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

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

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

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

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

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 NACABeverly 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

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

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

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.

Amazon's Under-the-Radar Coupon Page Features Deals on Home Goods, Electronics, and Groceries

Stock Catalog, Flickr // CC BY 2.0
Stock Catalog, Flickr // CC BY 2.0

This article contains affiliate links to products selected by our editors. Mental Floss may receive a commission for purchases made through these links.

Now that Prime Day is over, and with Black Friday and Cyber Monday still a few weeks away, online deals may seem harder to come by. And while it can be a hassle to scour the internet for promo codes, buy-one-get-one deals, and flash sales, Amazon actually has an extensive coupon page you might not know about that features deals to look through every day.

As pointed out by People, the coupon page breaks deals down by categories, like electronics, home & kitchen, and groceries (the coupons even work with SNAP benefits). Since most of the deals revolve around the essentials, it's easy to stock up on items like Cottonelle toilet paper, Tide Pods, Cascade dishwasher detergent, and a 50 pack of surgical masks whenever you're running low.

But the low prices don't just stop at necessities. If you’re looking for the best deal on headphones, all you have to do is go to the electronics coupon page and it will bring up a deal on these COWIN E7 PRO noise-canceling headphones, which are now $80, thanks to a $10 coupon you could have missed.

Alternatively, if you are looking for deals on specific brands, you can search for their coupons from the page. So if you've had your eye on the Homall S-Racer gaming chair, you’ll find there's currently a coupon that saves you 5 percent, thanks to a simple search.

To discover all the deals you have been missing out on, head over to the Amazon Coupons page.

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10 Killer Facts About The Evil Dead

Bruce Campbell in The Evil Dead (1981).
Bruce Campbell in The Evil Dead (1981).
New Line Cinema

From Peter Jackson to Edgar Wright, Sam Raimi’s The Evil Dead has influenced many of today’s biggest directors. As it should. Famous for its practical effects and then-unprecedented amount of gore, the campy 1981 horror flick—about a group of friends who travel to a cabin in the woods and unleash killer demons—showed the world the power of guerilla-style indie filmmaking.

Raimi, star Bruce Campbell, and producer Robert Tapert fought through no CGI, sticky cocktails of blood made from everyday household items, and the reluctance of major studios to get on board to make a cult classic that has since spawned two sequels, Evil Dead II (1987) and Army of Darkness (1992); an Army of Darkness video game; a 2013 remake; Ash vs. Evil Dead, a TV series that ran for three seasons on Starz; and an upcoming fifth movie, Evil Dead Rise, that is planning to start production in 2021.

Get to know more about every cinephile’s favorite horror-comedy with this list of things you might not know about the production.

1. The Evil Dead was based on Sam Raimi’s short film, Within The Woods.

Before getting to work on The Evil Dead, good friends Robert Tapert, Sam Raimi, and Bruce Campbell created the 30-minute Super 8 film, Within the Woods. In a 1982 interview with John Gallagher, Raimi—who was 20 when he shot The Evil Dead—explained, “We used [Within the Woods] to show the investors what kind of film they’d be buying into … They needed tangible proof that we could make a movie of professional quality.”

On why the trio chose to make a horror film in the first place, producer Robert Tapert told The Incredibly Strange Film Show, “Sam and I first decided to do horror films after doing research on what did well in the markets ... Horror is the entry level that most people use.”

2. Joel Coen got his first break as an assistant editor on The Evil Dead.

Before becoming the Oscar-winning filmmaking duo he and his brother Ethan are today, Joel Coen got his start as an assistant editor on The Evil Dead. Inspired by Raimi’s DIY filmmaking, Joel and his brother created a pitch trailer (much like Raimi’s Within the Woods) to raise money for their first feature, Blood Simple. While Dan Hedaya stars in the final film, Bruce Campbell plays the lead in the two-minute trailer.

3. The Evil Dead, which is famous for its practical effects, even used real, live ammunition.

The meager budget on The Evil Dead didn’t allow for any star accouterments. As Bruce Campbell detailed to DVD talk, among the many hellish situations the cast and crew dealt with were diving into freezing cold swamps and Raimi getting chased by a bull. “We are going to rural Tennessee, 1979, where there's moonshine, squatters, and it was the real deal,” said Campbell. “The south was the south in 1979. There was no franchise this or franchise that. It was a completely different world and mentality ... We used real ammunition in the shotgun and we shot it at a real cabin in the woods, with hunters and howling dogs in the background.”

4. The Evil Dead’s infamous melting corpse is made up of everything from oatmeal to cockroaches.

Conscious of toeing the line of MPAA ratings, make-up and visual effects supervisor Tom Sullivan used different colors of goo to keep the body from seeming like it was spewing real blood. “I wanted to make it seem like their biology actually changed,” said Sullivan during the film’s 30th anniversary reunion, hosted by Spooky Empire. Among the many ingredients used to concoct the mush coming out of the melting corpse’s skull, Sullivan cites oatmeal, snakes, guts made out of marshmallow strings, and Madagascar cockroaches, which they acquired at Michigan State University.

