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.

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

Emmy Noether – Original in More Ways Than One

Emmy Noether c. 1910 (source)

Emmy Noether c. 1910 (source)


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

Ada Lovelace by Alfred Edward Chalon (source)

Often women in the 18th and 19th 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)

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.

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

Mary Fairfax Somerville, c. 1834, by Thomas Phillips

Mary Fairfax Somerville, c. 1834, by Thomas Phillips (source)

“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.”

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)

Laura Bassi by Carlo Vandi

Laura Bassi by Carlo Vandi (source)


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

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

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

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

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

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

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

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

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

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

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

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

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

Read about other Famous Women Mathematicians and Scientists.