Emmy Noether – Original in More Ways Than One

Emmy Noether c. 1910 (source)

Emmy Noether c. 1910 (source)

 

“Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.”  ~ Albert Einstein

If you ask anyone to name a famous woman mathematician, the names that come to mind will usually be Hypatia, Ada Lovelace, Emilie du Chatelet, or Maria Agnesi, if they can name any at all. I must admit that these women were the ones who attracted my attention as well when I started reading the history of mathematics. Each of these has something that attracts us apart from mathematics: Hypatia’s brutal death, Ada’s famous father, Emilie’s famous lover, or Maria’s piety. Yet with each of these women there are debates about how much original work they actually did and how much was primarily building on the work of others. There is no doubt that they were all brilliant and deserve to be remembered, but there is one who undoubtedly did work that was so original that it changed the way we do mathematics and is virtually unknown outside of specialist circles: Emmy Noether.

Emmy Noether made groundbreaking contributions to theoretical physics and abstract algebra. She developed several formulations to support Einstein’s General Theory of Relativity, in fact he wrote to David Hilbert, “You know that Frl. Noether is continually advising me in my projects and that it is really through her that I have become competent in the subject.” The principle behind Noether’s Theorem is foundational to quantum physics proving that the laws of physics are independent of time and space. And yes you can even blame her for “New Math,” her approach, just very, very, watered down. In spite of all of this, she worked almost her entire life without pay because she was a woman.

The facts of Emmy’s childhood are pretty normal for the time. She was born Amalie Emmy Noether on March 23, 1882, in Erlangen, Bavaria, the oldest of four children in a well-to-do Jewish family. Her mother, Ida Amalie Kaufmann, came from a wealthy family and her father was a well-respected Mathematics professor at the university in Erlangen. Emmy was the only girl and while her three brothers followed the traditional educational track for boys, she was schooled in music, religious instruction, language, child care, household management, etc. Girls were not admitted to universities in Germany, so there were no college-preparatory schools for them. When Emmy completed her instruction around age 15, she entered a teacher training program with the idea of teaching French and English. She did very well, except in her practical teaching skills.

Emmy was very likeable and easy to get along with. She was interested in mathematics, showed a definite aptitude for it, and was certainly exposed to it. One of her brothers went on to be a math professor and a good family friend Paul Gordon would be a very important mentor to Emmy in her early professional life. Her father was supportive and spent time with her teaching her mathematics even though it wasn’t part of her course of instruction. So why the teacher training? As a child Emmy was clever, friendly, and sociable, but she was also considered plain and ordinary. She spoke with a slight lisp, was near-sighted, and later in life would be described as loud and “heavy of build.” Emmy said herself that she didn’t have the patience to be a wife or mother, and she seemed to have little interest in clothes. Her mother may have expected Emmy to have to support herself, so she encouraged the teaching career.

Emmy passed her examinations to teach, but when she finished her course of instruction some of the university rules were being relaxed and she decided she wanted to study mathematics. Women still couldn’t officially enroll, but they could audit with the permission of the professor, so with the support of her father and Paul Gordon, she took classes over the next two years and prepared to take the university entrance exams. In 1903, she passed these exams and even though she still couldn’t officially enroll, she went to Göttingen to study mathematics. Göttingen had the leading math department in Germany led by Felix Klein, who was a proponent of admitting women to higher education. While there she met David Hilbert and was exposed to his work in abstract algebra. Hilbert is considered by some to be the greatest mathematician since Gauss, and he would later have a great impact on Emmy and her work.

Hilbert, considered by some to be the greatest mathematician since Gauss, was a proponent of admitting women to the university. (source)

Emmy only spent one semester at Göttingen and returned home, possibly due to illness. During this time, the University at Erlangen had decided to admit women and Emmy officially enrolled as a student. Working closely with Paul Gordon, she completed her dissertation and in 1907 at the age of 25 was awarded highest honors. Over the next seven years, she worked at the university, writing papers, speaking abroad, and filling in for her father as his health declined, all without pay. The money wasn’t important to Emmy as long as she could do mathematics.