5. Sam Raimi worked himself so hard on The Evil Dead that he passed out during filming.

Ellen Sandweiss in The Evil Dead (1981).Anchor Bay Entertainment

At Spooky Empire’s reunion, Bart Pierce, who worked on the visual effects of the film, noted just how much filming took a toll on Sam Raimi. As his story goes, Raimi fainted during the shooting of the film’s dismemberment sequence. The director stayed up all night shooting, and wrote all day, basically working himself 24/7. To wake him up, the crew took an ice-cold bucket of water and threw it at him, and left him there until he regained consciousness.

6. Everything in The Evil Dead was real—even the drugs.

Bruce Campbell has said it before: everything was real during filming. At a Spooky Empire event, Campbell playfully recalled, “The illegal substance known as marijuana was somehow forced upon us in Tennessee ... I was forced to ingest this marijuana by a local reprobate and I therefore became, let’s just say, affected by THC ... I therefore lost any sense of time and where I was, and that’s the time that Sam Raimi decided that he needed to shoot Ash having a breakdown.”

7. The Morristown, Tennessee cabin where The Evil Dead was shot has its own real-life horror story.

Adding to the spookiness of filming at an actual cabin in the woods, Raimi noted the location’s inherent eeriness is completely justified. During an interview with John Gallagher, Raimi recounted a horror story involving three generations of women (a grandmother, mother, and daughter) who previously occupied the cabin. “One night, during a thunderstorm, this little girl woke up and was scared by the lightning happening around the cabin. She ran into her mother’s room and pulling back the covers climbing into bed with her, she found that her mother was dead. She was so frightened she ran into her grandmother’s room and somehow that same evening, she had died also,” Raimi recalled. “The little girl ran into the storm ... to this little farmhouse and [the family living there] found her screaming and banging on the doors. They took care of her after that and no one lived in the cabin since. The [little girl], who’s now an old woman, during thunderstorms after that ... would often be found wandering around the woods.”

The kicker, however, was that story came to life during the film’s shoot. Raimi continued, “As we were shooting, this fella [from the farmhouse that took in the little girl] was looking for the [now old] woman, saying that because there was a thunderstorm the night before, he was looking for this woman, because it was possible that she had returned to the cabin ... As far as we know, they never found [her.]”

8. The most difficult moments during The Evil Dead shoot were stopping for months at a time to raise money.

According to Sam Raimi, the most difficult part of production wasn't the physical toll it took on the crew, but that they'd have to stop filming for months at a time to raise more money. “We’d reach stretches where we’d run out of money and have to stop whatever we were doing and put on our suits and get our briefcases and cut our hair short and shave ... and go around knocking on doors asking for more money," Raimi recalled. On initially raising money for the film, Raimi told the Incredibly Strange Film Show, “Tapert, Bruce Campbell, and myself ... all dropped out of school. Then we worked as waiters, bus boys, cab drivers. I was 18, Bruce was 19, and Robert was 22.” Added Campbell: “We’d sit down and pretend we were businessmen. We thought it was part of the process.”

In an episode of Dinner for Five, Campbell note another lucrative source of cash: dentists. “We had one guy give us money because he didn’t go to Vegas that year. He says ‘I usually take two grand and blow it in Vegas. Well, here’s my Vegas money.’ So he sends me 17 times his money. We were pretty happy about that.”

9. Sam Raimi regrets the infamous The Evil Dead scene where a teen girl is assaulted in—and by—the woods.

The initial release of the film was met with plenty of backlash worldwide, including being banned in Finland, Germany, Ireland, and Iceland for its extreme violence. Beyond the excessive blood, the scene in which Cheryl (Ellen Sandweiss) is assaulted by a tree caused an uproar among viewers and critics, and almost got the film banned from being released on home video. To this day, even Raimi regrets that scene. “It was unnecessarily gratuitous and a little too brutal,” Raimi tells the Incredibly Strange Film Show. “My goal was not to offend people ... My judgement was a little wrong at that time.”

10. Sam Raimi and Bruce Campbell started a rumor about an on-set injury on The Evil Dead as a joke.

Just to see who’d believe it, Campbell and Raimi spread a rumor that Campbell broke his jaw when Raimi accidentally slammed his camera into Campbell’s face while filming one of the final shots. Campbell put this rumor to rest at Dallas Comic Con, saying: “The lie that we put out was that the final shot [where] this evil entity comes racing through the cabin and crashes into my face ... The big lie is that... [Raimi] rode a motorcycle through all the doors and he just had to hit me ... I was willing to do it as long as we got [the shot], took it for the team ... But no, no broken jaw.”

This story has been updated for 2020.