Mathematicians – Women's History and More

Emmy Noether – Original in More Ways Than One

“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.

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.”

320px-Entrance_Bryn_Mawr — The entrance to Bryn Mawr, where Emmy spent the last year and half of her life.

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.

Ada Byron Lovelace – “Enchantress of Numbers”

Ada Lovelace by Alfred Edward Chalon (source)

Often women in the 18^th and 19^th centuries overcame significant odds to study mathematics or science, but as with every rule there is the exception. Ada Byron Lovelace is one of those exceptions. In Ada’s case, not only did she have a parent who approved of her interest, but one who pushed her to develop that interest; and it wasn’t her father who pushed her, but her mother.

Augusta Ada Byron, born December 10, 1815, was the daughter of Annabella Milbanke and the poet Lord Byron. The marriage was short-lived and Ada never got to know her father. Only a few weeks after her birth, Lord Byron left England and went to the continent, her mother made the separation official and took custody of Ada, something that was unusual for the time. Annabella was well-educated with a particular interest in mathematics and was determined that her daughter would be as well. (Lord Byron referred to Annabella as “princess of parallelograms” and later as the “Mathematical Medea,” which may give us a feel for her expertise in math, but also their relationship.) She researched the best education techniques and obtained the best tutors for Ada. Because they were of the aristocracy (in 1856, Annabella became Baroness Wentworth in her own right,) Ada also had access to some of the best intellectual minds of the time; including Mary Somerville, Augustus De Morgan., Michael Faraday, Charles Dickens, William Frend, Charles Wheatstone, and Woronzow Greig.

Annabella was a domineering mother. Some say that she wanted to suppress any tendency that Ada might have toward the mental instability of her father, so she insisted on strict lessons focused on rational pursuits and the avoidance of any romantic subjects such as poetry. (One anecdote says that Annabella fired a tutor for giving her daughter too much geography and not enough math.) Although Ada’s mother may have pushed her, Ada did have the talent for mathematics. Even though she was often ill as a child, suffering from blinding headaches and a period of paralysis, she worked hard to achieve the goals her mother set for her. De Morgan once wrote to Annabella that Ada had the capacity to become “an original mathematical investigator, perhaps of first-rate eminence.” Of course, he proceeded this by saying “if she were a man entering university.”

In 1833, Ada entered London society and was introduced at court to King William IV and Queen Adelaide. During one of the many social events they attended during the year, Ada and her mother were introduced to Charles Babbage, a noted mathematician and inventor of the Difference Machine. During that time astronomical tables were created by giving the calculations to two people (often women) and then comparing the results for discrepancies. Once when going over some of these calculations with Sir William Herschel, the astronomer, and finding many mistakes, he declared that he wished the calculations could be done “by steam,” meaning by machine. Babbage went on to design such a machine which he called the Difference Machine, so when Ada and her mother met him they were both very interested in learning more about it. They arranged to go see a prototype that Babbage had built and Ada asked to see the blueprints. For whatever reason, Babbage agreed to show this teenaged girl and her mother his plans, and a life-long friendship and collaboration was born.

Ada Lovelace by Margaret Sarah Carpenter (source)

As much as she enjoyed it, mathematics didn’t interfere with Ada’s social life and in 1835 she married William King who would become the Earl of Lovelace in 1838. They had several large homes, lived well, some might say too well, and had three children: Byron (1836), Anne Isabella (1837), and Ralph Gordon (1839). Ada doesn’t seem to have had much to do with her children; in fact her mother seems to have had more to do with their upbringing than she did. Certainly after Ada became sick and died, her mother directed the education of the children. King was supportive of Ada’s continued work in mathematics and from the time she met Babbage in 1833 until around 1842, she continued studying mathematics and corresponding with the best mathematicians of the day, including Babbage.

Analyzing the personality of a historical person is difficult and a number of different things have been said of Ada; that she was a hard drinking gambler; she inherited her father’s mental instability; and that she led a rather boring life, except of course for the rather long horseback rides with a man from a neighboring estate! What does seem clear from her letters is that she had fluctuating moods and that she did go to the horse races. However, over the course of William’s life he sold off many of his estates and by the end of his life was borrowing money. Considering he lived much longer than Ada, it seems likely that he was the primary source of the gambling debt, although Ada may have contributed to it. I’m not sure about the drinking, but Ada died of what is believed to have been uterine cancer, so for the last several years of her life she surely would have been prescribed laudanum (an opiate) for pain.

