Sophie Germain: Mathematical Genius Emerging from the French Revolution

The Storming of the Bastille, artist unknown (source)

The Storming of the Bastille, artist unknown (source)

Born on April 1, 1776 in Paris, Sophie Germain grew up during a turbulent time. She was 13 years old in 1789 when the Bastille fell and life on the streets became very dangerous. Her parents, Ambroise-Franҫois and Marie-Madeline Germain, were wealthy. Ambroise was a merchant (some sources say silk, some say goldsmith) and elected as a deputy to the Estates-General. Sophie and her sisters would surely have heard intelligent conversation in their home, especially politics and philosophy.

The Germains were able to keep their daughters safe, but it did require remaining indoors most of the time. To keep herself occupied, Sophie turned to her father’s library. It wasn’t long before she ran across the story of the death of Archimedes in a book called The History of Mathematics by Jean-Étienne Montucla. Legend has it that Archimedes was so engrossed in a geometry problem that he didn’t realize Roman soldiers were about to kill him. Sophie thought that geometry must be very fascinating to cause Archimedes to ignore a threat to his life, so she decided to study math. This idea, however, didn’t please her parents.

Sophie Germain (source)

Sophie Germain (source)

Studying math and science wasn’t thought appropriate for women and girls except among the aristocrats. There wasn’t a need for it and some thought it harmful to a girls mind. Her parents did everything they could think of to discourage Sophie. When they forbid her to study these subjects, she appeared to comply, but waited until they went to sleep and studied by candlelight. When they discovered what she was doing, they took away her candles, put out her fire, and took away her clothes after she went to bed, so that she would sleep. She simply kept a stash of hidden candles, wrapped herself in quilts and continued. Even when it was cold enough to freeze the ink in the inkwell, they would find her asleep over her books. Finally, they gave in and let her choose her subjects.

Sophie studied philosophy, classics and math, even learning Latin and Greek to be able to read Newton, Euler and Virgil. She worked through all the math books she found in her father’s library eventually moving on to differential calculus.

The École Polytechnique opened in 1794, when Sophie was 18. Because she was a woman, she couldn’t attend lectures, but she borrowed lecture notes from friends. She also began to submit her work to Joseph Lagrange under the name Monsieur Le Blanc. When Lagrange found out her true identity, he supported her and encouraged her to correspond with other mathematicians.

Historic building of the École Polytechnique by Juan Antonio Cordero (source)

Historic building of the École Polytechnique by Juan Antonio Cordero (source)

Probably the most famous and accomplished mathematician with whom Sophie corresponded was Karl Friedrich Gauss, considered by many to be the “greatest mathematician since antiquity.” Again, she chose to use the name M. Le Blanc and Gauss was impressed with her work in number theory. They corresponded for several years and then Sophie became concerned with Gauss’s safety. He lived in a German town which was soon to be occupied by French troops. Knowing his devotion to mathematics and thinking of Archimedes, she contacted a family friend in the French army and asked him to ensure Gauss’s safety. He did, but Gauss was confused because he didn’t know Sophie Germain by her real name.

Karl Friedrich Gauss c. 1887 by Gottlieb Biermann (source)

Karl Friedrich Gauss c. 1887 by Gottlieb Biermann (source)

The confusion was soon sorted out via correspondence, and much to Sophie’s pleasure and surprise, Gauss was delighted. “How can I describe my astonishment and admiration on seeing my esteemed correspondent M LeBlanc metamorphosed into this celebrated person. . . when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarising herself with knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius.” (emphasis mine)

Sophie contributed significantly to number theory including the foundation 20th century mathematicians would build on in attempting to solve Fermat’s Last Theorem, but she also became interested in physics. In 1808, Ernst Chaldni gave a demonstration before the Paris Academy of Sciences on vibrating surfaces. The experimental results were intriguing and caught the attention of Napoléon. He convinced the Academy to run a contest to “give the mathematical theory of the vibration of an elastic surface and to compare the theory to experimental evidence.” Sophie decided to enter.

One of Sophie’s challenges was her lack of rigor in her mathematics, probably due to her lack of formal education in the field. This was part of the problem that caused the rejection of her submission to the contest in 1811. But Sophie didn’t give up. The contest was extended and Sophie submitted another paper in 1813. This time she was awarded an honorable mention, although there were still problems with her calculations.

