15 Female Mathematicians Whose Accomplishments Add Up

Katherine Johnson at NASA in 1966
Katherine Johnson at NASA in 1966
NASA, Wikimedia Commons // Public Domain

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 Chatelet portrait by Latour
Maurice Quentin de La Tour, Wikipedia // Public Domain

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

A portrait of Mary Somerville
Thomas Phillips, Wikipedia // Public Domain

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

A portrait of Augusta Ada, Countess Lovelace
Hulton Archive/Getty Images

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

A black-and-white photograph of Florence Nightingale
London Stereoscopic Company/Getty Images

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

Portrait of Emmy Noether
Wikipedia // Public Domain

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 in Germany was short-lived. Because of growing anti-Semitism, she and other Jewish mathematicians had to flee the country 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


Dorothy Vaughan (left) at NACA
Beverly Golemba, Wikipedia // Public Domain

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 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 effects of the 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

Katherine Johnson receiving the Presidential Medal of Freedom in 2015
NASA, Wikimedia // Public Domain

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 so 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

Photograph of Mary Winston Jackson
Wikipedia, NASA // Public Domain

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

Color photograph of Dr. Christine Darden
NASA, Wikipedia // Public Domain

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 (1977-2017) 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: 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 taught math at Stanford University. Curtis McMullen, her doctoral advisor at Harvard, described her as having “a fearless ambition when it comes to mathematics.” 

This story first ran in 2017.

Disney's 10 Scariest Movies

Lynn-Holly Johnson, Bette Davis, and Kyle Richards in The Watcher in the Woods (1980).
Lynn-Holly Johnson, Bette Davis, and Kyle Richards in The Watcher in the Woods (1980).
Walt Disney Pictures

Disney: Known for catchy songs, cute animal sidekicks, brave Princesses … and occasionally scarring children for life. A lot of Disney’s more famously upsetting moments have to do with deathBambi’s mother and Mufasa’s father, for instance—but sometimes the studio goes plain horror movie with it. As Halloween approaches, here are 10 of Disney’s scariest movies.

1. Return to Oz (1985)

Return Oz establishes its “wait, what the hell am I watching?” cred early on, when Dorothy Gale—back in Kansas following her adventures in Oz—is shipped off to the doctor for a round of electroshock therapy to cure her insomnia and “delusions.” Dorothy is saved from her One Flew Over the Cuckoo’s Nest fate and whisked off to Oz again, where she finds that the Nome King and Princess Mombi—Nicol Williamson and Jean Marsh, who also played the doctor and head nurse—have destroyed the Emerald City and turned most of its inhabitants to stone. Playing Dorothy in her first feature film role is Fairuza Balk, who would go on to star in perpetual Halloween favorite The Craft. Return to Oz is the only film directed by legendary editor Walter Murch, most famous for his work on Apocalypse Now.

2. Something Wicked This Way Comes (1983)

The collected works of Ray Bradbury have been adapted into dozens of films, only a handful of which were written by the late author himself. The final feature film to be written by Bradbury is 1983’s Something Wicked This Way Comes, which in its first act is a typical, sweet—if somewhat dark—drama about two young boys growing up in a small town in the Midwest. Then a carnival rolls into town, and things get real messed up. Running the carnival is Mr. Dark (Jonathan Pryce), who grants the townspeople’s wishes in ways that … well, let’s just say they’re not very nice.

3. Mr. Boogedy (1986)

“Made-for-TV ‘80s movie about a gag gift salesman and his family” doesn’t scream terror, but Mr. Boogedy defies the odds to have some legitimately creepy moments. Granted, it’s not a subtle film: a family that moves into a dilapidated mansion in a town called called Lucifer Falls shouldn’t really expect to have an easy go of things. The mansion, believe it or not, is haunted by not one but three spirits: a widow, her child, and the eponymous Mr. Boogedy, who back in Colonial times sold his soul to Satan for a cloak that gives him magical powers. It’s Mr. Boogedy’s character design that gives the movie its biggest ick factor; the film’s makeup designer, Rick Stratton, would go on to win two Emmys. Mr. Boogedy’s cloak is eventually sucked into a possessed vacuum cleaner.

4. The Watcher in the Woods (1980)

Director John Hough’s The Watcher in the Woods isn’t only scary because it gives Bette Davis and current Real Housewives of Beverly Hills star (and then-child actress) Kyle Richards a decent chunk of shared screen time. Based on a 1976 novel, the film—like Mr. Boogedy—follows a family that moves into a mysterious house haunted by some mysterious presence. In The Watcher in the Woods, that presence is thought to be Karen, the long-disappeared daughter of the house’s owner, played by a collecting-those-paychecks Davis. Spoiler alert: There are actually two presences. One is Karen. The other is an alien. The original ending of The Watcher in the Woods actually showed the alien, but the effects were so bad that the premiere audience broke out laughing, causing Hough to reshoot the climactic final scene with the aliens as a vague blur of light.

5. The Adventures of Ichabod and Mr. Toad (1949)

Released in 1949, The Adventures of Ichabod and Mr. Toad is made up of two half-hour, kid-friendly literary adaptations, the first from The Wind in the Willows and the second from “The Legend of Sleepy Hollow.” Neither segment is particularly scary … up until the last few minutes of “Sleepy Hollow,” when the animators went all-out to make schoolteacher Ichabod Crane’s flight from the Headless Horseman a contender for Disney’s scariest scene. Clyde Geronimi, who with Jack Kinney directed the “Sleepy Hollow” sequence, would go on to co-direct Cinderella, Alice in Wonderland, Peter Pan, Lady and the Tramp, Sleeping Beauty, and 101 Dalmatians.

