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.

11 Masks That Will Keep You Safe and Stylish

Design Safe/Designer Face Covers/Its All Goods
Design Safe/Designer Face Covers/Its All Goods

Face masks are going to be the norm for the foreseeable future, and with that in mind, designers and manufacturers have answered the call by providing options that are tailored for different lifestyles and fashion tastes. Almost every mask below is on sale, so you can find one that fits your needs without overspending.

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The breathable, stretchy fabric in these 3D masks makes them a comfortable option for daily use.

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Prices subject to change.

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21 Defunct Disney Park Rides and Lands

Some of Disney's most beloved rides and attractions have gone the way of the Dodo.
Some of Disney's most beloved rides and attractions have gone the way of the Dodo.
Paul Rovere/Getty Images

Over the course of their 65-year history, Disney's parks have hosted a lot of rides—including many that didn't last. Here are a few defunct rides and lands you should know about, adapted from an episode of The List Show on YouTube.

1. Superstar Limo

Did you know that Jackie Chan, Whoopi Goldberg, and Cher were once featured in a Disney ride? It sounds fun, but Disney visitors were not a fan of Superstar Limo, which didn’t even make it a single year at California Adventure in the early 2000s. It was a slow ride through Los Angeles featuring audio animatronics of those celebrities and others. Maybe it would have been more successful as one of the later ideas for the ride: Miss Piggy’s Limo Service.

2. ExtraTERRORestrial Alien Encounter

Walt Disney World once had an attraction inspired by the movie Alien. During ExtraTERRORestrial Alien Encounter, guests were terrorized in the dark by an escaped alien. It was frightening enough that only people over the age of 12 were recommended to experience the Encounter. While the attraction was in early stages, it was going to be called Alien Encounter and feature a Xenomorph from the Alien movies. But the park’s Imagineers objected to building a ride around R-rated fare in Tomorrowland, which was meant to have an optimistic vision of the future. As a result, the creature ended up just becoming a generic—but still very scary!—alien. It did have another cool Hollywood connection, though: George Lucas was one of the designers. ExtraTERRORestrial Alien Encounter lived in the Magic Kingdom from 1995 to 2003, when it was replaced with a Lilo and Stitch attraction (which was itself dismantled in 2018).

3. Cinderella Castle Mystery Tour

This ride in Tokyo Disneyland opened in 1986 and was operational for 20 years. A tour guide took groups on a journey involving confrontations with Disney villains from Snow White, Sleeping Beauty, Fantasia, and Pinocchio. These were done the way that Disney does best: a combination of video and animatronics. The big finale featured the Horned King from the film The Black Cauldron. It involved him saying that the guests were now trapped and would be sacrificed to the cauldron. One person who was given a sword earlier on the tour pointed it at the Horned King and "destroyed" him (there was a flash of light, then he disappeared).

4. Submarine Voyage

For almost 40 years, Disneyland maintained the Submarine Voyage ride. Riders would enter a submarine that was on a track. The submarine then looked like it was being submerged in water and proceeded to move slowly past various creatures, like turtles, fish, and mermaids. When the ride opened in 1959, the submarines were gray and named after actual U.S. navy submarines. In the ‘80s, they were painted yellow and given exploration-related names like "Explorer" and "Seeker." In 2007, the ride reopened at Disneyland with a Finding Nemo theme. At that time, more sub names in line with the explorer theme were added, like "Seafarer" and "Voyager." A Walt Disney World version similar to the original lasted from 1971 through 1994.

5. and 6. Rainbow Mountain Stagecoach Ride and Rainbow Caverns Mine Train

Two of the earliest rides at Disneyland were the Rainbow Mountain Stagecoach Ride and the Rainbow Caverns Mine Train, which were part of Frontierland. The Stagecoach Ride had actual stagecoaches led by actual horses going through a desert. It opened in the mid-’50s and closed in 1959.

The Mine Train journeyed through illuminated caverns, and would later turn into Mine Train Through Nature’s Wonderland. In 1979, Big Thunder Mountain Railroad took over the spot. But if you ride that roller coaster, you can still see evidence of the Mine Train. In the queue for Big Thunder Mountain, there are pieces from a town that were part of the old ride. The same queue leads you through a Ventilation Service Room where there’s a map with a section labeled “Rainbow Caverns.”

7. Flying Saucers

Flying Saucers existed for five years in the early 1960s at Disneyland. They looked like bumper cars, but they were slightly lifted above the ground thanks to air vents beneath the ride. Like air hockey, but with flying saucers. According to the site Yesterland, Flying Saucers used technology that was developed and patented especially for the ride. When it opened, the Los Angeles Times reported, “The Flying Saucer ride cost $400,000 to build, Each saucer is ‘blown’ 8 inches off the ground and is under constant control of its pilot,” a.k.a., a park guest, who moved the saucer by shifting their body in the direction they wanted to go. Part of the problem was that only people within a specific weight range could do that effectively. Flying Saucers was ultimately closed for a redesign of Tomorrowland.