Babbage meanwhile, received financial support for building his Difference Machine, but had instead designed a more complex machine, the Analytical Engine. Where the Difference Machine could only perform basic addition and subtraction, the Analytical Engine could perform many more calculations, basically the equivalent of a modern day calculator. It is the earliest design of its kind that we are aware of and quite remarkable for its time. In 1842, Babbage was persuaded to give a lecture on the Analytical Engine at the University of Turin. One of the attendees, Luigi Menabrea, an engineer and the future prime minister of Italy, wrote a paper on the Engine and published it in a Swiss Journal, in French of course.

After Menabrea’s paper was published, Babbage asked Ada to translate it into English. At Babbage’s suggestion, Ada added notes to the paper explaining the concepts in more detail and adding information. The resulting paper was three times as long as the original and was well received. Included in the notes is an algorithm, a sequence of steps, which would allow the engine to calculate Bernoulli numbers, a series of numbers used in various branches of mathematics. Today we would call this a computer program, which is why Ada is often called the world’s first computer programmer. There is some controversy surrounding this, however. Many people believe that Ada was not the originator of the algorithm; that Babbage, in fact, wrote all the mathematics contained within the paper. She and Babbage were close friends and corresponded on a regular basis often multiple times during the day, so it is sometimes difficult to determine. He seems to have thought highly of her and referred to her as an “enchantress of numbers.”

Ada did contribute something that is significant and was acknowledged by Babbage to be her idea. She envisioned the machine being used to produce music. She was familiar with the Jacquard loom, which used punch cards similar to the Analytical Engine to produce complex patterns in weaving. Ada reasoned that if numbers could represent other things such as frequencies, that the engine could be programmed to produce frequencies in a particular way and produce music. This idea of using numbers to represent other things or as symbols was ahead of her time and prophetic of our present day computers.

Unfortunately, the paper on the Analytical Engine would be Ada’s crowning achievement. She died on November 27, 1852 at the age of 36 from what seems to have been a type of uterine cancer. Her mother came to take charge preventing any of her friends from seeing her in the last months of her life, including Charles Babbage. At her request, she was buried beside her father. Many mathematicians do their best work at an early age, but Mary Somerville, one of Ada’s mentors, began doing her best work in her 40s, so who knows what Ada might have achieved had she lived.

Learn about other Famous Women in Mathematics and Science.

Resources
Notable Women in Mathematics edited by Charlene Morrow and Teri Perl
Women in Science: Antiquity through the Nineteenth Century by Marilyn Bailey Ogilivie
Pictures of Babbage’s Difference Machine at the Computer History Museum in CA and a short NPR piece.

BBC show “In Our Time” – Melvyn Bragg with Patricia Fara, Senior Tutor at Clare College, Cambridge; Doron Swade, Visiting Professor in the History of Computing at Portsmouth University; John Fuegi, Visiting Professor in Biography at Kingston University.

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

Sketch of the Analytical Engine invented by Charles Babbage by L. F. Menabrea – this is the translation of Menebrea’s paper with Ada’s notes.

Mary Fairfax Somerville – Mathematics by Candlelight

“I was annoyed that my turn for reading was so much disapproved of, and thought it unjust that women should have been given a desire for knowledge if it were wrong to acquire it.”

Mary Fairfax Somerville

The 17th and 18th century women mathematicians and scientists that we’ve looked at so far have been accepted into intellectual circles. Their intelligence and works were recognized and in Italy they were even allowed to teach. They were accepted that is, once they got there. Maria Agnesi, Emilie du Chatelet, and Laura Bassi all had one advantage – parents, or at least fathers, that indulged their intellectual curiosity and gave them the education they craved. Mary Fairfax Somerville did not have this advantage.

