1. Gendered working realities in Enlightenment mathematics Jeanne Peiffer (CNRS) EWM 2011

2. Introduction A trip to a remote past which is like a trip to a foreign country The fields and epistemological contours of the new sciences were not yet defined, and strange professional constellations were no exception. An artist like the German Albrecht Dürer contributed to mathematics and did so at the scientific level of the time. Mathematics, part of the artes liberales, was taught in the philosophy class at the colleges. No university degrees in mathematics.

3. Institutionalization of the sciences In the 19 th century, the sciences became institutionalized and embodied at the universities and academies Specialization and professionalization Science distanced itself from the earlier forms of scientific work and methods which were devaluated

4. Society of the ancien régime Dominated by ranks and titles. The place in a lineage – where and of whom you were born, whom you married – determined your place in the world. People never spoke to each other as equals : one was of higher or lower status, from the simplest peasant girl all the way to the king. Even the poorest Parisian guarder his right to use the public fountains before someone of a lesser rank.

5. Different patterns for women to participate in the mathematical life Humanistic ideal of the puella docta, or the learned virgin, a prodigy. Taught by her (wealthy) father or male tutor who produced her in private academic gatherings. Noble women, esp. married ones, enjoyed some freedom, once they had fulfilled their duties : childbearing, supervising the details of the household, assisting her husband in maintaining the familys finances, in improving the wealth, position anda authority of their family.

6. Maria Gaetana Agnesi (1718-1799) Testimony of Charles de Brosses, conseiller au parlement de Dijon, travelling in 1739 to Milan where he was invited to a gathering in Palazzo Agnesi, an accademia domestica, similar to an academic disputation of the kind in which young boys were trained in religious colleges. Describes Gaetana debating, in Latin, on issues such as the nature of tides, the properties of curves, etc.

7. A treatise on calculus (1748) Agnesi arranged for private printing in her own home. Dedicated to the empress Maria Theresa. Argues for womens right to access to the sublimes sciences. Earned her much fame.

8. Émilie du Châtelet (1706-1749) After the birth of her second son, in 1733, she got excited with mathematics. Lessons with Maupertuis who had already achieved the highest ranks at the Académie royale des sciences.

9. Impressive record of publications Institutions de physique (1740), a textbook for her son French translation of Newtons Philosophiae naturalis principia mathematica (1687) Memoir on the nature of fire submitted to the Academy for a prize

10. Marie-Victoire-Éléonore de Thil (1690-1777) A close friend of Émilie du Châtelet Une géomètre impitoyable, qui méprise M. de Mairan parce quil ne connaît pas assez bien à son gré les forces vives (Madame de Graffigny, 20.8.1749) Hers was a mathematical library

11. Du 8 octobre aud[it] an mil sept cens soixt[ant]e dix sept [...] suit l'inventaire des livres qui se sont trouvés tant dans la bibliothèque étant au cabinet du premier etage que dans celle inventoriée au second etage [...] N° 2. Item. Douze volumes in quarto et in octavo dont Traité de dynamique prisé vinqt quatre livres cy 24 […] N° 13. Item. Vingt un volumes in douze dont traité de physique prisé dix huit livres cy 18 [...] N°. 19. Item. Seize volumes in quarto dont Elémens de geométrie prisé quarante livres cy 40 [...] N°. 24. Item. Onze volumes in quarto dont Analise démontrée prisé trente six livres cy 36 N° 25. Item. Douze volumes in quarto dont Histoire des mathematiques prisé soixante livres cy 60 N° 32. Item. Dix volumes in quarto dont Academie des sciences prisé trente six livres cy 36 N° 33. Item. Onze volumes in quarto dont Academie des sciences prisé trente six livres cy 36 N° 38. Item. Quarante deux volumes in quarto dont Academie des sciences prisé soix[an]te livres cy 60

12. What about the other women ? Poorly educated, often illiterate Changing our image of Science Considered not only an occupation for aristocrats or a few learned and professional men Collective enterprise involving a wide range of people, and also a wide array of unacknowledged collaborators to be found at home, from wifes and children through domestic servants

13. Spatial turn in History of science Where did early modern natural inquiry (and mathematics) take place ? Sites recognizably devoted to the pursuit of natural and mathematical knowledge, like observatories, laboratories, botanical gardens, anatomy theaters, etc. But also within the natural philosophers own homes and households

14. Example of Johannes Hevelius (1611-1687) Educated lawyer and wealthy brewer in Danzig, astronomer in his leisure time Had a large platform built on his roof upon which to store his instruments and from which to gaze at the stars Collaborated with his second wife, Elisabeth Koopmann (1647-1693).

15. Machina coelestis (1673) Title page …these observatories were all conveniently contained within the limits of my house, so you dont even need to leave the house, or cross the street … to get to another observatory (p. 446-447). His study was handily located just down the stairs, and his print shop, with its engraving equipment, was even closer, on the second floor.

16. Household was the basic organizational form of early modern society (under the authority of its head) Ex.: crafts, shops, peasants, but also natural inquiry through collecting, observing, calculating, letter writing, … Family as the unit of economic production and inheritance Provided work-related socialization and education of children A hierarchical structure based on gender, age, and class. Household, the basic production and reproduction unit

17. Household as a site of scientific production Professors taking in students as boarders and teaching mathematical courses in their residences. Example of Johann Bernoulli teaching Maupertuis No clear distinction between private and public The household model for natural inquiry was to demonstrate its staying power by enduring well into the 19 th century.

18. (Gendered) division of labor Members of the household – including close relatives, guests, clients, domestic servants, cooks, chambermaids, etc - played different roles. While sons had a strong tendency to inherit the occupations of their fathers. Domestic servants, wives, sisters, daughters, and visitors, assisted the pater familias as invisible technicians. Example of Madame Lepaute, wife of a noted clockmaker, who assisted Clairaut and Lalande in the daunting task (that took 6 months) of computing the return of Halleys comet in 1759.

