Recent zbMATH articles in MSC 01A50https://zbmath.org/atom/cc/01A502024-03-13T18:33:02.981707ZWerkzeugUnderground mathematics. Craft culture and knowledge production in early modern Europehttps://zbmath.org/1528.010022024-03-13T18:33:02.981707Z"Morel, Thomas"https://zbmath.org/authors/?q=ai:morel.thomasIn the book under review, the author, professor in the history of mathematics and its teaching at the Bergische Universität Wuppertal, focuses on the origins and evolution of \textit{Markscheidekunst} from its origins up to the beginning of the nineteenth century. Mathematics, technology, politics, economics and history are combined to the pleasure of the readers in order to lift the veil on a neglected domain of practical mathematics, so fundamental to the economy of the Holy Roman Empire: \textit{Markscheidekunst}. This is the German term for `` `the art of setting limits'. Concretely, it encompassed all measuring operations used in the delimitation of concessions and in the daily running of metal mines'' (p.~5). Thus, the \textit{Markscheider} is the surveyor, who has to determine boundaries between mining concessions. Differences between \textit{Markscheidekunst} and classical surveying exist because of boundaries underground: it is precisely the main objective of the subterranean geometry, born in the mining pits of the Holy Roman Empire. This ``discipline fell outside of the academic geometry of its time, and vastly differed from the deductive implementation of theories that early modern scholars labeled `applied' or `mixed' mathematics'' (p.~5). The author points out that ``the history of subterranean geometry illustrates the growing reliance on numbers and geometric figures in civil society at large'' (p.~6), and he tries to clarify the tortuous relationships between scholars and practitioners. Hence, the book under review provides a very interesting insight into the general history of mathematics, and into the history of the mathematization of nature.
The book is scholarly, really well-edited and well-illustrated, which doesn't spoil anything. The reading is very comfortable. In addition, numerous footnotes and an impressive 28-page bibliography (pp.~253--280, with three sections: primary sources, printed primary sources and secondary sources) make for in-depth reading. The unique index (pp. 281--292) -- bringing together the index \textit{nominum}, \textit{locorum}, \textit{rerum} and \textit{verborum} -- is very useful.
The author divides his book into seven chapters. In the first chapter ``Of scholars and miners'' (pp.~20--49), focusing on treatises from two humanist Renaissance scholars: the \textit{De re metallica} written by Agricola (1494--1555) and the \textit{Vom Marscheden kurtzer und gründlicher Unterricht} by Reinhold the younger (1538--1592), the author shows that their scholarly underground geometry, established in academic circles, is largely different from the actual surveying of a \textit{Markscheider}. ``\dots\ there was an important gap between the crafts and the books that were written about it'' (p.~49).
In the second chapter ``A mathematical culture. The art of setting limits'' (pp.~50--82), the author examines in detail the art of setting limits used in metallic mines developed within a specific technical, administrative, and economic context. He ``dissect[s] the actual procedures of underground geometry in order to understand the encroachment of mathematics into human affairs'' (p.~51). His knowledge of various sources (not necessarily mathematical, as mining laws, customs and rulings, sermons or town chronicles) is extensive. He shows, among others, how surveying tasks become more and more complex, how the surveyors made their mark with their knowledge and practices required for successful mining, how \textit{Markscheider} turns into a specialized profession established on a specific mathematical culture, or how religion is so important in the daily life of miners. Finally, ``the omnipresence of measurements, combined with their legal and religious recognition, ultimately conferred a higher status to the discipline'' (p.~16).
In the third chapter ``The mines and the court'' (pp.~83--117), the author explores ``two dynasties for Saxon practitioners [the Öders and the Rieses] whose careers illustrate the interplay between the mines and the court'' (p.~84). He considers those two dynasties, subterranean surveyors for the first family and reckoning masters for the second, as paradigmatic in the context of the mining towns of the Empire.
The fourth chapter ``Writing it down'' (pp.~118--148) is an opportunity to reappraise the general conception about the seventeenth-century mining literature, by studying unpublished manuscripts included in a new original scribal tradition \textit{Geometria subterranea} or \textit{New subterranean geometry}. This tradition, largely detailed is this chapter, was allegedly created by the mining official Balthasar Rösler (1605--1673). The author shows how those manuscripts were used to train the apprentice surveyors, as ``the subterranean geometry was not an art taught in schools'' (p.~129).
In the fifth chapter `` `So fair a subterraneous city' '' (pp.~149--182), the main subject is Abraham von Schönberg (1640--1711), Captain-general of the Saxon mining administration, and his effort to develop the mining map. A large part of this chapter is devoted to the \textit{Freiberga subterranea}, ``a gigantic cartography of the Ore Mountains running continuously over several hundred sheets'' (p.~151). Thus, the author reveals with strong arguments that ``drawing mining maps and working on them became widespread in the second half of the seventeenth century, gradually replacing alternative tools such as written reports of visitations, wood models, or annotated sketches'' (p.~17).
In the very valuable sixth chapter ``How to teach it?'' (pp.~183--212), the author describes (in his own words, p.~183) ``the challenges met by the mining culture of mathematics during the eighteenth century, its evolution, and how it finally came to be taught around a new kind of institution, the mining academies''. He sheds light on a very slow maturation in the whole century ``trying to standardize and improve existing practices without getting lost in abstract or unpractical solutions'' (p.~14), with a special emphasize on the biography of a mining master and autodidact mathematician: Johann Andreas Scheidhauer (1718--1784).
Finally, in the seventh chapter `` `One of geometry's nicest applications' '' (pp.~213--242), the author focuses on the very interesting history of the Deep-George Tunnel (1771--1799), a 10\,km long drainage tunnel at a depth of 284\,m, following testimonies and scientific writings of Jean-André Deluc (1727--1817), Swiss scholar, fellow of the Royal Society and foreign associate to the Académie des Sciences.
As one may have guessed from my review, the book is an enjoyable read, thanks to the quality of the writing (particularly the clarity of the plan) and the quantity and nature of the sources used. Historians of mathematics will discover a vast, hitherto unexplored field.
Reviewer: Marc Moyon (Limoges)