xy)=xdy+ydx\)'' (p. XII). Leibniz found this result on November 21, 1675, his manuscript has been published by Gerhardt in 1848. Leibniz did not find Cramer's rule in 1678 (p. 181) but in 1684. The relevant treatise was published in 1972 etc.NEWLINENEWLINE But the worst of it is that the author completely ignores any German language publication on Leibniz and his work though a large number of the most important contributions to the research regarding Leibniz is written in this language. Moreover many German authors have published their results in English or French, too. They do not exist in the closed world of the author. Such an ignorance is an unacceptable offense.