Emmy’s dissertation and Gordon’s style of work was very dense, full of many equations and calculations. Although, Emmy thought very highly of Gordon, she was not entirely happy with this approach, and she began to apply Hilbert’s abstract approach to algebra. She had written some very important papers already in her career, but this is where she would make her greatest contribution. In 1915, with the help of her father, she arranged to go back to Göttingen to study with Felix Klein and David Hilbert. It wasn’t long before Klein and Hilbert both felt that Emmy deserved a teaching position. They met with a lot of resistance. It wasn’t until 1919 that she was allowed to teach classes on her own, but it had to be as Hilbert’s assistant. The classes would be registered under Hilbert’s name, but Emmy would be the professor, and she still wouldn’t be paid. Fortunately, her mother’s brothers had set up a small trust fund for her, so she had some income. By 1923, she had gained more recognition and was granted a position with a small stipend.

Emmy had a unique teaching style. She had little patience with presenting established concepts, rather she would often work out her own research with the class. Needless to say many weren’t able to follow her, but the students who stuck with her were very loyal and were sometimes referred to as “Noether’s boys.” They would come to her house to discuss math and even when school was officially out, she would meet them at a local café for discussions. Gordon had often continued teaching during what he called “math walks” and Emmy adopted this style as well. One of her students from her time at Byrn Mawr in the 1930s said that they had to watch to keep her out of the streets or from running into things, because she would get so involved in talking about math. She had an enthusiastic style, often ending up disheveled by the end of class with her hair coming out of its pins.

Throughout the 1920s, Emmy established herself as one of the leading mathematicians in the new field of abstract algebra. At the same time, she contributed greatly to the work of others. There seemed to be no jealousy or resentment in her at all. In 1933, with Hitler’s rise to power, many Jews lost their positions at German universities. Emmy was one of the first six to be dismissed from Göttingen. Yet she continued to hold clandestine classes in her home for the students who would come. One of her favorite students Ernst Witt would come to her home in his Brownshirt uniform. As far as the university was concerned she had three strikes against her; she was a Jew, a liberal pacifist, and she was a woman. But for Emmy, it was all about the math, nothing else mattered. If someone wanted to learn or work with her she would do it.

After her dismissal from the university, her friends began to try to find her a position out of Germany. She initially wanted to go to Oxford, or Russia where her brother went, but finally ended up at Bryn Mawr in Pennsylvania in the United States. This also gave her the opportunity to lecture at the Institute for Advanced Study at Princeton as well where Einstein was working. At the age of 51, she had her first real salary as a professor of mathematics. Her time here was good, but it was short. In 1935, Emmy went into the hospital for surgery to remove an ovarian cyst. The surgery appeared to go well, but four days later, her fever spiked and she lost consciousness. Emmy Noether died on April 14, 1935.

At her memorial, her close friend Hermann Weyl had the following to say about her:

“It was too easy for those who met her for the first time, or had no feeling for her creative power, to consider her queer and to make fun at her expense. She was heavy of build and loud of voice, and it was often not easy for one to get the floor in competitions with her. . . But she was a one-sided human being who was thrown out of balance by the over-weight of her mathematical talent . . . The memory of her work in science and of her personality among her fellows will not soon pass away. She was a great mathematician, the greatest, I firmly believe, that her sex has ever produced and a great woman.”

The entrance to Bryn Mawr, where Emmy spent the last year and half of her life. (source)

Resources
Nobel Prize Women in Science by Sharon Bertsch McGrayne
(Note: There is no Nobel Prize in Mathematics. Noether is included in this book because she contributed significantly to the mathematics involved in Einstein’s theories.)
Notable Women in Mathematics
edited by Charlene Morrow and Teri Perl
Women in Mathematics by Lynn Osen
Women in Science: Antiquity through the Nineteenth Century
by Marilyn Bailey Ogilivie

Dame is a Four Letter Word – an audio recording about the life of Ada Lovelace and Emmy Noether.

