Women in Eighteenth-Century Mathematics
Women in Eighteenth-Century Mathematics
Even before Aristotle (384-322 b.c.) declared women to be "imperfect men" and incapable of rational thought, women in the ancient world were denied education. There were exceptions, like Hypatia of Alexandria (a.d. 370?-415), a legendary mathematician and astronomer. During the Middle Ages women were educated in convents, giving them an opportunity, however limited, for intellectual expression. Hildegard von Bingen (1099-1179), was a twelfth-century mystic, writer, and composer—but her achievements, like Hypatia's, were well outside the norm.
During the Enlightenment, Parisian noble-women presided over gatherings of scientists and thinkers in their salons, cultivating a social climate that became a driving force of progress in the Age of Reason. Throughout most of Europe, though, scholarly achievement for women remained unthinkable. A few remarkable women, however, managed to become prominent mathematicians, despite society's restrictions.
During the 1700s the University of Bologna boasted several women professors, among them the famous mathematicians Laura Bassi (1711-78) and Maria Agnesi (1718-99), the anatomist Anna Manzolini (1716-1799), and Clotilda Tambroni (1758-1817), who taught Greek literature. Despite the university's liberal policies, Laura Bassi had to fight the Bologonese senate to keep her position, and was forced to petition the administration for funds to conduct her experiments. She prevailed. Fortunately the climate in Italy was just tolerant enough for these exceptional women to succeed. Bassi's contemporary, Maria Agnesi, in fact, was one of the most accomplished female mathematicians of all time.
Maria Gaetana Agenesi, born in Milan to a wealthy and educated family, was the eldest of 21 children. Both parents encouraged her extensive education in languages, philosophy, and mathematics. Agnesi was a brilliant student, especially in math. At age seventeen she wrote a paper about ballistics and planetary motion that was admired by contemporary scholars.
Agnesi authored Analytical Institutions, a classic mathematical text on differential and integral calculus in two volumes; the first volume was about mathematical process, the second about analysis. Her book was adopted as a textbook in France where the Academy of Sciences arranged for its translation into French. Still, the Academy could not accept Agnesi as a member because regulations prohibited females from joining.
At Cambridge University in England, mathematics professor John Colson was so impressed by Agnesi's text that he learned Italian in order to translate her book. It was Colson's translation error that caused Agnesi to be associated with the term "witch." Agnesi had used the Italian word versiera to refer to a versed sine curve. Colson mistakenly thought the Italian word was versicra which means "witch," and so the curve became known as "the witch of Agnesi." Agnesi held her position as honorary chair at the University of Bologna for two years. After her death, Italians named several streets, scholarships, and a school after Maria Agnesi.
Eighteenth-century France was somewhat different. Frenchwomen were denied access to universities, but noblewomen of the Enlightenment found another way to be part of the era's amazing intellectual developments. Wealthy women established and presided over salons, or parlors—glittering rooms in affluent homes that were frequent gathering places for the literate and educated. Despite the social protocol that limited them to playing hostess at these meetings, two Frenchwomen managed to became great mathematicians.
Emilie de Breteuil, marquise du Châtelet (1706-1749) was very tall and not considered good-looking as a child. As her parents were not optimistic about her marriage prospects, they agreed that she should have a tutor in order to have some life as a single woman. De Breteuil was clearly a genius; she quickly learned Latin, Greek, and English, and she excelled at and loved mathematics. At the age of 19 she married the marquis du Châtelet, who allowed her to continue to study mathematics. In order to meet with other scientists, she would often disguise herself as a man because women were never allowed to join intellectual discussions. Her brilliance and wit were widely acknowledged and even won over Voltaire; the two were inseparable companions for years. Châtelet wrote several books, including the only French translation of Isaac Newton's (1642-1727) Principia and a text on introductory physics. She died at the early age of 43, days after the birth of her fourth child.