19. Family settings crucial resources for the pursuit of knowledge Especially in astronomy, wifes and daughters participated in the observations and calculations. Rich records of women writing down observations in the notebooks of their husbands. These diaries of observation were used to prepare publications - ranging from calendars to scientific papers – or as basis for the international exchange (correspondences)

20. Working reality of Maria Margarethe Winkelmann At lunch time, shortly after eleven oclock, I began my observation. I was working at the big quadrant [upstairs], Christinchen downstairs, with the small quadrant. By knocking I indicated to her that I had measured the altitude. We had intermittent sunshine with clouds Archiv der Berlin-Brandenburgischen Akademie der Wissenschaften, Beobachtungstagebuch Maria Margarethe Winkelmann von 1713, f. 8

21. Transmission By structuring the division of labor among household members, the household also ensured the continuity of knowledge and skills, and their transmission to the next generation. Example of the Musschenbroeks in Leiden, who spent several generations manufacturing air-pumps and microscopes before finally breaking into the physics professorate. Sons and daughters inherited the intellectual capital of a family project, and also its physical capital: tools, instruments, collections, books.

22. Sons and widows carrying on the family project Acta eruditorum, one of Europes pre- eminent learned journals Published in the first papers on calculus by Leibniz and the Bernoulli brothers Edited by Otto Mencke in Leipzig from 1682 to 1707 After his death, his son Johann Burckhard Mencke took over the editorship of the journal His grandson Friedrich Otto Mencke became Johann Burckhards successor Example of a family project The family invested large sums from its own private capital, but was also supported by the Dresden court. After the death of Friedrich Otto in 1754, his widow Johanna Catharina Mencke, obtained an extension of the privilege of publishing the Acta Resistence of a group of scholars Privilege for her daughter Johanna Dorothea rejected.

23. Case study on the interrelations between an astronomical household and the Academy Gottfried Kirch (1639-1710), trained in astronomy by Johannes Hevelius Maria Margaretha Winkelmann, daughter of a Lutheran pastor who is said to have supported and encouraged her interest in mathematics. Trained in Latin. Hired as a maid in the household of a wealthy farmer, who carried out astronomical research in his spare time. There she learned the basics of astronomy, meteorology, and observation techniques

24. Kirch-Winkelmann household Kirch and Winkelmann married in 1692 Three children : Christfried, Christine and Margaretha The family produced astronomical-astrological calendars, which sold well The family members, including the children, were all involved in the working process

25. An astronomical household with an Academic connection At the foundation of the Königliche Societät der Wissenschaften, founded in 1700 by Gottfried Wilhelm Leibniz, Gottfried Kirch became official astronomer.

26. Frederick I, the Prussian king, gave his Academy the monopoly of calendar making, major source of the Academys funding. The Winkelmann-Kirchs proved to be vital to this project. Royal observatory built, partly in use from 1706 onwards and inaugurated in 1711 The research still took place in the same household environment. The family made observations day and night. Kirch the only recognized mediator between both working systems.

27. Major changes to the working division after Gottfrieds death (1710) Johann Heinrich Hoffmann was elected to succeed Kirch as astronomer and was made member of the Academy. His lack of skill was soon noticed. The skills and knowledge acquired in the Kirch household could obviously not be easily transferred or acquired elsewhere. Margaretha petitioned to be allowed to carry on her husbands calendar production, but her applications were rejected. Without the Academys salary, the female household continued the production and distribution (outside Prussia) of calendars

28. Competition between household and Academy After Hoffmanns death, in 1716, Christfried Kirch was hired by the Academy (as an observator). Christfried mentions hardly anything about the cooperation among family members, but indirect signs of the active participation of his sisters. Christfried observed at home, a fact which was criticised by the Academy. The inyention of the Academy was to establish the observatory as the only place where research was performed.

29. Arrangements with the sister household (1740-1772) After Christfrieds death, the sisters were financially supported by the Academy and received a regular salary. A close study of the bookkeeping reveals that different salaries were paid to the sisters who received in 1769 a yearly income of 400 Reichstaler, to be compared to the salary of their brother who had been paid 249 Reichstaler. The sum was divided and paid out in separate payments, most probably in order to hide the fact that a woman was paid more than some men.

30. A new institutional environment In 1772, the Academy officially thanked Christine (then 75) for her service and asked her to teach Johann Elert Bode the skills of calendar making. The knowledge and skills acquired in the context of the household were thus directly conveyed to a male astronomer, who used this knowledge in his position within the new working system at the Academy. A form of inclusion of women despite formal exclusion as members. A form of cooperation with women that maintained representational exclusion.

31. What to conclude from this case study ? An almost uninterrupted succession of women within the same family made the astronomical work, needed for the survival of the Academy, possible. The education was transferred through women over two generations. The case study clearly shows which possibilities were made impossible as maleness became the deciding factor for participation in the scientific community. In the Academy, the Kirchs could not openly participate in a project that had been made possible by their work.

32. Gender as regulator The two production systems – the household and the working system in the Academy – were systematically intertwined. Between the two systems gender functioned as the regulator of an institution that used female research, but officially only allowed men to participate. The Academy consciously tried to render female achievements invisible. The shadow economy of the Kirchs astronomical production was extremely profitable for the Academy. Gender strongly affected the institutionalization of the sciences

33. Bibliography Cf. Monika Mommertz, The Invisible economy of science in Judith P. Zinsser, ed., Men, Women, and the Birthing of Modern Science, DeKalb:Northern Illinois University Press, 2005, p. 159-178.

34. Were the Kirchs and astronomy an exception ?