Read about other Famous Women Mathematicians and Scientists.

Laura Bassi – Italian Physicist (1711 – 1778)

Laura Bassi by Carlo Vandi

Laura Bassi by Carlo Vandi (source)

 

The entrance of women into the sciences has been a long process beginning several centuries ago. It’s not easy to find these women in the 18th century, but those that made a name for themselves did so because they were far from ordinary. Admittance into this formerly all male club seems to have begun in Italy (at least for post-Renaissance Europe,) specifically the University of Bologna where Laura Bassi became the first woman professor of physics in Europe.

Born November 29, 1711, Laura Bassi was the only child in her family to survive to adulthood. As with many (maybe most) scientifically inclined women prior to the 20th century, she received an education because her father recognized her ability and brought tutors into their home. This was a privilege reserved for the well-to-do, if not exclusively for the aristocracy. Bassi’s father was a successful lawyer, but the family was not of the nobility.

From the age of five Laura was instructed in French, Latin, and mathematics by a cousin, and later by the family physician in philosophy, natural philosophy, metaphysics, and logic. Her abilities were known throughout the city attracting attention of people who would visit her home to meet her. Similar to the salons in France, the intellectual elite in Italy would gather in homes to discuss philosophy, literature, science, mathematics, etc. Laura seems to have been put on display in her home in much the same way Maria Agnesi was.

In 1732, in a public debate Laura presented and defended her ideas regarding Newton and the new physics. She was awarded her doctorate and offered a position teaching at the University of Bologna. This required another public examination where she was successful, becoming the first woman professor of physics in a European University. As with Maria Agnesi, there is disagreement among scholars as to the extent of her teaching responsibilities. Some think that she was limited to occasional lectures, others believe she had a full teaching load. It seems to be a matter of propriety. Lectures in public would attract both women and men, but teaching at the university would usually entail being alone in a classroom with all male students.

Medal commemorating Laura Bassi, Italy 1732 (source - Wellcome Images)

Medal commemorating Laura Bassi, Italy 1732 (source – Wellcome Images)

This situation was relieved when in 1738 she married Giovanni Guiseppe Veratti, a fellow scientist and professor. As a married woman, the university made allowances for Bassi to lecture in her home. Bassi and her husband had eight to twelve children. There is disagreement on the number of children, but baptismal records seem to support eight, five of whom survived to adulthood. Laura and her husband shared a love of science, created a laboratory in their home, and performed experiments together. Teaching from her home gave her more flexibility to perform experiments and to choose which topics she taught.

During her examination for her professorship, she attracted the attention of Cardinal Prospero Lambertini (later Pope Benedict XIV) who was impressed and extended his support to Laura in her studies. In 1745, he appointed her to an elite group of scholars known as the Benedettini in which she was the only woman. Originally intended to be a group of 24, Lambertini met with resistance when he wanted to appoint Bassi to one of the positions. He then added a twenty-fifth position for her. After Bassi’s death this seat remained vacant until the 1800s. The purpose of the Benedettini was to encourage scientific advancement in Italy. Each member was responsible for writing and presenting a paper to the pope each year. Lambertini also arranged for Bassi to have access to scholarly documents in the Vatican which were usually restricted to male scientists over the age of 24

The scientific community was small in Europe at the time and Bassi communicated with leading scientists. She appears to have been instrumental in getting Voltaire admitted to the Academy of Sciences at Bologna and I’m sure through him she would have been familiar with Emilie du Chatelet’s works on mathematics and physics. At the beginning of her career, Newton’s ideas were still new and somewhat controversial and it’s easy to believe that she may have had a hand in introducing them to Italy. Bassi’s surviving papers however, are related to compression of air, hydraulics, a couple of dissertations on mathematics, and later electricity.

