A female mathematician who loved mathematical analysis and God

Anezi was an Italian mathematician, philosopher, theologian and philanthropist.



I may disappoint you, but the “witch Agnesi” is a curve that students of mathematics usually learn in the course of mathematical analysis. She is not like a witch, nor a hat, nor even a broom. This is just a sloping, smooth curve.



If modern math textbooks mention Agnesi, after which the curve is named, they usually write that Maria Gaetana Agnesi was an 18th-century mathematician who became the first woman to write a serious textbook on mathematical analysis. They may also add that the name of the curve is an incorrect translation of the Italian versiera , a term coined by the mathematician Guido Grande on the basis of a Latin word for “turning curve”. Translator John Colson confused him with the word "avversiera", meaning "demoness" or "witch."



This is ironic, to say the least - a pious Catholic woman who has devoted decades of her life to serving the poor has become associated with the witch thanks to a curve that she didn’t even think of. But in a sense, this seems appropriate. According to science historian Paula Findland from Stanford University, this seems to be a mathematical “Freudian clause” - the Italian word “curve” has become an Italian word meaning devil-obsessed woman. Wonderful math joke. Whether it was a deliberate pun, or not, but Colson's erroneous translation perpetuated Agnesi's place in the teaching of mathematical analysis.



Reading the biography of Anezi, you catch yourself thinking that she constantly lived in the shadow of the expectations and demands of society and her own family. However, if we avoid the temptation to interpret her way of thinking through the prism of our perception, then we will begin to understand this woman from her own point of view.



Born in 1718, Agnesi was the eldest child of a wealthy Milan silk merchant, Pietro Agnesi. Probably, her learning began by chance, after the teachers began to teach her younger brothers. She was a precocious student, especially in studying languages, and Pietro quickly recognized her talent. In an effort to raise the social status of the family, he forced her and sister Maria Teresa, a musical prodigy, to perform in front of guests in the salons of Palazzo Agnesi. Gaetana, in several languages, talked about various scientific and philosophical topics, and her sister played music, often in her own composition. Pietro used talented daughters to make his home an important place for the high society of Milan.



The sisters Anezi were among the few girls geeks in northern Italy of that time. Laura Bassi (1711-1778), a physicist from Bologna, who became the first female professor at a university in Europe, was also a wunderkind. The historian of science from the University of California at Berkeley, Massimo Matsotti , who wrote the book "The World of Maria Gaetan Agnesi, a Mathematics from God, " calls this the strategy of "adapting and curbing the phenomenon of an educated woman." Rich families gave their daughters a limited education - literature, French, religion - but women could not attend school outside their home.



The phenomenon of the girl prodigy "was one of the ways in which outstanding talent and abilities were given a socially acceptable form in a world where, strictly speaking, women had no place in places where they received and studied knowledge."



Nevertheless, Matsotti notes that the status of a “girl prodigy” combined with the father’s wealth and ambitiousness revealed Agnes and a “small window of opportunity” that allowed her to get an education and make a greater contribution in the chosen field than many women of that era.









The upper figure is a curve known as the “Witch of Agnes”, from Agnes's own textbook. (Maria Agnesi, Instituziioni Analitiche, MIlan: 1748. David Eugene Smith Collection, Rare Book & Manuscript Library, Columbia University)



When her mother died in childbirth in 1732, Agnesi managed to reduce the number of public speeches, which allowed her to spend more time caring for her younger brothers and sisters, as well as more and more influence the process of her own education. In 1739, she told her father that she wanted to become a nun. He resisted, but allowed her to study mathematics and theology more. According to Findland, "she managed to break free from the shackles of the stereotype of an educated woman from Milan speaking to the public." Anezi never went to the monastery, but she also never got married and did not give birth to children, having chosen another way - a modest Catholic who devoted her life to charity.



In just 30 years, Agnesi completed her most important mathematical work: Instituzioni analitiche ad uso della giovent italiana (“Analytical Structures for Italian Youth”) - a textbook on mathematical analysis, published in 1748. This impressive two-volume work was devoted to differential and integral calculus. The first volume outlined the algebraic apparatus necessary for understanding the mathematical analysis of the second volume. Probably, her younger brothers and sisters were the first Italian young people to whom her work was devoted: Pietro had 21 children from three wives, but few survived to adulthood.