8. If You Had Wings

Disney is really into flying. Between 1972 and 1987, Walt Disney World had a ride sponsored by Eastern Airlines called If You Had Wings. Passengers got on an omnimover—that line of cars that you can, in theory, board without them ever stopping—which “flew” them around the world (the world being animatronic scenes of places like Mexico, Bermuda, and Puerto Rico).

9. and 10. If You Could Fly and Delta Dreamflight

If You Had Wings briefly became known as If You Could Fly, and in 1989 turned into Delta Dreamflight. That’s right: a new sponsor. The idea was similar, but it was now an homage to airplanes. Passengers got a glimpse of aviation’s history and potential future. Buzz LightYear’s Space Ranger Spin is now where If You Had Wings and Delta Dreamflight once were.

11. Horizons

From the mid-1980s through the late-'90s, Horizons was a hugely popular ride at Epcot. Guests rode through 24 animatronic, futuristic sets. (According to Disney, the future holds robot butlers, robot chefs, and domesticated seals.) At the end of the ride, the car would let you vote on how you wanted to be returned home—through a space, desert, or ocean scene. Nowadays, Mission: SPACE sits in Horizon’s place.

12. Rocket Rods

Rocket Rods only lasted about three years. It was a high-speed thrill ride that used an old track that had belonged to the much slower People Mover ride—which ended up being its demise. The coaster broke down too often and permanently closed in 2001.

13. Adventure Thru Inner Space

Starting in 1967, for almost two decades, Disneyland guests could experience what it was like to be microscopic while riding Adventure Thru Inner Space. People waiting in line would watch as passengers sat in pods, went through a 37-foot-long microscope and were "shrunk" (in reality, they were replaced by 8-inch tall replicas on screen). While on the ride, they’d go through scenes of becoming smaller than a snowflake, mostly by watching videos.

14. Body Wars

On Body Wars—which was located at Epcot’s Wonders of Life Pavilion and operated from 1989 until January 1, 2007—40 riders took a journey through the human body. They were jostled around, causing motion sickness for many, as they watched a video of their dramatic chase. Fun fact: The video was directed by Spock himself, Leonard Nimoy. Even funner fact: The other famous Wonders of Life pavilion attraction was The Making of Me, where Martin Short learned how he was conceived. (Apparently they had a disclaimer about all the sexy stuff at the entrance to the attraction.)

15. Maelstrom

Maelstrom lasted a bit longer at Epcot, between 1988 and 2014, before it was replaced by a Frozen ride. It was a boat journey through the “history” of Norway, though that history involved some embellishment ... like an animatronic three-headed troll.

16. The Great Movie Ride

The Great Movie Ride was at Walt Disney World’s Hollywood Studios from 1989 through 2017. Guests entered a building that looked like the famous Grauman’s (now TCL) Chinese Theatre, boarded a car, and traveled through scenes from 12 movies, including Raiders of the Lost Ark, Alien, Singin’ in the Rain, and The Wizard of Oz, as well as a montage of a bunch more classic films. Drama ensued when a live actor hijacked the ride. It closed in 2017.

17. and 18. Rocket to the Moon and Mission to Mars

In 1955, Disneyland had a simulation called Rocket to the Moon that showed patrons what it would be like to, well, travel to the moon. It closed in 1966, and a year later was replaced by Flight to the Moon, which became way less exciting when Apollo 11 actually landed on the moon in 1969. The area became Mission to Mars in 1975. That ride closed in 1993, and later, the space became … ExtraTerrorestrial!

19. Holidayland

Holidayland, part of Disneyland between 1957 and 1961, was actually a 9-acre area just outside of Disneyland. It was less ride-oriented and instead contained picnic spots, sports fields, and a large tent for performances.

20. Camp Minnie-Mickey and Beastly Kingdom

In the early days of Disney’s Animal Kingdom Theme Park, the company wanted to include a Beastly Kingdom in homage to fake creatures like dragons and unicorns. While prepping for that, Camp Minnie-Mickey went up in 1998, intended to be a temporary placeholder until Beastly Kingdom was ready to be built. Well, now we don’t have either; Beastly Kingdom never came to be and the camp-themed section closed in 2014.

21. Lilliputian Land

Finally, one land that never became a land: Lilliputian Land. We know that Walt Disney wanted part of Disneyland to be based on a section of the book Gulliver’s Travels thanks to a map drawn in 1953. With everything in that area made to look tiny, like fake people, guests would feel like giants. It’s thought that some of the DNA of Lilliputian Land can still be seen on the Storybook Land Canal Boats.