Bassi took on additional teaching positions later in her life. In 1766, she assumed a position teaching physics for the Collegio Montalto, a free seminary where students were taught in professor’s homes and earned degrees in theology or law. In 1776, Bassi’s husband was an assistant to Paola Battista Balbi the Chair and Institute Professor of Experimental Physics when Balbi died leaving a vacancy. Although her husband would have been the obvious choice, Bassi petitioned to be considered for the post. It seems that her skills in mathematics made her a more logical choice and she received the appointment. When Bassi died two years later, her husband took the post and was later succeeded by their son Paolo keeping it in the family until 1796.

I had never taken notice of Laura Bassi until recently. She doesn’t appear at all in several books I have on women in science and math and where she does appear it is cursory. I’m not sure why, because she had a life long career in science. It could be because she didn’t publish major works that were accessible to a lay person. Her works were scholarly and original. Unlike Agnesi, who went on to do work among the poor and destitute after the death of her father, even though she was concerned for the poor, it wasn’t Bassi’s primary focus. And of course, Emilie Du Chatelet was a scientist, but also the lover of a famous man, Voltaire, and we all seem to love to hear about a scandalous woman. Regardless of the reason, we should take note of Laura Bassi. She had tremendous staying power, a long career in a man’s field, and she raised a family. Sounds like something that many contemporary women are trying to do and would be inspired by.

Oh and she has a crater on Venus named for her – what more could you ask from a woman!

Resources
Women in Science: Antiquity through the Nineteenth Century by Marilyn Bailey Ogilivie
Women in Science by H. J. Mozans
Laura Bassi“, Encyclopedia of World Biography, 2004

Read about other Famous Women Mathematicians and Scientists.

Mary McLeod Bethune – “Genius Knows No Racial Barriers”

Mary McLeod Bethune

In 1904, a young woman with faith in God and a passion for education opened a school in Daytona Florida with $1.50 and five young African-American girls. Over the next fourteen years, the school would add a four-story building containing dormitories for students and teachers, a two-story addition containing kitchen and domestic science facilities, a twelve acre farm for growing vegetables, raising cows and practical training for the girls, another six acre tract and an auditorium. The woman with the drive and passion to do this was Mary McLeod Bethune and this was only the beginning of her amazing and productive life.

Mary McLeod was born in 1875 to Samuel and Patsy McLeod on a small cotton and rice farm in South Carolina. Her parents were former slaves and she was one in a very large family. She worked on the farm as a young child, but was always ambitious. Eventually, she was able to go to a small mission school in Mayesville, SC. Then with scholarship assistance she continued her education at Scotia Seminary in Concord, NC and Moody Bible College in Chicago.

Mary’s goal was to be a missionary to Africa, but she was told that black missionaries weren’t needed, so she returned to teach school in South Carolina. In 1898, she married Albertus Bethune. They had one son, Albert. She worked as a teacher and in social work until in 1899 the family relocated to Palatka Florida where Mary taught in a mission school. Mary felt strongly that an important way to improve the lives of African-Americans was to educate the girls. She was inspired by both Emma Jane Wilson the teacher in the mission school where she was educated and by Lucy Craft Laney who founded the Haines Normal and Industrial Institute in Augusta Georgia. Bethune spent a year teaching at the Haines Institute and was very impressed with Laney’s educational philosophy.

The Literary and Industrial Training School for Negro Girls in Daytona was founded in 1904 when Mary rented a small house for $11 a month. With five girls as students, her son, and the help of local parents and churches she began the hard work of creating a school that would eventually become the Bethune-Cookman University in 2007.  In addition to academic classes, the girls were given a rigorous Christian foundation and practical skills such as dressmaking, millinery, and cooking.