If a modern student who studies a mathematical analysis of a student discovers the Analytical Structures of Maria Agnes, the language will seem to him a little old-fashioned, but the general approach will be familiar. In fact, because of this clarity, modern mathematics students find it difficult to realize the importance of the work of Anezi. At her time, most people considered mathematical analysis important in the context of application in physics, and modern books on mathematical analysis are more or less a collection of problems in applied mathematics. Agnesi was interested in mathematical analysis in itself, as an intellectual puzzle and a way of sharpening its own logical constructions. Her book was one of the first in which there was no emphasis on the application in physics.



According to Matsotti, this book was born with a different idea of ​​the utility and interestingness of mathematics.



In addition, the book was written in Italian at a time when training was mainly conducted in Latin. Annezi wrote it in a public language because she wanted the book to be understandable to less educated students. Despite this, as well as the fact that the work was written by a woman, she deserved the respect of mathematicians throughout Europe thanks to an unusually clear approach to the topic. Decades after its publication, mathematician Joseph Louis Lagrange recommended the second volume as the best way to study mathematical analysis.



Since then, the " Analytical Structures " have been translated into English and French. In the preface to the English edition of 1801, the editor wrote that these volumes are "well known and highly valued on the continent," and that the previous translator of the work, the late Reverend John Colson, a Lukas mathematics professor at the University of Cambridge, painfully tried to learn Italian only in order to translate this work into English, so that the British youth can use it as much as the youth of Italy. ”









Portrait of Marie Agnes by French artist Jean-Baptiste Francois Bosio.



Agnesi lived to 1799. However, the authors of some articles on Agnesi, according to Findler, "treat her as if she died at the moment when she ceased to be interesting as a scientist." After the publication of the Analytical Structures , she gradually began to move away from the life of the mathematician. Sometimes they speak of her as the first woman professor of mathematics, but she never taught or even visited the city of her professorship. Pope Benedict XIV, who helped Bassi get a position, also offered an Aesi post at the University of Bologna, and for many years she had an honorary position there. After her father died in 1752, she finally felt free and was able to devote herself to studying theology and charity. Later, she became director of the women's home for the poor and sick Pio Albergo Trivulgio.



Annesi is difficult to adjust to any stereotypes. On the one hand, her religious zeal may seem a little alarming in the modern view. Although today we often think of science and religion as opposing forces, many important figures in the history of European science, especially before the 19th century, were Jesuits or members of other religious orders. Isaac Newton himself, along with the invention of mathematical analysis and revolutionary discoveries in physics, wrote treatises on alchemy and religion, including the secret messages in the Bible. In the era of Anezi, it was believed that mental exercises could be a form of zealous service to God. Anezi was interested in the work of Nicolas Malbranche, who wrote that "attention is the natural prayer of the soul." A deep study of topics such as mathematical analysis was like prayer to Agnes.



According to Matsotti, she believed that “the mind is necessary to be a good Christian. If you work on strengthening your intellect, then you are doing work to improve your spiritual life. ” In old age, her religious works became closer to mysticism, but at the peak of her mathematical activity, her attitude to religion was more intellectual and rational. And even when her religious practices became more mystical, she still considered the mind and passion as two complementary parts of religious life. “The human mind contemplates [the virtues of Christ] with admiration, and the heart imitates them with love,” she wrote in an unpublished mystical essay.



On the other hand, Agnesi’s decision to leave mathematics can confuse those who would like to make an icon of the history of women in science out of it. “She became one of those rare women who managed to do science, but what did she want to do when she had all the opportunities? She just gave up everything, ”says Findland. “We do not want to see our scientists doing interesting things, and then abandon them for the love of God. It does not fit into modern ideas. ”



“Her biography is divided, as it were, between those who see her almost as holy as the Catholic Church, especially next to her native Milan, and who study the history of mathematics and women in science. Often, these two groups of people almost do not overlap, ”Matsotti says. He notes in the introduction to his book: “I first learned about Agnes as a child, running along the nave of San Nazaro [Milan Basilica].” She was so famous for her piety and charity that she was portrayed in church pamphlets. Later, studying the history of mathematical analysis, Matsotti wondered what connects the woman, whom he learned in the church, with one of the mathematicians of the past.



Reading her story, you can decide that the conditions of a society that was not able to accept the scholarship and free will of women were put under pressure at Annezi. But in the tightly limited framework of her position in the world she managed to pave her own path. She did not become a nun, nor a wife or mother. She was respected in society both as a mathematician and as a Catholic who was involved in charity. One simultaneously submitted and rebelled against the demands of her own family. “It seems to us to be so conservative, outdated and completely non-radical, but perhaps this is just our limited understanding of the world,” says Findland.