As a young girl, Mary Fairfax, born in Jedburgh, Scotland on December 26, 1780, was by her own admission a “wild creature.” Her father, a Vice Admiral in the British Navy, was away from home for long periods of time and her mother was quite permissive. With the exception of learning to read the Bible, the catechism, and daily prayers, she received no academic lessons. She was taught “useful” skills, how to care for the garden, preserve fruit, tend the chickens and cows, tasks reserved for the women of the household. Apart from these chores, there were few demands made on her time, so she would roam the countryside and seashore near her home in Burntisland, Scotland observing sea creatures and birds, collecting things, and learning the names of the plants around her home. At night, the stars she could see from her window held equal fascination.

When she was about nine years old, this carefree existence came to an end when her father returned from a long voyage to learn that Mary’s reading skills were minimal and she couldn’t write. At least the basics were expected of young women, so Mary was sent to a school run by Miss Primrose. In spite of her intellectual curiosity, Mary didn’t fair well at the school where she was expected to prepare lessons laced into stiff stays and steel busks designed to improve her posture. The teaching techniques focused on memorization including pages from the dictionary and gave little room for curiosity or critical thinking. After one year at the school, she returned home and continued her wandering existence, but at least she had increased reading skills that allowed her to enjoy a small number of books in their home. Mary’s only other formal education was a year spent in a local school where she learned to “write a good hand”, basic arithmetic, and the womanly arts of needlework, painting, music, etc.

Mary’s interest in mathematics was piqued by a couple of chance encounters. Once during a party she was paging through a women’s magazine and came across a puzzle. When she looked at the answer it had x’s and y’s in the solution. Curious, she asked a friend who told her that it was something called algebra, but she couldn’t tell her what it was. The second conversation that would set the stage for her life long interest was an overheard conversation between a painting instructor and a male student. The instructor told him that he should study Euclid’s The Elements about geometry to better understand perspective.

Now Mary knew the names of two things she wanted to study, algebra and geometry, but how could she get the required books? To do this she conspired with her brother’s tutor. His skills were limited, but he agreed to obtain books for her and demonstrate the first problems in The Elements. She was on her way! Each night after the rest of the household retired, Mary would study mathematics by candlelight. But then the candle supply started to diminish and it was noticed.

For many people during this time, keeping women away from intellectual pursuits wasn’t just a matter of propriety. Some people believed that women’s minds couldn’t handle it and it would drive them crazy, or that mental exertion would take away from their ability to have children. In essence, that they had a “delicate constitution” that had to be protected. In her recollections of childhood, Mary recalls her father saying, “Peg, we must put a stop to this, or we shall have Mary in a straight-jacket one of these days. There was X who went raving mad about the longitude.” So when her parents discovered that she was studying at night, the servants were instructed to take away her candles. However, at this point she had already progressed through the first six books of Euclid, so she depended on her memory and worked through the problems in her mind each night until she knew them thoroughly.

In 1804, Mary was married to a distant cousin, Samuel Greig. Although not interested himself, it seems that Greig tolerated Mary’s intellectual interests, but the marriage was short-lived. Greig died in 1807 leaving Mary with two boys and a small inheritance. She returned to her parent’s home, but her inheritance gave her an independence that allowed her to continue her studies. She began reading The Mathematical Repository, a journal which aimed at exposing the general public to some of the new developments in mathematics. Through the journal, she began a correspondence with William Wallace a professor at the University of Edinburgh. Wallace provided Mary with a list of important books on mathematics and science, and she began to accumulate a library.

Mary’s second marriage to another cousin, Dr. William Somerville, inspector of the Army Medical Board, was completely different. Dr. Somerville didn’t just tolerate Mary’s interests, he encouraged them. Together they raised a family, traveled, collected specimens, and associated with some of the greatest scientists and mathematicians of the day. They would remain together for the rest of their lives.

Mary’s first work was published in the Philosophical Transactions of the Royal Society of London and titled “On the Magnetizing Power of the More Refrangible Solar Rays.” Although she was not a member of the Society at the time (1826) and her paper had to be presented by her husband, it attracted the attention of Lord Brougham, of the Society for the Diffusion of Useful Knowledge. He commissioned her to write what would become probably her greatest and most well-known work, a translation of Laplace’s Mécanique Céleste. The purpose of the Society of the Diffusion of Useful Knowledge was to make new scientific discoveries accessible to the general public that might not have the educational background to read the original documents. As it turned out Mary had a gift for this type of writing.