Finally, in 1816, Sophie submitted a paper under her own name which won the prize. She was the first woman to win a prize from the Academy, but was still unable to attend its sessions. (The only women admitted were the wives of the members!) However, now she was allowed to attend lectures at the École Polytechnique. Sophie continued her work on elasticity, publishing her results in 1821 and a refined version in 1826.

Although Sophie’s work was always affected by her lack of formal education, she was seen  as ingenious and earned the respect of many of her colleagues. Gauss was sufficiently impressed to recommend to the University of Göttingen that she be awarded an honorary degree. Sadly, she died before this could happen.

In 1829, Sophie learned that she had breast cancer. Although some of her philosophical works were published posthumously, she ironically finished her last mathematical publication to the sounds of the Second French Revolution in the summer of 1830. On June 27, 1831, Sophie Germain died at her home in Paris.

Sophie Germain's headstone, photo by Miek Messerschmidt (source)

Sophie Germain’s headstone, photo by Miek Messerschmidt (source)

Read about other Famous Women Mathematicians and Scientists.

Resources
Celebrating Women in Mathematics and Science by The National Council of Teachers of Mathematics (NCTM)
“Sophie Germain” by Mary Gray in Complexities: Women in Mathematics, ed. Bettye Anne Case and Anne M. Leggett
Women in Mathematics by Lynn Osen
Women in Science by H. J. Mozans
Women in Science: Antiquity Through the Nineteenth Century : a Biographical Dictionary with Annotated Bibliography by Marilyn Bailey Ogilvie

“Les Trois Grandes Dames” of Impressionism – Part 3 – Berthe Morisot

"Berthe Morisot Painting" (1865) by Edma Morisot (source)

“Berthe Morisot Painting” (1865) by her sister Edma Morisot (source)

The Salon de Paris was the official annual exhibition of the Académie des beaux-arts in Paris. Sponsored by the government (until 1881) and judged by academicians, it was the place to be recognized as an artist in France of the 19th century. As time went on the juries became more conservative, specifically they were not receptive to the artists who came to be called Impressionists. So these artists broke away and held their own exhibitions beginning in 1874. Three of the women, dubbed “les trois grandes dames” of Impressionism by Gustave Geffroy, were among these artists: Mary Cassatt, Marie Bracquemond, and Berthe Morisot.

Unlike Cassatt and Bracquemond, Berthe Morisot’s artistic aspirations were supported by her family. Her parents were even warned by Joseph Guichard, the artist who gave Berthe and her sisters lessons, “Given your daughters’ natural gifts, it will not be petty drawing-room talents that my instruction will achieve; they will become painters.” Of the three daughters two of them did just that, Edma and Berthe. Although Edma gave up painting after her marriage to a naval officer, Berthe went on to an illustrious career. Edma always supported Berthe’s decision to continue painting, even after her marriage, and they remained close throughout their lives.

Born on January 14, 1841, Berthe was the third child of an affluent bourgeois family. After the daughter’s initial instruction, and in spite of Guichard’s warning, Edma and Berthe followed in the footsteps of other artists and registered as copyists at the Louvre where they met and became friends with other artists. Both are thought to have studied under Camille Carot, who encouraged them to begin painting outdoors (plein air) and under Achile Oudinot, both painters of the Barbizon School. Berthe also briefly studied sculpture as well, but none of her pieces are known to survive.

"The Mother and Sister of the Artist" (1869/70) by Berthe Morisot (source)

“The Mother and Sister of the Artist” (1869/70) by Berthe Morisot (source)

Berthe’s first acceptance in the Salon was in 1864 when she was 23 years old. Edma was also accepted and they both exhibited together until Edma married in 1868. Berthe continued to exhibit regularly at the Salon until 1873, and beginning in 1874 exhibited with the Impressionists. By 1872, her career was firmly established when a private dealer, Druand-Ruel, purchased 22 of her paintings.

