In many periods of history, women have been discouraged from applying their minds to mathematics—but a few persevered. The world-altering contributions of these 15 notable female mathematicians include making hospitals safer, laying the groundwork for the computer, and advancing space flight.

#### 1. HYPATIA

Hypatia (c.355–415) was the first woman known to have taught mathematics. Her father Theon was a famous mathematician in Alexandria who wrote commentaries on Euclid’s *Elements* and works by Ptolemy. Theon taught his daughter math and astronomy, then sent her to Athens to study the teachings of Plato and Aristotle. Father and daughter collaborated on several commentaries, but Hypatia also wrote commentaries of her own and lectured on math, astronomy, and philosophy. Sadly, she died at the hands of a mob of Christian zealots.

#### 2. EMILIE DU CHATELET

Emilie Du Chatelet (1706–1749) was born in Paris in a home that entertained several scientists and mathematicians. Although her mother thought her interest in math was unladylike, her father was supportive. Chatalet initially employed her math skills to gamble, which financed the purchase of math books and lab equipment.

In 1725 she married an army officer, the Marquis Florent-Claude du Chatalet, and the couple eventually had three children. Her husband traveled frequently, an arrangement that provided ample time for her to study mathematics and write scientific articles (it also apparently gave her time to have an affair with Voltaire). From 1745 until her death, Chatalet worked on a translation of Isaac Newton’s *Principia*. She added her own commentaries, including valuable clarification of the principles in the original work.

#### 3. SOPHIE GERMAIN

Sophie Germain (1776–1831) was only 13 when she developed an interest in mathematics, one that could be blamed on the French Revolution. Since the fighting raged around her home, Germain could not explore the streets of Paris—instead she explored her father’s library, teaching herself Latin and Greek and reading respected mathematical works. Germain’s family also tried to discourage her academic leanings. Not wanting her to study at night, they denied her a fire in her room, but she lit candles and read anyway, bundled in blankets.

Since women’s educational opportunities were limited, Germain studied secretly at the Ecole Polytechnique, using the name of a previously enrolled male student. That worked until the teachers noticed the dramatic improvement in the student’s math skills.

Although Germain never worked as a mathematician, she studied independently and wrote about the subject. She is best known for her work on Fermat’s Last Theorem, considered at the time to be one of the most challenging mathematical puzzles. A 17th century mathematician named Pierre de Fermat claimed he could prove that the equation x^n + y^n = z^n had no integer solution when n was greater than 2, but his proof was never written down. Germain proposed a new way of looking at the problem.

Germain also became the first woman to win a prize from the Paris Academy of Sciences, for writing about elasticity theory. Today that prize is known as the Sophie Germain Prize.

#### 4. MARY SOMERVILLE

Mary Somerville (1780–1872) was born in Scotland, and was not particularly interested in academics as a child—she only attended school for a year. However, when she encountered an algebra symbol in a puzzle at age 16, she became fascinated with math and began studying it on her own. Her parents tried to discourage her, worried that her intellectual preoccupations might drive her insane. (At the time, a popular theory held that difficult study could damage a woman’s mental health.) But Somerville continued to study, teaching herself Latin so she could read earlier versions of works by Euclid.

She also corresponded with William Wallace, a professor of mathematics at Edinburgh University, and solved mathematical problems posed in contests, winning a silver prize in 1811.

Somerville’s first husband did not encourage her interests, but when he died, she remarried. Her second husband, Dr. William Somerville, an inspector of the Army Medical Board, was proud of her work in mathematics and astronomy. For her work translating a book titled *Celestial Mechanics* and adding commentary, she was named an honorary member of the Royal Astronomical Society.

Physicist Sir David Brewster called her “certainly the most extraordinary woman in Europe—a mathematician of the very first rank with all the gentleness of a woman.” When John Stuart Mill petitioned the British government for women’s votes, he filed his petition with Somerville’s signature first. She was proof that women were men’s intellectual equals.

#### 5. ADA LOVELACE

The next time you download some electronica, you may want to remember Augusta Ada King-Noel, Countess of Lovelace (1815–1852). Lovelace was born during the brief marriage of poet George, Lord Byron and Anne Milbanke, Lady Wentworth. Her mother did not want her to be a poet like her father and encouraged her interest in mathematics and music. As a teenager, Ada began to correspond with Charles Babbage, a professor at Cambridge. At the time, Babbage was working on his ideas for a calculating machine called the Analytical Engine, now considered a precursor to the computer. Babbage was solely focused on the calculating aspects, but Lovelace supplied notes that helped envision other possibilities, including the idea of computer-generated music.