Mary had studied Laplace’s work, but being largely self-taught and having doubts about her ability to do it justice, she extracted a promise from Lord Brougham and her husband that if it wasn’t sufficient it would be burned. She spent the next four to five years working on it and when it was complete it was much more than Lord Brougham needed. Her introduction alone met his needs and was published separately, but the entire work was published as The Mechanism of the Heavens and became a favorite among students at Cambridge. She had a gift of being able to communicate in clear, concise terms, complicated subjects, translating as she said “algebra into English.” Her later works include On the Connection of the Physical Sciences published in 1846, Physical Geography in 1848, and Molecular and Microscopic Science in 1860.

Mary Somerville continued writing for the rest of her long life. She died in Naples, Italy on November 28, 1872. Her legacy is one of excellently written scientific books that continued in use for many years, but also one of what a woman can do when she has a drive to do it. As she said herself it is indeed “unjust that women should have been given a desire for knowledge if it were wrong to acquire it.”

Resources
Personal Recollections from Early Life to Old Age of Mary Somerville by Martha Somerville
Women in Mathematics by Lynn Osen
Notable Women in Mathematics edited by Charlene Morrow and Teri Perl

Read about other Famous Women Mathematicians and Scientists.

Laura Bassi – Italian Physicist (1711 – 1778)

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 18^th 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 20^th 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.

bassi_coin2 — A coin was minted to commemorate Bassi’s acceptance as a professor at the University of Bologna.

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

Read about other Famous Women Mathematicians and Scientists.

Émilie du Châtelet – “femme savant” and paramour

Émilie du Châtelet by Maurice Quentin de La Tour

Depending on where you have heard of Émilie du Châtelet you know her as a mathematician and scientist, or the paramour of Voltaire. She was both, a complex woman stimulated by intelligent conversation and study, but also a coquette. On the one hand very unusual for a woman of the 18^th century, on the other a product of her time.

Gabrielle-Émilie Le Tonnelier de Breteuil led a privileged life. Her father was an official in the court of Louis XIV at Versailles. At the time of Émilie’s birth, he held the position of Introducer of Ambassadors at court. This put him in the midst of all of the important social happenings of the time in France. Her mother Gabrielle Anne de Froulay was brought up in a convent and well educated for a woman of that time. The family owned a home in Paris and an estate in Touraine.

Émilie was born in 1706, the only girl of six children. Three of her brothers survived to adulthood, although only one lived to an old age becoming an abbé and later a bishop. As with many women of the time, Émilie was educated because her father recognized her genius and promoted it by providing tutors for her. Although Émilie’s mother was educated in the convent, there is some evidence that she resisted the rigorous education that her husband gave Émilie. In spite of this, tutors were brought to the house to teach her astronomy, mathematics, and physics. She became fluent in German, Italian, Latin, Greek, and as an adult, published translations of literary as well as scientific works into French. In spite of her recognized brilliance, her education wasn’t strictly academic. She received training in fencing, riding, the harpsichord and opera. However, her preference in study was for mathematics and philosophy, certainly unusual for a woman of the 18^th century. In a somewhat scandalous application of her abilities, she used her knowledge of mathematics as a teenager to prosper as a gambler. The proceeds were, of course, used to buy the science and mathematics texts she wanted.

All young aristocratic women of the time were expected to make a good marriage and Émilie was no exception. A marriage was arranged and in 1725, she married Marquis Florent-Claude du Chastellet-Lomont. She became the Marquise du Chastellet. (The spelling Châtelet was introduced later by Voltaire.) Émilie was nineteen and Claude was in his early thirties. The marriage doesn’t seem to have been a very passionate affair. It would survive infidelities on both sides. They did, however, have three children: Françoise Gabriel Pauline (1726), Louis Marie Florent (1727), and Victor-Esprit (1733) although Victor died in 1734.

