## Infographic Transcript

You don’t have to look far to identify women who have impacted mathematics. From antiquity to modern day, famous women mathematicians have not only advanced mathematical understanding, but applied findings to other scientific fields. Contributions of the following women mathematicians span astronomy, education, number theory, computer programming, mathematical analysis, algebra, geometry, space and flight, game theory, statistics, engineering, and theoretical mathematics.

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Explore Degree## 10 Famous Women Mathematicians Through the Ages

Here are some of the most famous women mathematicians.

### 1. Hypatia (370-415)

Hypatia is the first woman known to have taught mathematics. Most consider her to be the first female to have made a significant contribution to mathematics.

Hypatia was trained by her father, Theon of Alexandria, a famous scholar who edited Euclid’s mathematical treatise, *Elements*. They collaborated on commentaries of famous mathematical works, and Hypatia is believed to have developed commentaries of her own. Eventually, she replaced her father as the leading mathematician of Alexandria. Hypatia was also an accomplished astronomer and perhaps best-known as a Neoplatonist philosopher. Neoplatonism was a strand of Platonic philosophy that began in the third century.

### 2. Sophie Germain (1776-1831)

Sophie Germain battled gender discrimination on multiple fronts. Although she was denied a career in mathematics, she worked independently, making significant contributions to the field.

Germain’s interest in mathematics began around the age of 13 when the French Revolution began and she was confined to her home. As a result, she spent a great deal of time in her father’s library, which sparked an interest in mathematics. Her parents tried to stop her, even going as far as denying her a fire in her room to make her stay in her bed at night. However, she hid blankets and candles so that she could study. Her parents eventually relented, and Germain was free to study advanced topics like differential calculus. She even taught herself Latin and Greek so that she could study classic mathematical works.

When Germain turned 18, the Ecole Polytechnique was founded in Paris to train mathematicians and scientists. She couldn’t enroll because of her gender, but she obtained lecture notes and later submitted a paper to J.L. Lagrange, a prominent mathematician, using the name of a previously enrolled male student. He was impressed and, after finding out her identity, agreed to tutor her. Germain studied alongside Lagrange and other leading thinkers. Her greatest achievement is her work on Fermat’s Last Theorem; her analysis was used to solve the problem nearly two centuries later. Germain was the first woman to receive a prize from the Paris Academy of Sciences for her work on elastic theory.

### 3. Ada Lovelace (1815-1852)

Ada Lovelace is well-known for her contributions to computing. She is a mathematician and writer who is considered to be the first computer programmer.

Lovelace never knew her father, the poet Lord Byron. Shortly after her birth, Lovelace left England with her mother, who insisted that her daughter would not become a poet. Instead, Lovelace would be privately tutored — an unusual education for a woman at the time — to become a mathematician and scientist.

When Lovelace was a teenager, she began a long working relationship with professor Charles Babbage, who was working on what he called the “Analytical Engine.” It would be the precursor to the modern computer. Babbage and others were focused on how the engine could crunch numbers, but Lovelace noticed the potential for more. In her translations, she went beyond the task, also supplying notes about the machine, such as the possibility of computer-generated musical compositions. She also added a computer-based algorithm for calculating Bernoulli numbers, which earned her the title as the first computer programmer.

### 4. Sofia Kovalevskaya (1850-1891)

Sofia Kovalevskaya was the first woman to obtain a doctorate in mathematics. Her impact led historian Ann Hibner Koblitz to call Kovalevskaya “the greatest known woman scientist before the twentieth century,” in the book “A Convergence of Lives: Sofia Kovalevskaya: Scientist, Writer, Revolutionary.”

Kovalevskaya’s father provided her with private tutoring, which included calculus at the age of 15. However, he didn’t let her travel abroad to further her education, and Russian universities didn’t accept female students. To escape these barriers, Kovalevskaya entered a marriage of convenience with a paleontology student, and they headed to Heidelberg, Germany. She began her studies there, and, years later, she moved to Berlin and received private lessons with Karl Weierstrass, often referred to as the father of modern analysis.

Kovalevskaya became the first woman to receive a doctorate in mathematics after presenting three papers to the University of Göttingen. They covered partial differential equations, the dynamics of Saturn’s rings, and elliptic integrals. The university was so impressed that it awarded her the doctorate without the need for oral examination and classes. At Stockholm University, Kovalevskaya became the first woman in Europe to hold a position as full professor. The French *Academie Royale des Sciences* awarded her the Prix Bordin award for her work on Saturn’s rings.

### 5. Emmy Noether (1882-1935)

Emmy Noether has been described by her contemporaries as the greatest woman mathematician, and that assessment may hold today.

Noether was born to a Jewish family. Her father, Max Noether, founded algebraic geometry and was described by physicists Leon Lederman and Christopher Hill as “one of the finest mathematicians of the nineteenth century,” in their book “Symmetry and the Beautiful Universe.” Emmy Noether followed in her father’s footsteps, obtaining a doctorate for a dissertation on algebraic invariants. However, she battled discrimination, as it was virtually impossible for German women to obtain academic positions. She instead lectured for no pay and then received an unofficial position as a professor until the Nazi government dismissed Jews from university positions.

Noether accepted a position at Bryn Mawr College in Pennsylvania, where she taught until her death. Her mathematical career spanned three periods, according to mathematician Hermann Weyl. The first period involved insights into algebraic invariants and number fields; several of her concepts were included in Einstein’s general theory of relativity. In the second period, she altered abstract algebra with a classic paper on the theory of ideals in commutative rings. The third period covered her interest in noncommunicative algebra, which was spearheaded by two major publications published in the German mathematical journal *Mathematische Zeitschrift*.