Daytona Normal School in 1919 (source)

Bethune served as president of the school until 1942, but her time was increasingly taken up with fund raising. In spite of this, she was also involved in other activities that raised awareness and improved the lives of African-Americans, specifically women and children. She served as the Florida president and national president of the National Association of Colored Women (NACW.) She attended the Child Welfare Conference called by President Calvin Coolidge in 1928 and was appointed to the White House Conference on Child Health by President Herbert Hoover in 1930. In 1935, Mary brought together 28 agencies to form the National Council of Negro Women. The NCNW sponsored the White House Conference on Negro Women and Children in 1938.

Through these organizations, Mrs. Bethune was instrumental in getting African-American women into officer positions in the Women’s Army Corps during WWII as well as ensuring that black colleges participated in pilot training programs. She lobbied the National Youth Administration to include black youth in their programs. During this time she became close friends with Eleanor Roosevelt. Because of this she had easy access to the White House and became a member of the “Black Cabinet” a group of well respected African-Americans that met informally, but had influence over issues affecting all African-Americans. Among her many honors was being the only African-American woman present at the founding of the United Nations in 1945. She represented the NAACP with W. E. B. Dubois and Walter White.

She believed that education about black people was important not only to promote pride in black children, but to promote understanding among all races.

“Not only the Negro child but children of all races should read and know of the achievements, accomplishments and deeds of the Negro. World peace and brotherhood are based on a common understanding of the contributions and cultures of all races and creeds.”

It seems that she made significant progress toward her goals When Mary McLeod died in 1955, she was remembered in many newspapers across the country for her achievements. Three quotes that I found in Wikipedia sum this up nicely:

She was, “one of the most potent factors in the growth of interracial goodwill in America.”  The New York Times

“So great were her dynamism and force that it was almost impossible to resist her… Not only her own people, but all America has been enriched and ennobled by her courageous, ebullient spirit.”  The Washington Post

“To some she seemed unreal, something that could not be… What right had she to greatness?… The lesson of Mrs. Bethune’s life is that genius knows no racial barriers.”  Daytona Beach Evening News

Mary Jane McLeod Bethune, photographed by Carl Van Vechten, April 6, 1949 (source)

Resources
Women of Achievement by Benjamin Brawley (in the public domain)
Mary McLeod Bethune by Emma Gelders Sterne (in the public domain)
These books can be found at the Internet Archives.

Sonya Kovalevsky – A Marriage of Convenience

Sonya Kovalevsky in 1880, photographer unknown (source)

Sonya Kovalevsky in 1880, photographer unknown (source)

“Ask him to marry one of us?  You’re crazy,” said Inez.

“It’s the perfect solution”, replied Sonya’s sister Anna.  “A lot of people are doing it.  Women can’t study in Russia.  At least the aristocracy can’t. It’s considered improper,” as she rolled her eyes.  “But married women can travel.”

“And?”

“Don’t you see? If one of us gets married, we can both travel to a foreign university to study.  When we get there he can go his own way.  Strictly a marriage of convenience!”

So the conversation might have gone, in the winter of 1867 in St. Petersburg, Russia.  Anna Krukovsky, her sister Sonya, and their friend Inez wanted to be a part of the new revolution among Russia’s young people.  They wanted to see freedom, progress, and a rise in the standard of education for women in their country.  In the 1860s and 70s, quite a few young Russian women among the aristocracy were leaving their parents homes to study.  They did this by marrying young men of like mind, going abroad to study, and then going their separate ways.

Sonya, born January 15, 1850 in Russia (new style date), was the daughter of Vasily Korvin-Krukovsky and Yelizaveta Shubert both well educated members of the Russian aristocracy.  But, they, like most of us, were products of their own time. This dictated that girls were educated in the home and only in certain subjects. Sonya was raised, primarily, by a nursery maids and governesses.  The first governess that she recalls in her fictionalized autobiography of her childhood, The Sister’s Rajevsky, was the “abominable French woman.” This woman was sent away when it was discovered that Anna could barely read.  She was replaced by a Russian woman who had been living in England and had completely absorbed the English way of life. She brought a much needed discipline into the household.  Under this new governess, Sonya discovered her affinity for science and mathematics.  Her uncle, Pyotr Vasilievich Krukovsky , spoke about mathematics and it is said that the walls of her bedroom were papered with pages from a book on differential and integral calculus. Even though she didn’t have the background to understand it at the time, mathematics captured Sonya’s imagination. What she learned, however, was strictly controlled in the household.  It had to be “proper” for a young woman.