6. Pinocchio (1940)

Jiminy Cricket hopping around and The Blue Fairy singing “When You Wish Upon a Star” might be the most enduring images from Disney’s second-ever animated feature, but let’s not forget that Pinocchio could be scary when it needed to be. The film’s most potent bit of nightmare fuel comes in the scene where a bunch of children are magically transformed into terrified, crying donkeys so they could be sold away as slave labor. Looks like Disney had a taste for causing childhood trauma early on.

7. “The Skeleton Dance” (1929)

Spooky and cute: Why not both? The 1929 short “The Skeleton Dance” threads the needle deftly, with its depiction of a quartet of skeletons dancing around a graveyard maintaining the goofy tone that marks most of the early Disney shorts while still providing an ample dose of the shivers. “The Skeleton Dance” was drawn by Ub Iwerks, who several years earlier had designed Mickey Mouse.

8. Fantasia (1940)

Most of the segments in Disney’s Fantasia are markedly un-creepy—unless you consider ballet-dancing hippos disturbing, which makes a fair amount of sense—but with “Night on Bald Mountain,” Disney went full dark and stormy night. Set to the title song by composer Modest Mussorgsky, the film depicts the ancient Slavic deity Chernabog (whose name means “black god) calling all sorts of assorted demonic creatures to him before being driven away by the rising of the sun. Bela Lugosi served as a live-action reference for Chernabog, spending a day at Disney Studios striking a series of ominous poses. Nothing that Lugosi provided was ultimately used, as animator Bill Tylta was unimpressed by it.

9. The Black Cauldron (1985)

The Black Cauldron was an infamous failure for Disney, earning a mere $20 million domestically against a budget that made it, at the time, "the most expensive animated feature ever made.” With the film, Disney ditched the songs and lighthearted feel that marked its animated features up to that point in favor of a darker fantasy epic; notably, The Black Cauldron was the first Disney animated feature to earn a PG rating. Though it’s notoriously regarded as a flop, there’s one area in which The Black Cauldron is quite successful: making its villain, the Horned King, absolutely terrifying. Even the way he dies is nightmare-inducing: The magical black cauldron that the Horned King hoped would give him power to take over the world with an undead army instead melts his flesh off. It’s a bit more gruesome than the typically death-by-falling most Disney villains get.

10. Hocus Pocus (1993)

Initially released in 1993 to middling box office returns (Disney made the odd choice to release this Halloween-themed movie in July), director Kenny Ortega’s Hocus Pocus has gone on to achieve cult status. Omri Katz, since retired from acting, stars as Max Dennison, who with neighbor Allison and younger sister Dani must defeat the Sanderson sisters, a trio of witches who were hanged during the Salem witch trials. One of the witches was played by Sarah Jessica Parker, whose ancestor Esther Elwell was accused of being a witch in 17th-century Salem; she escaped execution when prosecution from witchcraft was done away with.

9 French Insults You Should Know

Rawf8/iStock via Getty Images
Rawf8/iStock via Getty Images

Ah, France—internationally synonymous with fine wines, fashion, and elegant cheeses. As it turns out, the country is home to some pretty fine insults, too, as the list below demonstrates. If you need some more ways to express your distaste in a foreign language, we've also got you covered with insults in German. (If historical insults are more your speed, you can peruse these old English insults, or learn how to level a sick burn like Teddy Roosevelt.)

1. Va te faire cuire un oeuf // "Go cook yourself an egg."

Figuratively speaking, this means “leave me alone.” Historically, the idea is that men would criticize their wives cooking dinner, who would then respond, "Go fry yourself an egg"—reminding their mates that they're incapable of cooking anything other than an egg.

2. Bête comme ses pieds // "You are as stupid as your feet."

The feet are the furthest part of the body from the brain, so supposedly, the most stupid. Besides, have you ever seen smart feet?

3. Péter plus haut de son cul // "To fart higher than your ass."

If you have gas in your stomach and try to expel it above your behind, you will fail. It's just too ambitious. This phrase means that a person is arrogant, or thinks they are able to do impossible things. They're a show-off, basically.

4. Poule mouillée // "Wet chicken"

Chickens are not known for their bravery. Especially when it rains, they try to hide, as ridiculous as that may be. A wet chicken is someone who is afraid of everything.

5. Mange tes morts // "Eat your dead."

You use this insult when you are very mad at someone. The original meaning is "You have no respect." It's said to have started among the Yenish people—a European ethnic minority with nomadic origins.

6. Sac à merde // "Bag of sh**"

No need for explanation right? Speaks for itself. Often used while driving.

7. Tête de noed // "Knot face"

Someone stupid. Literally, the knot refers to the tip of the penis, but in essence the term has a meaning similar to (but even ruder) than the English dickhead.

8. Couillon/Couillonne // "Little testicle"

A relatively mild insult that means something like "idiot" in English.

9. Con comme une valise sans poignée // "As stupid as a suitcase without a handle."

What good is a suitcase if you can't carry it? In a similar vein, "con comme un balais" means "as dumb as a broom."

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