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.

6 Explosive Fart Controversies

iStock/MaryValery
iStock/MaryValery

Last week, the world of professional darts became embroiled in controversy after a player competing in the quarter finals of a major tournament partly blamed his loss on his opponent’s noxious flatulence. The loser, Wesley Harms, told the Dutch television station RTL7, "It’ll take me two nights to lose this smell from my nose." (Harms’s rival Gary Anderson denied being the fart’s founder, saying, "It was bad. It was a stink. It thought it was him, and he started playing better, I went, 'He must needed to get some wind out.'") Now that the niche world of competitive darts is clouded in Fartgate, it seems like an appropriate time to step outside and dutifully reminisce on a few other gassy controversies.

1. German police fine man over $1000 for letting it rip

In 2016, police in Berlin detained a man at a party and asked for his ID. Instead of offering his name, the man gave the police a whiff of his unique perfume, sending two rocketing farts in the direction of the officers. The police summarily fined the offender €900 (just over $1000) for disrespecting law enforcement. The ensuing "Crazy Toot Trial" would involve 23 officials and prompt a public outcry over wasteful public spending.

2. Fart sparks regime-change in Ancient Egypt

Around 570 BCE, the Egyptian Pharaoh King Apries had a problem: Invaders had slaughtered some of his soldiers and people's morale was low. So Apries sent his best general, Amasis, to quell the troops' discontent. Instead, the troops rallied around Amasis and declared him their personal king. When King Apries sent a messenger to accost Amasis, Amasis let out a fart and effectively said, "You can send that message back to the king!" Hearing this, King Apries unwisely decided to punish his messenger. That decision made King Apries even more unpopular and gave the gassy Amasis a chance to stage a revolt and successfully oust his old boss.

3. Cargo plane makes emergency stop because of reported goat gas

In 2015, a Singapore Airlines cargo flight was forced to make an emergency stop in Bali after more than 2000 goats reportedly filled the cargo hold with too many toots, setting off the fire alarm. "The smoke indication was identified to be the result of exhaust gases and manure produced by the sheep," The Aviation Herald reported. Despite this initial report, Singapore Airlines refused to acknowledge that the cause of the stopover was fart-related.

4. Fart fuels mid-flight fight

On a 2018 flight from Dubai to Amsterdam, a Transavia Airlines plane had to make an unscheduled stop in Vienna after an elderly man refused to stop cutting the cheese—even after receiving instructions from the pilot to cease firing. The man's stinkers fueled so much consternation among the surrounding passengers that a fight broke out, prompting police to remove four people from the flight.

5. Canada's Parliament debates the appropriateness of saying "fart"

In November 2016, Canada’s parliament began to spontaneously debate whether it was appropriate for members to use the word fart on the chamber floor. The discussion rose after Conservative MP Michelle Rempel asked, “Why does the government treat Alberta like a fart in the room that nobody wants to talk about or acknowledge?” Eventually, the rules regarding “unparliamentary language” had to be read aloud and the offense was taken under advisement. (You can read a transcript of the exchange here.)

6. Secret Service takes the blame for Presidential retarade

The Secret Service will not only take a bullet for the president, they’ll also take the blame for the Commander-in-Chief’s errant cheek squeaks: Gerald Ford, the 38th President of the United States, would often fart and blame it on his Secret Service agents, loudly saying, "Jesus, was that you? Show some class." (This must have come as a shock to Lyndon B. Johnson, who once said, “Jerry Ford is so dumb he can’t fart and chew gum at the same time.")

Every New Movie, Series, Documentary, and Special That's Coming to Netflix in December

Alfonso Cuarón directs Roma (2018)
Alfonso Cuarón directs Roma (2018)
Carlos Somonte, Netflix

Netflix has made no secret of its desire to bring top-tier entertainment to streaming devices around the world. After successfully testing the waters with a range of critically acclaimed series, from Stranger Things to The Crown, the streaming giant is now making a major push into the feature film market—which we’ll see play out in December with the release of Alfonso Cuarón’s Roma and Susanne Bier’s Bird Box.

Much has already been made about how these films, along with the Coen Brothers’ recently-recently The Ballad of Buster Scruggs, are disrupting the line between streaming and cinemas. How will it all play out come Oscar time? We’ll just have to wait to see.

In the meantime, here’s every new movie, television series, documentary, and comedy special making its way to Netflix in December.

DECEMBER 1

8 Mile
Astro Boy
Battle
Bride of Chucky
Christine
Cloudy with a Chance of Meatballs
Crossroads: One Two Jaga
Friday
Friday After Next
Hellboy
Man vs Wild with Sunny Leone: Season 1
Meet Joe Black
Memories of the Alhambra
My Bloody Valentine
Next Friday
Reindeer Games
Seven Pounds
Shaun of the Dead
Terminator Salvation
The Big Lebowski
The Last Dragon
The Man Who Knew Too Little

DECEMBER 2

The Lobster

DECEMBER 3

Blue Planet II: Season 1
Hero Mask
The Sound of Your Heart: Reboot Season 2

DECEMBER 4

District 9

DECEMBER 6

Happy!: Season 1

DECEMBER 7

5 Star Christmas
Bad Blood
Dogs of Berlin
Dumplin'
Free Rein: The Twelve Neighs of Christmas
Mowgli: Legend of the Jungle
Nailed It! Holiday!
Pine Gap
ReMastered: Who Killed Jam Master Jay?
Super Monsters and the Wish Star
The American Meme
The Hook Up Plan (Plan Coeur)
The Ranch: Part 6

DECEMBER 9

Sin senos sí hay paraíso: Season 3

DECEMBER 10

Michael Jackson's This Is It

DECEMBER 11

Vir Das: Losing It

DECEMBER 12

Back Street Girls: Gokudols
Out of Many, One

DECEMBER 13

Wanted: Season 3

DECEMBER 14

Chilling Adventures of Sabrina: "A Midwinter's Tale"
Cuckoo: Season 4
Dance & Sing with True: Songs
Fuller House: Season 4
Inside the Real Narcos: Series 1
Inside the World’s Toughest Prisons: Season 3
Prince of Peoria: A Christmas Moose Miracle
Roma
Sunderland Til I Die
The Fix
The Innocent Man
The Protector
Tidelands
Travelers: Season 3
Voltron: Legendary Defender: Season 8

DECEMBER 16

Baby Mama
Kill the Messenger
One Day
Springsteen on Broadway
The Theory of Everything

DECEMBER 18

Baki
Ellen DeGeneres: Relatable
Terrace House: Opening New Doors: Part 5

DECEMBER 21

3Below: Tales of Arcadia
7 Days Out
Back With the Ex
Bad Seeds
Bird Box
Wolf (Boru)
Derry Girls
Diablero
Greenleaf: Season 3
Last Hope: Part 2
Perfume
Sirius the Jaeger
Struggle: The Life and Lost Art of Szukalski
Tales by Light: Season 3
The Casketeers

DECEMBER 24

Hi Score Girl
The Magicians: Season 3

DECEMBER 25

Watership Down: Limited Series
Anthony Bourdain: Parts Unknown: Season 11
Marvel Studios' Avengers: Infinity War

DECEMBER 26

Alexa & Katie: Season 2
You

DECEMBER 28

Instant Hotel
La noche de 12 anos
Selection Day
When Angels Sleep
Yummy Mummies

DECEMBER 30

The Autopsy of Jane Doe

DECEMBER 31

The Bill Murray Stories: Life Lessons Learned From a Mythical Man

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