Claude was a military man, this kept him away from home quite a bit and by the time Émilie had her third child, she was bored. Tired of being away from society and ready to resume her active life and her studies, she reemerged on her own terms. Although Émilie didn’t actively resist convention, she was determined to live her life as she saw fit. She lived life enthusiastically and with boldness. Unfortunately, this approach had its consequences and she became the focus of a fair amount of malicious gossip. Lynn Osen, in her book Women in Mathematics, states that Émilie committed two unforgivable sins: “She refused to give up her serious study of mathematics” and “she stole the heart of Voltaire.”

In eighteenth century French society, as in many other times, the issue that concerned people in their gossip was not whether or not a woman had affairs, but was she discreet. There are three names that are associated with Émilie ’s love life. Although Émilie knew these unwritten rules, at the end of her first affair she broke them in a very indiscreet way. There are a couple of different versions of how it came about, but the result is the same, she attempted suicide. Whether this was an attempt at emotional blackmail or just evidence of her passionate nature, it was thwarted by her lover when he discovered her and got her immediate medical attention.

Voltaire c. 1724, by Nicolas de Largillière

Émilie ’s second affair, and a friendship that would last until her death, was with Voltaire. She may have met him when she was young, but her adult friendship began with him in 1733 after the birth of her third child. Even though intellectual women were the butt of many jokes during that time not only in society, but also in literature and the theater (“femme savant” was not a compliment), intellectual men often still sought out these women as their companions. Émilie and Voltaire were companions in every sense. Over the next 15 – 16 years before Émilie ’s death in 1749, they would rarely be separated and would challenge each other to produce work that has stood the test of time.

Voltaire was often in trouble with the powers that be and was exiled to Britain at one point. When his exile seemed imminent again, Émilie suggested that they go to one of her husband’s country estates at Cirey. Claude seems to have liked Voltaire and if not welcoming of his wife’s affair at least accepting of it. Émilie and Voltaire set up a laboratory, accumulated a library and did substantive work during their time here. Émilie came into her own in mathematics and science and began to make a name for herself.

You could think of them as collaborators of a sort, but although they had many interests in common, their strengths were different. One early example of how they did collaborate was when Voltaire entered a contest for an essay on the scientific properties of heat and light. Émilie worked with him on his experiments and ideas, but at some point she disagreed with his conclusions and decided to enter the contest herself. Neither won, but both were recognized for their work by having it published. The prize was jointly awarded to three men one of whom was Euler. (That will give some of you an idea of the competition they were up against.)

Although, Émilie translated literary works and wrote Biblical Commentary on Genesis and the New Testament, there are two major works for which Émilie du Châtelet is best known. One is Institution de physique, “Lessons in Physics.” Originally intended as a text for her son, it was her assessment of the latest ideas in science and mathematics. In it she attempted to reconcile and explain the works of the major thinkers of her time, such people as Newton, Leibniz, etc. These were concepts that few people could really grasp at the time.

Émilie ’s most outstanding achievement is her translation of Newton’s Principia Mathematica into French with commentary. It was a complete translation of all three books with a commentary that summarized and explained Newton’s theories. She also applied the new mathematics of calculus to his ideas. This was the only complete translation of Newton’s work into French and remains the standard today. Émilie worked on this up to the time of her death and Voltaire ensured its publication ten years later.

The third name associated with Émilie ’s love life is the poet Jean François de Saint-Lambert. In the winter of 1747 – 1748, Émilie traveled with Voltaire to Lunéville, the home of the duke of Lorraine. Here she met and fell in love with Saint-Lambert who was ten years her junior. She also became pregnant. Although Voltaire may have been hurt, it is also possible that by that time their relationship had settled into one of companionship rather than lovers. In either case, he remained by her side and with Saint-Lambert returned to Cirey. I’ve read a couple of theories about what happened next. One is that the three of them conspired to get her husband back to Cirey to convince him that the child was his. The other which seems more likely to me is that he cooperated and returned to spend time there in order to give the child legitimacy. In either case, they were all three with her when the child, a daughter, was born in September of 1749. Although, the delivery seemed to go well, Émilie died a week later.

Some people may have viewed Émilie primarily as Voltaire’s muse, but she was much more. She was a brilliant, sometimes contradictory, woman who chose as much as possible to live life on her own terms.

Resources
Women in Mathematics, Lynn Osen, 1974.
An Eighteenth Century Marquise, Frank Hamel, 1910.