Sophie Germain (1776-1831), often referred to as "The Hypatia of the eighteenth century," was born in Paris. Germain decided to become a mathematician at age 13, and against her parents' wishes at first, she taught herself mathematics and calculus. She couldn't attend courses at the Polytechnique but did get the lecture notes. She submitted a research paper using a man's name, fearing that the professor would reject it if he knew that a woman had written it. The professor, however, was most impressed by her work and agreed to sponsor her. She still continued to write under a man's name and carried on a long correspondence with German mathematician Carl Friedrich Gauss (1777-1855), who acknowledged that Germain was a genius.
The French Academy of Sciences awarded Germain its grand prize in 1811 for her theory of elasticity. Her work in number theory led her to develop a theorem, known as Germain's theorem. Sophie Germain died from breast cancer at the age of 55, and despite her scientific accomplishments and prizes, she was referred to merely as a property holder on her death certificate. Today Germain is regarded as an important founder of mathematical physics and a pioneer in the area of elasticity.
German mathematician and astronomer Caroline Herschel (1750-1848) also faced parental disapproval as a girl when she wanted to study arithmetic. Born in Hanover, Hershel was told by her father that she would probably never marry because she was not beautiful. Her mother ignored her daughter's requests for a proper education and only wanted her to do the housework. Caroline's brother William (1738-1822), eleven years older, saved Caroline from this dreary existence. He had relocated in England, where he studied astronomy and wanted his sister to join him. Their mother acquiesced only when William agreed to provide a housemaid to replace Caroline.
Brother and sister left Germany for England in August 1772. Caroline quickly learned English, studied accounting, and enjoyed discussing astronomy with her brother, even helping him build a telescope. She diligently studied geometry and logarithmic tables, and was responsible for many calculations and reductions. She arranged calculations of 2,500 nebulae and the reorganization of a catalog that listed almost 3,000 stars.
After William's death, Caroline returned to Germany, where she remained until her death in 1848 at the age of 97. She received many awards, including an honorary memberships and a gold medal from the Royal Astronomical Society, election to the Royal Irish Academy, and a gold medal of science from the King of Prussia. Although her contributions to mathematics did not include any original work in pure mathematics, Herschel's work in applied mathematics is invaluable.
The accomplishments of eighteenth century mathematicians Maria Agnesi, the marquise du Châtelet, Sophie Germain, and Caroline Hershel cannot be overestimated. Prohibited a university education due to their gender, these extraordinary women nonetheless excelled in a field that was dominated by men. Mostly self-taught, their genius and resolve led them to produce exceptional and innovative research. Furthermore, their efforts eventually led universities to change their admittance policies and allow women to attend universities.
During the political revolutions of the 1700s, these women bravely waged an intellectual revolution. The struggle, however, was not an easy one. In the nineteenth century, a woman at Cambridge University who wanted to attend a mathematics lecture had to sit behind a screen at the rear of the classroom in order to be separated from the men. In Germany a woman student was warned not to enter the university lab when men were present. Nevertheless, several universities in the nineteenth century gradually started to admit women as students at the undergraduate and graduate levels. In 1876 the University of London began to grant degrees to women. In 1885 the University of Göttingen awarded the first official Ph.D. to a woman by a German university. Cambridge, however, did not allow women to receive degrees until 1948.
When women's colleges such as Girton at Cambridge and Bryn Mawr in the United States were established, these colleges accepted women as students and then as professors. This practice contrasted sharply to that of the major universities. In 1885 the only woman professor at a European university was Sofia Kovalevsky (1850-1891), who was teaching mathematics at the University of Stockholm. When the brilliant German mathematician Emmy Noether (1882-1935) was offered the chance to teach at Göttingen, it was an unpaid position. By the twentieth century, however, universities around the world had overcome their gender bigotry and accepted women not only as university students but also as professors. The bold crusade begun by the brave, bright women mathematicians of the eighteenth century had finally succeeded.
Morrow, Charlene, and Teri Perl, eds. Notable Women in Mathematics. Westport, CN: Greenwood Press, 1998.
Osen, Lynn. M. Women in Mathematics. Cambridge, MA: MIT Press, 1974.
"4,000 Years of Women in Science." http://crux.astr.ua.edu/4000WS/4000WS.html