Anna Jaclard, Sonya's sister, before 1887, artist unknown (source)

Anna Jaclard, Sonya’s sister, before 1887, artist unknown (source)

Anna had a flair for literature and had defied the conventions by sending a couple of her stories to St. Petersburg to the attention of Fyodor Dostoyevsky.  They had been published and she had been paid.  Unfortunately, her father was the first to go through the post on the day her payment arrived, addressed to the housekeeper.  He insisted that the housekeeper open it in front of him and explain.  Anna was caught.  Her father felt betrayed and humiliated, and for a time refused to speak to Anna.

The girls began to work on their mother and eventually were able to convince their parents to hear one of the stories.  This resulted in a slight relaxing of restrictions.  Anna was allowed to correspond with Dostoyevsky, and they were allowed to order books on various topics.  Due to the influence of one of her father’s friends, a tutor was retained to teach Sonya science and mathematics, although, her father still considered it to be an “unusual and unfeminine” area of study.  Sonya flourished, but soon reached the extent of what her tutor could teach her. When Sonya began to hint at her desire to go abroad to study her father drew the line and refused to even consider it.

It was after this, during a winter in St. Petersburg, that the girls began their plotting.  The girls first approached a young man of the aristocracy with their proposal.  He was a young professor at the university and surely would understand.  He politely refused, but was sympathetic to their cause and didn’t expose them.  This rejection didn’t stifle the girls’ enthusiasm for the idea.  There don’t seem to be any romantic ideals attached to the idea. In their minds the proposal was strictly a matter of practicality and therefore the girls didn’t take the rejection personally.

While in their village Palibino, they had made the acquaintance of a young student.  The son of the vicar, Vladimir Kovalevsky was a serious young man who studied archeology and geology at the university and wanted to continue his studies in Germany. He had a disagreement with his father over a number of things, including his involvement with the young people in the new movement in St. Petersburg.  Because of this, he had moved out of his home, and into a small rented room in the city.  In discussing their circle of friends, they decided that Vladimir might be a likely candidate for their plan.

There were many opportunities for the young people to socialize under supervision, so the girls were able to get to know Vladimir.  They decided that he would be perfect for their marriage scheme.  The three of them approached him at a casual gathering in a friend’s house.  To their surprise, he agreed, with one change in the plan.  He wanted to marry Sonya.

Although Sonya had often felt unloved, all indications are that the Krukovsky parents loved their children though they may have been somewhat removed. They had been persuaded to allow Anna to write for publication and Sonya to study “unfeminine” subjects, but they were in many ways very conventional. Vladimir was young, but of good birth with a promising career ahead of him, so he would probably have been accepted as a match for Anna. She was 23 at the time, an age where she was a little old to be unmarried. However, Sonya was only 17 and of course the expectation was that the older daughter should be married first. Their father flatly refused to consider the match.

The girls were so determined that Sonya decided to force her father’s hand. One evening when the household was busy preparing for a dinner party and both of the girl’s parents had gone out in the afternoon, Sonya dressed for dinner and slipped out of the house without being seen.  She went to Vladimir’s room where he was waiting for her.  They waited anxiously for footsteps in the hallway, knowing it wouldn’t take long.  Sonya had left a note for her parents.  She asked them to forgive her, but to understand that this was what she wanted.  She knew that it would be humiliating for them, and that being found alone with Vladimir would require their marriage.