Read about other Famous Women in Math and Science.

Sonya Kovalevsky – A Marriage of Convenience

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 in January of 1850 in Russia, 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

Hypatia – A Martyr for the Truth

This was inspired by the life of Hypatia, who lived in the 4^th and 5^th centuries C.E. She was a real person and brilliant mathematician. Often she is the only woman mathematician mentioned in books on the history of math. The character writing is fictitious, but the events are true.

A Day in Alexandria

I arrived in Alexandria as the sun was going down. The trip from Cyrene had been a rough one and I was glad to have my feet on solid ground again. My teacher and mentor, Synesius, had corresponded with her for years. He raved about her brilliance, her inventions, her ability to teach others, and her original mathematical work. Hypatia! Finally, I would hear for myself. Little did I know what horrors I would witness and how the world would change from this year on.

This was my first trip to the great city of Alexandria. I planned to be here for a while to take advantage of the magnificent library (at least what was left of it) and many great teachers. I would eventually find a place to stay, but for now, I had a letter of introduction to a friend of my mentor. He very kindly invited me into his home and gave me a meal and place to sleep for the night. The political climate is very tense these days. It is the year 415 (A.D.) and the Christians are gaining strength in many places. They have very little tolerance for beliefs different from theirs. Cyril, the church patriarch, considers anyone of the neo-Platonic school of thought to be a heretic. But, there are still many of us who are members of this school, including Hypatia.

As we sat down to a simple meal, or rather reclined in the Greek fashion, my host began to tell me a little more about the city and Hypatia.

“You know her!”, I cried.

“Actually, I’m a friend of the family. More her father’s friend.” He replied.

“Please tell me. Are all the stories I hear of her true?”

He laughed, “Actually, many of them are, but what in particular are you interested in knowing?”

“They say she inspires great devotion in her students and anyone interested in learning.”

“She does. She’s a magnificent orator, devoted to teaching, and to the truth. I make sure that I hear her often and read most of what she writes. She has done quite a bit of original work in mathematics, written commentaries and built on the works of some of the greats – Diophantes, Apollonius, among others. ”

“And she is a scientist as well,” I added. “My mentor, Synesius, has been particularly interested in her inventions, such as the astrolabe and the planesphere for studying astronomy.”

“I know nothing of that field, but am told that she has a number of inventions that have added to it. I am more familiar with her writings in mathematics, although, she is very learned in many fields. Her father, Theon, my friend, was determined to produce the ‘perfect human being’ as he says. Many think that he has. Of course, he is a professor of mathematics at the university as well, so he had access to many resources and took charge of her education. I’m sure she picked up the love of mathematical elegance from him, but he didn’t stop there. She learned it all – astronomy, astrology, mathematics, religion. And he didn’t neglect the body. She is accomplished at rowing, swimming, horseback riding . And yes, she is very beautiful as well, even now in her mid 40s. She has also traveled extensively and basically made a name for herself.”

“Did you say she studied religion?”

“Yes, as in ALL religions, rather than one. Theon was particularly concerned that she NOT be caught up in any one religion to the exclusion of new truths. He feels that all dogmatic religions are false. If we can’t be open to new ideas, we have cut ourselves off from the truth. Hypatia has been raised to be very discriminating in her thoughts and acceptance of new ideas. As Theon frequently says, ‘Reserve your right to think, for even to think wrongly is better than not to think at all.’ . . . It hasn’t made it easy for her in the current climate. She is a close personal friend of Orestes, the prefect. I think that is one reason that her popularity is tolerated. But, ever since 412, when Cyril became patriarch, things have become more and more tense. Sometimes I fear for her and others who are seen as champions of other ways of thought.”

“She must be an amazing person. Is she married?”

“She is very beautiful, but no, she has never married. She has had opportunities, but always says that she ‘is married to the truth.’ But, I think you’re a little young for her,” he teased.

I was embarrassed, but still had to ask. “Do you think I could meet her?”

“Hmm . . . I think she has a gathering at her home tomorrow night. Her students often gather there and anyone is welcome. Right now though, it is getting late, and her lecture is the first of the day tomorrow. I had planned to go with you, but won’t be able to if I can’t get any sleep.”