Lovelace also translated an article about the Analytic Engine by French mathematician Louis Menebrea. Her notes include an algorithm showing how to calculate a sequence of numbers, which forms the basis for the design of the modern computer. It was the first algorithm created expressly for a machine to perform.

Lovelace was a countess after her marriage, but she preferred to describe herself as an analyst and a metaphysician. Babbage called her “the enchantress of numbers”—but she might also be called the world’s first computer programmer.

#### 6. FLORENCE NIGHTINGALE

Florence Nightingale (1820–1910) is best known as a nurse and social reformer, but a lesser-known contribution of hers continues to save lives. In her efforts to improve the survival rates of hospital patients, Nightingale became a statistician.

When the “lady with the lamp” returned from service during the Crimean War, she expressed sadness about how many soldiers had become sick and died while lying in the hospital. “Oh my poor men, who endured so patiently,” she wrote to a friend. “I feel I have been a bad mother to you to come home and leave you lying in your Crimean graves.”

As part of her plan to reform hospital care, Nightingale began gathering statistics. The figures she gathered indicated that a lack of sanitation was the primary reason for the high mortality rate. Efforts were instituted to make hospitals cleaner and thus safer.

Not only did Nightingale’s discovery save lives and change hospital protocol forever, but she also designed charts that were easy on the Queen’s eyes. Statistics had been presented with graphics only rarely before, and Nightingale’s work helped pioneer the field of applied statistics. She is particularly known for inventing a new kind of graph known as a coxcomb, which was a variation on a pie chart. She said that the graph was designed “to affect thro’ the Eyes what we fail to convey to the public through their word-proof ears.”

#### 7. EMMY NOETHER

Like Hypatia, Emmy Noether (1882–1935) had a well-known mathematician for a dad. Her father, Max Noether, was a German math professor, but becoming a math teacher would be a longer process for her. After being certified to teach English and French, she also wanted a degree in mathematics, but she had to wait—the University of Erlangen in Bavaria did not let women officially enroll until 1904. Noether eventually received her doctorate in mathematics, but because her university had a policy against hiring female professors, she instead helped her father in his work at the Mathematics Institute in Erlangen (without being paid), researching and writing papers on the side.

In 1918 she proved two theorems, one of which is now known as "Noether's Theorem." After that she researched ring theory and number theory, both of which would later prove useful for physicists. Finally, in 1922, she became an associate professor and received a small stipend.

But her teaching career was short-lived. Because of growing anti-Semitism, she and other Jewish mathematicians had to flee Germany in 1933. She moved to the United States, and taught at Bryn Mawr College until her death.

After her death in 1935, Albert Einstein described Noether in a letter to *The New York Times* with these words: "In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."

#### 8. MARY CARTWRIGHT

Mary Cartwright (1900–1998) achieved a few notable firsts: She was the first woman to receive the Sylvester Medal for mathematical research and the first to serve as president of the London Mathematical Society (1961–62).

In 1919 she was one of only five women studying mathematics at Oxford University. When she did not score well on her tests, she briefly considered giving up math. Fortunately, she chose to persevere, and went on to lecture at Cambridge University. She later earned a doctorate in philosophy and had her thesis published in the *Quarterly Journal of Mathematics*. After being awarded a research fellowship, she went on to publish more than 100 papers. One of her theorems, known as Cartwright's Theorem, is still frequently applied in signal processing. She also contributed to the study of chaos theory. In 1969 Queen Elizabeth II honored Cartwright’s accomplishments by proclaiming her Dame Mary Cartwright.

#### 9. DOROTHY JOHNSON VAUGHAN

The excitement of space travel was made possible by years of painstaking work conducted by “human computers”—specifically, a group of mathematically proficient women who calculated a variety of scientific and mathematical data at the National Advisory Committee for Aeronautics (NACA), which later became NASA. Dorothy Johnson Vaughan (1910–2008) was one of them, and her contributions are featured alongside those of several other African-American female mathematicians at NACA in the December 2016 film *Hidden Figures*.

After working as a math teacher, Vaughan took a job at NACA in 1943. In 1949, she was promoted to lead the division’s segregated work group West Area Computers, which was entirely composed of African-American female mathematicians. She became an expert in coding languages such as FORTRAN (now a popular language for high-performance computing). She described working in space research as being on “the cutting edge of something very exciting.”

#### 10. MARJORIE LEE BROWNE

Mathematician and educator Marjorie Lee Browne (1914–1979) was one of the first African-American women to acquire a Ph.D. in math. Becoming a respected educator meant overcoming personal tragedy (the death of her mother at a young age), as well as race and gender discrimination. Fortunately, her mathematically gifted father and teacher stepmother encouraged her educational interests. She attended a private school, graduated Howard University cum laude and earned her doctorate at the University of Michigan.

