It took until 1971 before the first organisation for supporting women in Mathematics was created. The Association for Women in Mathematics (AWM), was established in the United States, and despite extensive work which has followed to address the challenges women in mathematics face, women still encounter particular difficulties within their professional careers. Many of these difficulties have a long history stemming from deeply embedded cultural attitudes. What follows is a glimpse at some of the challenges faced by those who have produced or developed original mathematics in the previous one hundred and fifty years.
Women and mathematics in the 18th and 19th centuries
The first woman in the modern period to make a substantial contribution to mathematics was the Italian Maria Agnesi (1718-1799). In 1748, she published one of the earliest textbooks on the differential and integral calculus, Instituzioni Analitiche. The book was accessible to a broad audience and an important contribution to the development of the calculus in Italy. Two years after the book’s publication, she was appointed to the chair of mathematics in Bologna on the recommendation of the Pope, Benedict XIV, but she never took up the position or went to Bologna, preferring to devote her life to charity.
In the context of the general question about how women mathematicians were perceived in the 18th century, it is interesting to note that in a discussion about a French translation of Agnesi’s book, it was remarked that such a translation should be done by a woman, thereby implying that there was something specifically feminine about the way she had written the text.
Agnesi, along with other women in the 18th and early 19th century, such as Émilie du Châtelet (1706-1749), Ada Lovelace (1815-1852) and Mary Somerville (1780-1872), all made lasting and significant contributions to mathematics. They were not prevented from doing mathematics, in fact sometimes rather the opposite. Ada Lovelace was encouraged by her mother to study mathematics with Augustus De Morgan. They all came from a social class which allowed them to attend society functions at which they could discuss mathematics and natural philosophy with men on equal terms.
Although it was acceptable for women
to mix socially in mathematical and
scientific circles, they could not
hold an official position.
Both Somerville and Lovelace attended the scientific soirées of Charles Babbage (1791-1871) and they frequently visited him together to discuss his analytical engine. That Élisabeth Ferrand, (1700-1752), an important influence on Abbé de Condillac and a friend of Alexis Claude Clairaut, chose a page from Voltaire’s influential Eleménts de la philosophie de Newton (1738) - the book which introduced Newtonian physics to France - as the backdrop to her portrait is indicative of the acceptability of such learning among women in Enlightenment circles.
Voltaire was not the sole author of Eleménts de la philosophie de Newton, although his is the only name to appear on the title page. Co-authoring was not customary at the time, but there is no doubt that Émilie du Châtelet played a major role in the book’s production and Voltaire himself did not shy from acknowledging it. Du Châtelet’s name appears twice in the introductory matter where Voltaire explains their collaboration, and she also appears in the frontispiece where he has imagined her as a muse floating above him while holding a mirror reflecting Newton’s wisdom down onto his hand, implicitly admitting her scientific superiority.
Completing the first and only French translation of Principia
Some ten years later, du Châtelet completed her own and much more ambitious work: a translation from the Latin of Newton’s Principia. However, it was not just a translation: Newton’s geometry was rendered into algebra and du Châtelet provided an extensive commentary including recent research. She completed it while pregnant and died shortly after giving birth. It was not published until ten years after her death. The publication was timed to coincide with the year of the return of Halley’s Comet in 1759. Today it still remains as the only complete translation into French of the Principia.
Although it was acceptable for women to mix socially in mathematical and scientific circles, they could not hold an official position. Mary Somerville was able to make money from the sales of her books. Her Mechanism of the Heavens (1831), an acclaimed translation and commentary on the celestial mechanics of Pierre-Simon Laplace (1749-1827), became a recommended text for men studying for the Mathematical Tripos at Cambridge. She could have a paper published by the Royal Society of London, but there was no question of her being admitted as a Fellow of the Society.
In 1902, the physicist Hertha Ayrton (1854-1923) was formally proposed as a candidate for Fellowship of the Royal Society. One reason for not admitting her was the fact she was married, and married women had no status in law! Although the Royal Society would not admit Ayrton as a Fellow, they did allow her to read a paper before the Society - the first woman to do so - and in 1906 they awarded her the Hughes Medal. The Fellows of the Society were prepared to acknowledge that women could do science, and indeed do it very well, but they were not prepared to accept that women should or could be considered as their scientific equals. The first women were admitted in 1945. The first woman mathematician, Mary Cartwright (1900-1998), was admitted in 1947.
Denied “the very existence of a woman mathematician”
The first woman to be a professional academic mathematician in the modern sense was the Russian Sofia Kovalevskaya (1850-1891). Championed by the Swedish mathematician, Gösta Mittag-Leffler (1846-1927) who overcame strong opposition to secure her appointment at the Stockholm Högskola (now Stockholm University), she became a full professor in 1889. But despite Kovalevskaya’s acknowledged mathematical talent - she was awarded the Prix Bordin of the French Académie des Sciences in Paris in 1888 for her work on the spinning top - there was no chance for her to gain a position in one of the mathematical centres of Europe, such as Paris or Berlin.