"The Cradle" (1872) by Berthe Morisot (source)

“The Cradle” (1872) by Berthe Morisot (source)

Edma wasn’t the only one to fall in love in the 1860s. At some point (sources vary) the sisters became acquainted with Édouard Manet. The families became close with Manet and Morisot influencing each others painting over time. Through Édouard, Berthe met his brother Eugène Manet. They married in 1874 and had one daughter, Julie, born in 1878.

"Eugène Manet à l'Ile de Wight" (1875) by Berthe Morisot (source)

“Eugène Manet à l’Ile de Wight” (1875) by Berthe Morisot (source)

Berthe worked in oil, watercolor and pastel and tended to paint domestic life and portraits. She frequently used family and friends as models, including her daughter Julie. Her selection of subjects was somewhat hampered by her gender and social status, although she did eventually paint nudes later in her career. But what was appreciated by many and in fact made her work stand out, were her feminine subjects and style.

"Child Among the Hollyhocks" (1881) by Berthe Morisot (source)

“Child Among the Hollyhocks” (1881) by Berthe Morisot (source)

Eugène Manet died in 1892 and Berthe’s own health wasn’t good. She followed him in death on March 2, 1895. Julie was just 15 years old and was left in the care of Stéphane Mallarmé, the French poet and critic, and good family friend.

"Reading" (1873) by Berthe Morisot (source)

“Reading” (1873) by Berthe Morisot (source)

“Only one woman created a style, and that woman is Madame Morisot. Her pictures are the only pictures painted by a woman that could not be destroyed without creating a blank, a hiatus in the history of art.” ~ George Moore

Resources

Berthe Morisot“, The Famous Artists
Edma and Berthe“, Women in the Act of Painting

The Life of Thecla: When Chastity Gets You into Trouble

Saint Thecla (source)

Saint Thecla (source)

In the early days of Christianity, many people believed they were living in the last days. Life was difficult, persecution was increasing, and to many it made sense to live a life as unencumbered as possible. In his letter to the Corinthians, the Apostle Paul recommends that people remain celibate, but says that it is not a requirement. However, in the extra-canonical book The Acts of Paul he takes a much stronger stance saying that it wasn’t just preferable, but necessary. This was of course quite controversial, particularly when married women wanted to stop having sex or when virgins refused to go through with weddings.

One of the most well-known adherents to the teachings of Paul was a young woman named Thecla. It was in Iconium when she first heard him teach. Sitting in her window three nights in a row, she became enamored of Paul and his message much to the horror of her mother, Theocleia, and her fiancé, Thamyris. Thamyris, fearing that he had been deprived of his wife, stirred up a mob and had Paul brought before the governor. After a brief hearing, Paul was put in prison to be held for further questioning.

During the night, Thecla bribed the guards to let her into Paul’s cell where she spent the night listening to him and “kissing his fetters.” The next morning they were both brought before the governor. As an outsider, Paul was scourged and expelled from the city, but a more dire fate awaited Thecla.

The governor asked Thecla why she was refusing to marry Thamyris. She remained silent, refusing to answer and simply gazing at Paul. This was too much for Theocleia who cried, “Burn the lawless one! Burn her that is no bride in the midst of the theater, that all the women who have been taught by this man may be afraid.” (You have to wonder what Thecla’s mother was getting out of this marriage.) Although the text says that the governor wept and marveled at Thecla’s strength, he agreed and Thecla was led to the pyre. However, God had compassion and when the fire blazed, Thecla wasn’t burned. Then a cloud appeared bringing rain and hail to put out the fire saving Thecla and allowing her to escape.

Thecla fled the city and set out on the road to join Paul. Curiously, even though Paul had been praying that the fire wouldn’t touch her and after her miraculous escape, he refused to baptize her, “lest she fall prey to temptation.” In spite of this, Thecla travels with Paul to Antioch where once again a powerful man is smitten with her.

Fresco of Paul and Thecla from a cave at Bülbül Dag, above the ruins of ancient Ephesus (source)

Fresco of Paul and Thecla from a cave at Bülbül Dag, above the ruins of ancient Ephesus (source)

Thecla must have been very special because once they arrived in Antioch, a man named Alexander saw her on the street and fell in love with her. He first tried to buy her from Paul, who denied even knowing her. When that didn’t work, he tried to take her by force in the street. But Thecla wasn’t easily taken. She ripped his clothes and knocked the crown off of his head, much to the amusement of the crowd. Alexander was humiliated and once again Thecla found herself standing before city officials.