### 6. Dorothy Vaughan (1910-2008)

Dorothy Vaughan fought race and gender discrimination at the National Advisory Committee for Aeronautics (NACA), which later became NASA. She was the first black female supervisor at NASA. Vaughan is celebrated in the 2016 movie “Hidden Figures,” along with famous women mathematicians like Katherine Johnson and Mary Jackson.

After obtaining a bachelor’s degree in mathematics at the age of 19, Vaughan taught high school mathematics in Virginia. A little more than 10 years later, she responded to the call for workers who could support home-front efforts during World War II. She applied and was accepted as a “human computer,” or someone who makes mathematical calculations, at NACA, where she worked in the segregated West Area Computing unit. Her group was responsible for computations that engineers needed to conduct aeronautical experiments. About six years into her time at NACA, Vaughan was promoted to lead the unit, which continued when the NACA transitioned to NASA, also ending segregation of facilities. She advocated for other women to receive pay raises and promotions, regardless of race.

Vaughan paved the way for machine computers in the 1960s by teaching herself and her staff FORTRAN, a computing language used for numeric calculations. She also collaborated with human computers Vera Huckel and Sara Bullock to develop an algebraic methods handbook.

### 7. Katherine Johnson (born 1918)

Katherine Johnson is known for her work in complex manual calculations at NASA, and specifically, her work in orbital mechanics, which helped with initial and subsequent U.S. manned spaceflights. She received the Presidential Medal of Freedom in 2015.

Johnson grew up in a small town in West Virginia that didn’t offer schooling for black students past eighth grade. Her father drove more than 100 miles so that she could continue her education. Johnson flourished in high school, graduating by the age of 14, and her success extended in college. One of her professors — W.W. Schieffelin Claytor, who was the third black person to earn a Ph.D. in mathematics — was so impressed that he took it upon himself to help prepare her to become a research mathematician. That included creating a class in analytic geometry of space just for Johnson. Another notable fact is that in graduate school, she was handpicked along with two men to integrate West Virginia University.

Johnson joined the NACA, starting a 35-year career there at what would become NASA. She was assigned to an all-male flight research team, where she performed trajectory analysis for Alan Shephard, the first American to enter space. Later, she completed what she would become most well-known for: checking computers’ orbital equations for John Glenn’s mission. According to NASA, Glenn specifically asked for Johnson. “If she says they’re good,” Glenn reportedly said, “then I’m ready to go.”

### 8. Julia Robinson (1919-1985)

Julia Robison is known for her contributions to Hilbert’s tenth problem and decision problems. She was the first woman mathematician to be elected to the National Academy of Sciences and became the first female president of the American Mathematical Society.

Robinson battled illness multiple times. At the age of 9, she had scarlet fever followed by rheumatic fever, causing her to miss two years of school. With the help of a private tutor, she was able to complete grades 5-8 in just one year. Robinson graduated high school with honors in math and science, and attended the University of California at Berkeley, where she met her husband, an assistant professor. She became more devoted to mathematics after being told she couldn’t have children due to effects from rheumatic fever.

Robinson worked for decades on Hilbert’s tenth problem, one of 23 notoriously difficult problems posed by German mathematician David Hilbert in 1900. Her work alongside other mathematicians led to the problem being solved in 1970. Additionally, Robinson worked on topics in decision problems, game theory, and statistics.

### 9. Mary Jackson (1921-2005)

Mary Jackson worked as a mathematician and aerospace engineer at the NACA and NASA. She was NASA’s first black female engineer and became an advocate for hiring and promoting women in NASA.

Jackson earned a dual degree in mathematics and physical sciences, and then worked several jobs before joining the NACA as a human computer. After two years, Jackson worked for engineer Kazimierz Czarnecki in the Supersonic Pressure Tunnel, a 4-by-4-foot, 60,000-horsepower wind tunnel that could produce winds nearly twice the speed of sound. To qualify, she had to take graduate-level courses at an all-white high school. Jackson petitioned the school and received permission to do so, enabling her to become the first black female engineer at NASA. She studied air flow to enhance United States planes, also working in multiple NASA divisions and co-authoring 12 technical papers across NACA and NASA.

With nearly two decades of experience as an engineer, Jackson made a drastic career change: she accepted a demotion to become the Federal Women’s Program Manager. That allowed her to help women and other minorities advance their career in science, engineering and mathematics at NASA.

### 10. Maryam Mirzakhani (1977-2017)

Maryam Mirzakhani is the only woman and Iranian to be awarded with the Fields Medal, the most prestigious award in mathematics.

Mirzakhani initially wanted to be a writer. In high school, however, she fell in love with math. As a junior, Mirzakhani and her best friend became the only Iranian women to qualify for the International Mathematical Olympiad. The following year, Mirzakhani earned a gold medal with a perfect score. Later, she moved to the United States for graduate school at Harvard University. After becoming a research fellow and professor at two institutions, she became a professor at Stanford University, where she would work until her death.

Mirzakhani’s work concentrated on several branches of theoretical mathematics: hyperbolic geometry, symplectic geometry, Ergodic theory, moduli spaces, and Teichmüller theory. She was particularly fascinated with the geometric and dynamic complexities of curved surfaces, like doughnut shapes, spheres and amoebas. Her Ph.D. thesis was notable, as it led to the young mathematician being published in top mathematical journals across three separate papers. One paper contained a new proof for the Witten conjecture, which connected mathematics and quantum gravity. In 2014, Mirzakhani received the Fields Medal, a mathematical award often compared to the Nobel Prize.

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