Inculcating the Spirit

Academies

It is a commonplace to see organized science as "entirely recast under the dominion" of the scientific academies and societies of the 18th century.^[19] Scientific academies and societies played a significant role in establishing the importance and extending the application of mathematical or quantitative methods. Much recent literature addresses questions of the founding and organization of academies and societies, and may thus enlighten us about the 18th-century disciplinary map. It may also contain clues about the place of mathematics and the mathematically adept in these institutions and about the ways in which academic prestige or authority could encourage the use of mathematics. Recent studies look at academies and societies in general^[20] and in particular.^[21] Studies of the use of mathematical

methods in the 18th century might follow the lead of works that discuss the place of particular sciences in specific academic contexts.^[22]

Studies that examine the role of individuals in academies and hence in the life of science, especially in conjunction with archival or edited correspondence, promise useful information. Historians have begun, for example, to trace the powerful academic influence of Leonhard Euler.^[23] Analysis of the éloges of the Paris Academy of Sciences yields insights both about its perpetual secretaries, including Fontenelle and Condorcet, and about the scientific ideologies and standards they promoted.^[24] The publications and prizes of academies and societies served to spread the quantifying spirit, and deserve more attention.

Education

Educational institutions and strategies also played a role. The significance of science, especially mathematics, in the technical training establishment in France was sketched in older works that remain useful.^[25] Such works have recently been supplemented by studies of the royal engineering corps and military school in France;^[26] a comparative perspective is afforded by analysis of military and engineering training in old and New Spain.^[27] All need to be read against the evidence assembled in the work of Charles Gillispie,^[28] in biographical dictionaries of 18th-century engineers,^[29] in documentary histories of engineering,^[30] and in general histories of education.^[31] The roles played by academicians in beefing up the technical curricula bear more scrutiny.^[32] Data and studies of the teaching of mathematics and

science in colleges and universities offer possibilities for comparison.^[33]

The mathematical content, rhetoric, and appeal of popular courses and self-help books also helped to secure a place for quantification in popular culture. Studies of public courses and of the marketing of science thus warrant further investigation.^[34] So too do mathematical periodicals, textbooks for the self-taught, and the corps of mathematical author/practitioners.^[35]

For the end of the century, consideration of education and of the French Revolution raises twin issues of continuity and reform, both

pertinent to the place of mathematics in a revolutionary curriculum.^[36] Numerous studies unravel the organization and ideology of new institutions and trace their teachers, students, and lessons.^[37]