For her “assault” on Alexander, Thecla is sentenced to be thrown to the beasts. In most cases in these stories it’s pagan vs. Christian, but in this case all of the women protest the sentence calling it an “evil judgement.” Thecla asks that she be able to remain “pure” while waiting, so a wealthy woman named Tryphaena offered her protection. (I assume this is protection from sexual assault, hence remaining “pure.”) Tryphaena’s daughter had recently died and she becomes quite attached to Thecla, who prays for her, bringing her comfort.

On the following day, Thecla was taken to the arena, stripped, and cast into the stadium where bears and lions were released to attack her. As the animals came into the arena, a fierce lioness ran to her and lay down at her feet. The first animal to attack was a bear, which the lioness defeated. The second was another lion. The lioness killed the lion, but also died in the process. Thecla was now defenseless.

Statue of Saint Thecla at Ma'loula, Syria by Bernard Gagnon (source)

Statue of Saint Thecla at Ma’loula, Syria by Bernard Gagnon (source)

Realizing that her time might be short, Thecla saw a large vat of water and decided to baptize herself before she died. She threw herself into the water and cried, “In the name of Jesus Christ, I baptize myself on the last day.” Evidently, God approved because a flash of lightening killed all of the seals in the water before they could attack her.

One more attempt is made to kill Thecla. She was bound by her feet between two bulls and red-hot irons were placed under their bellies. They leapt forward, but instead of ripping Thecla apart, her bonds are burned through setting her free once again. Finally, it is all too much for Tryphaena and she faints. Tryphaena, however, is a kinswoman of Caesar and Alexander becomes afraid that any harm to her will bring Caesar’s wrath on the entire city, so he asks the governor to set Thecla free.

Of course Paul is long gone, and when she is released, Thecla once again sets out on the road to find him. This time, however, after telling him about her ordeal and her baptism, she informs him that she is returning to Iconium. Paul not only gives her his blessing, but commissions her to preach. When she returns home, she visits with her mother, finds out that Thamyris has died, and leaves for Seleucia, where she has a long life preaching the Christian gospel.

It must be said that The Acts of Paul is a forgery. Although it wasn’t unusual for documents to be attributed to a more well-known person, in this case the writer, in fact a church leader, was caught, confessed, and was excommunicated. However, that doesn’t mean there isn’t some truth in the story. It is likely that there was an oral tradition of a woman named Thecla and the author simply recorded events that had been passed down. In any case, she was extremely popular from the early 3rd century up through the middle ages, especially in Asia Minor (modern day Turkey), Syria, and Egypt.

One more note, we know about the forgery because of the writings of Tertullian, a 2nd century church father who disapproved of the document. Why? Because it portrays Thecla acting like a man! She preaches and baptizes (herself and possibly others), and of course in his thinking these things are supposed to be done only by men.

Saint Thecla monastery, Ma'loula, Syria by Bernard Gagnon (source)

Saint Thecla monastery, Ma’loula, Syria by Bernard Gagnon (source)

Resources

Lost Christianities: The Battle for Scripture and the Faiths We Never Knew by Bart D. Ehrman
The Other Bible: Ancient Alternative Scriptures ed. William Barnstone
The Acts of Paul and Thecla
(Translation probably by Jeremiah Jones, (1693-1724))
Early Christian Writings: The Acts of Paul

“Les Trois Grandes Dames” of Impressionism – Part 2 – Marie Bracquemond

Marie Bracquemond (source)

Marie Bracquemond (source)

I know little about art with the exception of a passing acquaintance with the Impressionists from taking French in school. Sadly, as in many other areas of my education, it was the male Impressionists we learned about not the women. Although left out of our books, they weren’t absent and today we look at Marie Bracquemond who, with Mary Cassatt and Berthe Morisot, has been called one of “les trois grandes dames” of Impressionism.

Marie Anne Caroline Quivoron was born on December 1, 1840 near Brest in northwestern France. Her father died shortly after her birth and her mother’s second marriage resulted in frequent moves before they finally settled in Étampes, south of Paris. As a girl, she first painted a birthday present for her mother using pigment from crushed flowers. A family friend, impressed by her efforts, gave her a box of watercolors.