Browne taught math at North Carolina College (now North Carolina Central University), where she was named chair of the math department in 1951. She helped her school acquire grants, including a 1960 grant to set up a computer center, one of the first of its kind. Thanks in part to her work, the school became home to a National Science Foundation Institute for secondary education in mathematics. Browne also received the first W.W. Rankin Memorial Award for Excellence in Mathematics Education.

#### 11. JULIA ROBINSON

Julia Robinson’s (1919–1985) early education was interrupted more than once by illness. One bout of rheumatic fever required a year of recuperation and would continue to affect her health. When Robinson returned to school in the ninth grade, she developed an interest in math. She graduated high school with honors in math and science classes, then eventually attended Berkeley, where she married an assistant professor named Raphael Robinson.

After being told she could not have children due to the residual damage caused by rheumatic fever, she renewed her devotion to math, receiving her doctorate in 1948. That year she began to work on the mathematical problem known as David Hilbert’s Tenth Problem, which occupied her for decades. Her work toward solving the problem with an international team of other mathematicians is the subject of a one-hour documentary titled “Julia Robinson and Hilbert’s Tenth Problem.” In 1975 Robinson was the first woman mathematician to be elected to the National Academy of Sciences. She also became the first woman president of the American Mathematical Society.

#### 12. KATHERINE JOHNSON

When Katherine Johnson (born 1918) wanted to study math, she faced a big obstacle. White Sulphur Springs, West Virginia, where she lived, did not offer schooling for black students past eighth grade. So, her father drove his family 120 miles so she could attend a high school in another town, leaving Katherine and her mother there while he continued to work in White Sulphur Springs. The math prodigy graduated by the age of 14. When she attended West Virginia State College, several professors recognized her unusual ability and mentored her. She graduated summa cum laude at the age of 18, with plans to teach. After doing that for a little while, she went to work for NACA as one of the mathematicians known as “computers who wore skirts.” Her knowledge of analytic geometry resulted in her assignment to the all-male flight research team, where she helped calculate the trajectory of Alan Shepherd’s first trip into space. She was so good at her job that she stayed on the research team after Shepherd’s trip, working at Langley Research Center from 1953 to 1986.

“I went to work every day for 33 years happy,” she said. Never did I get up and say I don’t want to go to work.” She received the Presidential Medal of Freedom in 2015, and her work is also celebrated in *Hidden Figures*.

#### 13. MARY JACKSON

Mary Jackson (1921–2005) grew up in Hampton, Virginia, graduating with honors from high school and receiving a bachelor’s degree from Hampton Institute in mathematics and physical science. She was hired as a research mathematician at the NACA campus in Langley, and was eventually promoted to aerospace engineer, specializing in aerodynamics.

“After five years of working in that department and taking additional courses at the Hampton Center of the University of Virginia I was invited to become an engineer-in-training through a special program and I’ve been an aerospace engineer ever since,” she said.

She later worked with flight engineers at NASA and was repeatedly promoted. After three decades, Jackson achieved the highest level of engineer, but then chose to focus on efforts to help women and minorities advance their careers. She is also featured in *Hidden Figures*.

#### 14. CHRISTINE DARDEN

Dr. Christine Darden (born 1942) is a mathematician, data analyst, and aeronautical engineer who spent her 25-year career at NASA researching sonic booms—the sound associated with the shock wave of an object traveling through air faster than the speed of sound. After a brief stint teaching and researching aerosol physics, she landed at the Langley Research Center. There she performed calculations for engineers, eventually writing computer programs to automate the process. She became one of the first female aerospace engineers at Langley, writing a computer program to measure sonic boom. After earning a doctorate in mechanical engineering, she became the leader of NASA's Sonic Boom Group. Darden conducted research on air traffic management, as well as other aeronautics programs, and has authored more than 50 publications. She is also featured in *Hidden Figures*.

#### 15. MARYAM MIRZAKHANI

As a girl, Maryam Mirzakhani (born 1977) was not very interested in math, and dreamt of being a writer. “I never thought I would pursue mathematics until my last year in high school,” Mirzakhani told *The Guardian*.

The choice turned out to be a wise one, and Mirzakhani is now highly respected in her field. In 2014 she became the first woman and the first Iranian honored with the prestigious Fields Medal, awarded for her work on hyperbolic geometry—a non-Euclidean geometry used to explore concepts of space and time.

Mirzakhani currently teaches math at Stanford University. Curtis McMullen, her doctoral advisor at Harvard, has described her as having “a fearless ambition when it comes to mathematics.” Her best work may be yet to come.