I was the one who had trouble sleeping that night because of my excitement. I was up with the sun and after a brief meal, we set out toward the university. It was a beautiful day as we walked along the bay. The sun was bright and the colors were vivid. It was a perfect complement to what I felt inside. We followed the coast for just a short period before we turned to go up to the main thoroughfare that led to the University of Alexandria. As we approached, it became noisier and more crowded as I expected. When we got closer, however, it seemed to be more of a mob than the usual crowds of a city.

“What is happening?” I asked my new friend.

“I’m not sure. This is unusual. I have friends who live here. Let’s go in and see if we can go up to the roof to get a better view.”

We were allowed entrance by one of the slaves who recognized my host and told us that the master was already on the roof observing. As we joined him, I could see that the street was crowded by an angry mob. In the center of the mob was a woman in her chariot. The crowd had brought the horse to a stop and was attacking the woman, hitting her, grabbing her hair, and throwing stones. I could already see where a clump of her hair had been pulled out. She was fighting back, but it was useless against so many. Someone yelled above the crowd, “to the church, to the altar.” At that point, strong hands grasped the woman and she was carried into the nearby Christian church.

“The poor woman, what can we do? Do you know who she is?”

“That,” whispered my host, “is Hypatia. . . I doubt we can do anything against that mob to help her, but we can try. I know a back way into the church.”

As we raced to the door, fear seized my heart for this woman I had never met, but heard so much about. The mob of people, mostly men, were obvious as Christians by the way that they dressed. I understood that they didn’t favor her teachings, but this anger seemed extreme.

We were unable to get through the door until it was too late. When we did, the extent of their depravity was overwhelming. The mob, whom I later learned was a group of monks from a monastery in the desert, had stripped her and peeled away her skin with bits of tile and pottery. Her limbs had been torn from her body. Her voice was silenced.

I couldn’t stay in Alexandria after that. It wasn’t really safe for a non-Christian foreigner, and besides, I didn’t have the heart for it. I heard rumors later about what had happened. Some said that Hypatia’s limbs were put on display in different parts of the city; some said her body was burned. Orestes fled and Cyril finally had what he wanted – power. I went to Athens to continue study, but everywhere things were changing.

Note: Although partially destroyed in 391 C. E. the library in Alexandria would be completely destroyed a few years after Hypatia’s death and the western world would be plunged into a period that has come to be known as the dark ages.

Carl Sagan speaks about Alexandria and Hypatia:

References

Hubbard, Elbert. Little journeys to the Homes of Great Teachers. Vol.23. New York. The Roycrofters. 1808.

Mlodinow, Leonard. Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace. New York. Simon and Schuster. 2001.

Osen, Lynn. Women in Mathematics. Cambridge, Massachusetts. The MIT Press. 1974.

Women gaining in STEM

I intended this to be a blog about women in history, as in not currently living, but I’ve already added a book review about a women currently fighting for human rights in Afghanistan and I can’t resist posting the link below about the gains women are making in STEM – Science, Technology, Engineering, and Math.

I studied math in college, both undergraduate (in the 70s) and graduate (in the mid 80s.) I remember how few women were in my classes. As a freshman and sophomore there were more, but as those who planned to teach moved on to education classes, there were fewer of us in the more technical classes. (I never really planned to teach high school math, it ended up being a fall back job for me about 20 years later.) When I got to graduate school I studied Applied Math which basically means I was in class with a lot of future engineers. It wasn’t unusual to be one of 4 or 5 women in a class full of men. Oddly enough, we didn’t usually hang out and study together. I guess we just worked on our “boy social dynamics” as Rebecca Allred says in the article. I feel very fortunate that I didn’t really run into any problems. I always had a few classmates to study with which was all I wanted.

Women have made great strides in fields that have traditionally belonged to men. I never really felt as though I had something to prove in those days, but I know many women did. From reading this article it seems as though maybe we really are moving into a time when women can just study and do what they like and are good at without thinking twice about whether it is a man’s field or not. Which is as it should be. Check out the article here.

Women making slow, sure strides in science, math

Maria Gaetana Agnesi – 18th century mathematician

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 18^th 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

Read about other Famous Women Mathematicians and Scientists