Beginning instruction in her teens under M. Wasser, she was accomplished enough by 1857 to have a painting accepted by the Paris Salon. This led to an introduction to Jean-Auguste-Dominique Ingres and work in his studio. Her exposure there led to commissions for original work as well as making important copies in the Louvre.

"Woman with an Umbrella", 1880, by Marie Bracquemond (source)

“Woman with an Umbrella”, 1880, by Marie Bracquemond (source)

She didn’t stay in Ingres’s studio for long, considering him a “despot” with “low esteem of women artists.” In a letter in 1860, she said of M. Ingres: “He wished to impose limits. He would assign to them [women] only the painting of flowers, of fruits, of still lifes, portraits and genre scenes. . . . I wish to work at painting, not to paint some flowers, but to express those feelings that art inspires in me.”

It was in the Louvre that Marie met Félix Bracquemond. Félix was a prolific printmaker, painter and ceramist. He was prominent in both literary and artistic circles and friends with many Impressionists, although he didn’t share their preference for color over line or working outside the studio. He was also loud, arrogant, and some would say obnoxious. Marie was always properly chaperoned by her mother and sister, Louise, and Félix asked a friend to arrange an introduction.

For two years Marie and Félix were inseparable in the Louvre. They analyzed masterpieces and surely discovered their differing tastes, but Marie found herself submitting to his dominant personality. Their engagement lasted for two years, but finally they married in 1869 in spite of her mother’s opposition. Their only son, Pierre, was born the following year. Always in delicate health, Marie’s health began to decline after the birth.

Their relationship was tempestuous. Félix had no prejudice against women as artists, but according to Pierre, no one, male or female, could change his staunchly held opinions. However, he did teach Marie quite a lot. He introduced her to many other artists as well as new media. Working together at the Haviland studio in Auteuil, Marie designed dinner service plates and created faience tile panels and became very accomplished.

"On the Terrace at Sèvres", 1880, by Marie Bracquemond (source)

“On the Terrace at Sèvres”, 1880, by Marie Bracquemond (source)

In the late 1870s, Marie’s style began to change under the mentorship of Monet and Renoir.  This was more than Félix could tolerate. According to Pierre, he only grudgingly allowed her to exhibit a few of her pieces, three in a private gallery in rue Lafitte and five at the Dudley Gallery in London in 1881. A further influence on Marie was Gauguin, who came to stay with the Bracquemonds in 1886 at Félix’s invitation.

Félix became increasingly critical of Marie’s work and called her ambitions “incurable vanity.” She also tired easily trying to work in addition to keeping up her household responsibilities, which she prioritized. Marie always attended Sunday mass, which gave Félix one more thing to criticize.

Weekly gatherings on Sunday at the Bracquemond home frequently ended in arguments. According to Gustave Geffroy, Félix was “both augumentative and authoritarian. He adored debate . . . but his weakness was that he always wanted to be too right, and if anyone disagreed with him ever so little it would end with growing rage.”

"Under the Lamp", 1887, by Marie Bracquemond (source)

“Under the Lamp”, 1887, by Marie Bracquemond (source)

Marie finally gave up the struggle, painting only a few private works after 1890. One of her last paintings was The Artist’s Son and Sister in the Garden at Sèvres. Most of what we know about Marie’s life comes from an unpublished memoir written by Pierre, La Vie de Félix et Marie Bracquemond. In it he fails to describe Marie’s last years. Evidently, Félix never stopped railing against the Impressionists, but Marie never stopped loving them.

Marie Bracquemond died in Paris on January 17, 1916. Three years after her death, 156 of her works were assembled for a show at the Bernheim-Jeune Gallery in Paris. Only four of those works are now on public display.

"The Artist’s Son and Sister in the Garden at Sevres", 1890, by Marie Bracquemond (source)

“The Artist’s Son and Sister in the Garden at Sèvres”, 1890, by Marie Bracquemond (source)

Resources

Jean-Paul Bouillon and Elizabeth Kane, “Marie Bracquemond“, Woman’s Art Journal Vol. 5, No. 2 (Autumn, 1984 – Winter, 1985), pp. 21-27

 

Yep, We Are Still Thinking Like Medieval Men!