Kovalevskaya reported examples of the prejudice that she had encountered. In 1869, early in her career, when she was visiting the London salon of the novelist George Eliot, she found Eliot, who had an interest in mathematics, very keen to introduce her to the philosopher Herbert Spencer because, as Eliot said, Spencer denied “the very existence of a woman mathematician.”
In December 1884, after her appointment as an assistant professor in Stockholm, she would write to Mittag-Leffler, “I have received from your sister, as a Christmas present, an article by Strindberg, in which he proves as decidedly as two and two make four, what a monstrosity is a woman who is a professor of mathematics, and how unnecessary, injurious, and out of place she is.”
“The first handsome mathematical lady”
As a gifted female mathematician, Kovalevskaya inevitably attracted attention, not just because of her mathematics. The assistant of the English mathematician, James Joseph Sylvester, on seeing a photograph of Kovalevskaya, declared that she was “the first handsome mathematical lady,” he had ever seen. (Of course one can wonder how many mathematical ladies he had ever seen!) After her untimely death - she died unexpectedly aged only 41, her fame escalated and interest in her appearance intensified. But no longer was there a consensus.
“Miss Scott has answered papers
set for the mathematical tripos in a manner which would have brought her high on the list of Wranglers, an achievement
of no common kind.
For some she was beautiful and for others she was not and there was no general agreement. Unsurprisingly, the debate was tied up with differing opinions about her mathematical achievements. Examining these opinions, which in the years immediately after her death led to a decline in her status as a mathematician, provides an insight into changing views about female mathematicians.
During the 19th century, Cambridge was the beating heart of British mathematics and the Mathematical Tripos was the most prestigious examination in Britain. It is hard to over-estimate the kudos attached to being senior wrangler, the top student of the year. From the second half of the century, women could study mathematics - Girton was founded in 1869 and Newnham in 1872 - but they had to obtain permission to sit the Tripos examination. Women could not do so by right, and they could not be awarded a degree.
Challenging and beating men at Mathematics
In 1880, Charlotte Scott (1858-1931) created a sensation by being judged equal to the eighth Wrangler. The newspapers and periodicals were full of her success as she had done better than 93 of the 102 men taking the examination. Reports provided an interesting insight into prevailing attitudes. The Spectator was typical:
“Miss Scott has answered papers set for the mathematical tripos in a manner which would have brought her high on the list of Wranglers, an achievement of no common kind. We hope that the ability which the new system brings out and fosters in women, will not be of a kind to give to those who possess it a character for deficiency in feminine gentleness. We do not believe that it will be so. But even in the rare cases where it is so, the world should remember that there have always been women of the masculine type - only that they have hitherto lacked the means of proving what they could do, though possessing amply the means of proving what they could not be.”
Scott’s achievement generated a growth in support for women students with the result that they were given the right to take the examinations and their results were published, albeit separate from the men. However, women still could not be awarded degrees.
An even greater sensation was created in 1890, when Philippa Fawcett (1868-1948) was judged to be above the senior wrangler. She had achieved what many believed impossible. Nevertheless, when the Tripos list was published, her name still appeared below that of all the men.
Breaking down barriers for women to study for a degree
After Fawcett’s success, the clamour for women to be awarded degrees grew louder, but still not loud enough to make a difference. Cambridge did not fully open its doors to women until 1947. Those who wanted degrees had to go to London, or from 1920 to Oxford. Those who wanted to study for higher degrees had to go abroad. The PhD did not come to Britain until after the First World War. Grace Chisholm (1868-1944), who sat the Tripos in 1892, completed her studies with Felix Klein in Göttingen, Germany and in 1895 became the first British women to gain a PhD in mathematics.
Shortly afterwards she married the mathematician W.H Young. Young was content for her to continue with mathematical research, but as he told her rather directly, publishing mathematical papers was a man’s game: “The fact is that our papers ought to be published under our joint names, but if this were done neither of us get the benefit of it. No. Mine the laurels now and the knowledge. Yours the knowledge only. Everything under my name now, and later when the loaves and fishes are no more procurable in that way, everything or much under your name.”
Although such a shocking situation no longer remains, recent analysis has shown, as noted by Marie-Françoise Roy in her paper, that “a systemic gender imbalance” in the publication distribution of mathematicians still exists.
Progress is made but at a slow rate
In Cambridge, Young was not the only man who believed in the capacity of women to do mathematics. Charlotte Scott studied algebraic geometry with Arthur Cayley, the Sadleirian Professor, and it was Cayley who recommended her for the position of head of mathematics at the newly opening Bryn Mawr College in the United States, a position which she took up in 1895. There was no equivalent opening being available to her in Britain. But for a long time men like Young and Cayley were in the minority. The belief that women were not capable of doing serious mathematics proved extremely hard to shift.
After 1947, women may have been able to get degrees at Cambridge, yet little changed in other respects and progress towards gender equality in mathematics has been glacially slow. In 1947 Mary Cartwright was the first female mathematician to be elected a Fellow of the Royal Society, but was not deemed worthy of a professorship. The first woman to be elected to a professorship in Cambridge was the applied mathematician Anne Davis in 2002. Move forward to 2018, and there has still not been a female professor in pure mathematics at Cambridge.