At home, Sonya’s parents had arrived late as expected.  When the guests had assembled and the table was set, they noticed that Sonya was missing.  Anna told them that she had gone out, and there was a note on her dressing table.  After reading the note, their father said nothing, but left the house.  When he returned he introduced Sonya’s fiancé to the guests.

The marriage proceeded as planned.  The young couple lived in St. Petersburg for six months until Vladimir finished his studies, then moved on to Heidelberg, Germany.  Here Sonya was able to study with celebrated mathematicians and scientists of the day.  Anna and Inez both eventually joined them.  They were able to travel and meet many well-known people, authors as well as scientists.

In her biography of Sonya, Anna Carlotta Leffler describes Sonya as a person who demanded a lot from her close friends and acquaintances. She tended to be jealous of other people and the things in their lives, even of her husband’s work. She says of Sonya that “Her own individuality was far too pronounced to allow her to live in harmony with others.” Sonya threw herself wholeheartedly into new activities such as dancing and horseback riding and gave this same devotion to writing literature and her study of mathematics. This devotion allowed her to become the first woman to be a member of the Russian Academy of Science and the first European woman to become a full professor at a university. This appointment was privately funded at the University of Sweden in 1884.

Although it began as a marriage of convenience with separate living arrangements, Sonya and Vladimir developed a close relationship.  They would often walk and talk all day.  Eventually, Anna moved to Paris and Inez moved on, leaving the couple alone.  They shared great intelligence and devotion to their work.  Later, they shared great devotion to their daughter, Foufi.  Unfortunately, their life together was short.  Vladimir died, Foufi was left with friends in St. Petersburg, and Sonya was alone.  She would spend most of the rest of her life this way.  To her friends, she seemed to always be searching for something.  Perhaps for the acceptance and love that she didn’t feel as a child, and didn’t find in a marriage of convenience.

Resources
Sonya Kovalevsky; a biography, and Sisters Rajevsky; being an account of her life by Sonya Kovalevsky by Anna Carlotta Leffler
Women in Mathematics by Lynn Osen
Notable Women in Mathematics edited by Charlene Morrow and Teri Perl

Maria Gaetana Agnesi – 18th century mathematician

Maria Gaetana Agnesi, artist unknown (source)

Maria Gaetana Agnesi, artist unknown (source)

“How long will I have to do this?” must have been the thought that frequently ran through the mind of Maria Agnesi as she stood in her parlor on Friday nights.  Maria Gaetana Agnesi was the oldest of 21 children born into the family of Pietro Angesi.  The Agnesi family was a well to do family in Milan, Italy in the 18th century.  Pietro came from a merchant class family who had made their money in cloth goods.  The family owned many properties and had furnished them exquisitely.

Pietro’s grandfather, father, and uncle had built the business into a sort of empire.  For some unknown reason, Pietro was never trusted with the business.  Even when his father died, provision was made in his will that prevented him from making any decisions concerning the business without the approval of his uncle.  However, when his uncle died childless, the responsibility for the business fell entirely onto Pietro’s shoulders.

Pietro was a very ambitious man.  He had almost everything that he could want, materially.  The one thing he didn’t have was a position in the aristocracy.  He tried many things to be recognized as a member of this class which eventually ran up a huge debt.  One of these things was hosting “conversazione” on Friday nights.  There were many such events held around the city for the wealthy to indulge themselves.  Some were for music and dancing, some for gambling, but at the Agnesi household discussions of philosophy were held.  These events served their purpose and attracted many distinguished persons to the Agnesi home such as Monsieur Charles Brosses, president of the parliament of Burgundy and Frederick Christian, heir to the throne of Poland.