I am pleased to welcome back Karen Harris and Lori Caskey-Sigety, authors of The Medieval Vagina and the hugely popular post Menses Madness: Menstruation Myths and the Medieval Mindset. They are with us today to address the question “Are we making progress, or is it true that ‘the more things change, the more they stay the same’”?

flow3On March 4, we presented a book signing followed by a discussion at Trident Booksellers in Boston. One of the questions that an audience member asked us concerned parallels between women’s issues today and during the Middle Ages. Admittedly, women’s issues were deeply entwined with patriarchy and a number of them have been resolved as women have gained more rights and powers. Sadly, we are still grappling with two important issues facing women…800-plus years after the end of the medieval era. These are rape culture/victim blaming and birth control freedoms.

Rape is a crime that transcends time and culture. In the Middle Ages, rape was viewed as a sexual attack, with the perpetrator so filled with lust that he could not control his actions. Today, we know that rape has less to do with sex than it does with power and dominance and terrorization. What hasn’t changed much since the Middle Ages is victim blaming. The male perpetrator was driven to act on his out-of-control lust because of something his victim did. Perhaps she was too pretty or her actions or attire were seductive or flirtatious. Whatever the reason, one thing was clear. It was the woman’s fault. This vile attitude continues to repeat itself. There have been countless court cases in which the rape victim herself was raked across the coals, watching her reputation be torn to threads, while character witness after character witness testified to the saintliness of her attacker. Have we all not heard stories of college girls who were raped being told with disclaimers such as “she shouldn’t have drank so much” or “she shouldn’t have walked home alone” or “what did she expect to happen when she wore those shorts”? Society still looks to the victim when a rape occurs, trying to find exactly what she did wrong to bring this attack upon herself. Centuries have passed since the Middle Ages and still this medieval mindset exists.

Rape culture and victim blaming has been deeply engrained in our societies and manifests in laws, policies, rules, and regulations, all telling women what they need to do to avoid unwanted advances of men. Little, however, is done to teach boys to change their behavior, to not advance those unwanted advances. Take school dress codes for example. Most are designed to restrict what the female students can wear so that they do not create a “distraction” for the male students. Just last week, top students at Downing High School in Iowa were sent letters inviting them to attend an awards ceremony. The letter included a dress code for the ceremony…two lines of rules for the boys to follow and FOUR PARAGRAPHS for the girls, including the line “Choose an outfit that is pretty enough to show you are a woman and covered enough to show you are a lady.” What this, and other female-specific dress codes, are really doing is reinforcing the idea that women are to blame if men are sexually aroused by them. Instead, schools should teach boys to respect girls and women no matter their attire so they won’t turn into young men who think it is okay to have sex with a woman who is passed out drunk or who refuse to take “no” for an answer from a girl in a tank top and mini skirt.

Getting birth control is so complicated!

Getting birth control can be so complicated!

Next, we will look at the second issue facing medieval women that is still prevalent today: birth control. In the Middle Ages, birth control was not just a woman’s issue. It involved the patriarchy…husbands, the crown, the church. As a second-class citizen, a woman was not free to make her own decisions about her reproductive rights. All decisions were made for her. Sound familiar? Even today, a woman’s uterus is the subject of legislation, laws, and religious debate. Remember Hobby Lobby? Remember the University of Notre Dame? No other part of a woman’s body is being regulated and controlled by outside entities, yet it is still believed that a woman is not capable of making all her own decisions regarding her womb. She needs help and guidance, so some still think, or else she may make the “wrong” decision. How archaic is this mindset?

Thankfully, much has changed since the Middle Ages and woman have come a long way, baby. But clearly, there is more work to be done. Banishing victim blaming and removing reproductive rights from the court system will both go a long way to removing the medieval mindset that we still see today.

The Medieval Vagina

 

Karen Harris and Lori Caskey-Sigety are the authors of The Medieval Vagina: An Historical and Hysterical Look at All Things Vaginal During the Middle Ages.

What do you think? Are we making progress? Leave us your thoughts and comments.