One thing Pietro never scrimped on, even when he was accumulating debt, was his children’s education.  He hired the best tutors from around Europe for both the boys and the girls.  This was during a time when women across Europe were rarely educated.  Genius was, however, recognized and Maria Gaetana was that – a child prodigy.  By the age of 11, she could speak, read, and write Italian, French, German, Spanish, Latin, Greek, and Hebrew.  At the age of 9, she translated a treatise written in Italian into Latin, memorized it, and delivered the oration at one of her father’s “conversations”.  The treatise was on the education of women, arguing that they should be allowed access to “the fine arts and sublime sciences”.

She and her sister were regularly put on display in the salon of their family home.  Here her father entertained many wealthy and noble men.  Maria Gaetana was asked questions by the participants and she would expound on the subject.  She was adept at discussing philosophy as well as the sciences and mathematics.  She was brilliant, and the men who attended were amazed that she could discuss the philosophy of Descartes as easily as celestial mechanics or the theory of gravitation.  Her sister, Maria Teresa, was a composer.  She would play the harpsichord and sing, sometimes accompanied by Maria Gaetana on the viola.

Maria Gaetana (1718 – 1799) was basically shy and reserved person.  She didn’t enjoy being put on display, but was obedient to her father’s wishes.  A devout Catholic, at one point during her teens, she approached him to ask if she could be excused from further events.  She wanted to enter the cloister.  Her father refused to allow this and she continued participating.  Maria Gaetana never married and most of her time was spent teaching the younger children and after her mother (Anna Brivio) died in 1732, managing the household.  What time she could spare, she gave in helping ill and homeless people, primarily women.

First page of "Analitical Institutions", 1748 (source)

First page of “Analytical Institutions”, 1748 (source)

As she got older, one of Maria Gaetana’s responsibilities was to tutor her younger brothers in mathematics.  She had a passion for scholarship including mathematics and had absorbed works by Newton, Fermat, and Descartes among others.  She found all of the texts available to be inadequate for the task of teaching her younger siblings.  For this reason she decided to write her own.  Originally, it was intended to be used only for their lessons but 10 years after she began it, Analytical Institutions was published to wide acclaim.  It was a comprehensive look at mathematical analysis at the time, from algebra through differential and integral calculus, infinite series, and differential equations.  She managed to synthesize work from many of the masters including Newton and Leibnitz to write a text that made these topics accessible to the lay person.

Maria had previously published Propositiones Philosophicae a volume of about 200 essays on various topics presented at her father’s conversations.  But she is primarily known for Analytical Institutions.  It is the earliest surviving math text written by a woman and was translated into English and French for use as a textbook.  She was honored by such people as Pope Benedict XIV with a gold medal and Empress Maria Theresa with jewels.  She was also elected to the Bologna Academy of Sciences.  This position included a faculty post.  There is some disagreement as to whether or not she ever taught there.

Whether or not Maria Gaetana taught outside the home, this would have ended when her father died in 1752.  He had left the family in tremendous debt and most of their possessions had to be sold to cover it.  This changed Maria’s lifestyle and set her free to pursue her passion.  Until her death in 1799, Maria Gaetana gave selflessly to others.  She worked with the ill and homeless people of Milan with both her time and what resources she had left.

The "Witch of Agnesi" curve (source)

The “Witch of Agnesi” curve (source)

Maria Gaetana Agnesi is most well known for a curve that she worked with called the “Witch of Agnesi.”  Known for, that is, outside of Italy.  In Italy she is known as a great humanitarian and woman of God.  She was buried in a common grave with 15 other women and her childhood home was destroyed during WWII.  But the city of Milan is proud of their daughter and there are monuments that have been erected to celebrate her life.

Bust of Maria Gaetana Agnesi, beneath the arcades of the courtyard of the Palace of Brera at Milan. Photographer: Giovanni Dall'Orto (source)

Bust of Maria Gaetana Agnesi, beneath the arcades of the courtyard of the Palace of Brera at Milan. Photographer: Giovanni Dall’Orto (source)

References
The World of Maria Gaetana Agnesi, Mathematician of God
by Massimo Mazzotti
Women in Mathematics by Lynn Osen

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