Emmy Noether

German mathematician Emmy Noether. Photo courtesy of NCRI Women’s Committee

Born in Erlangen, Germany, in 1882, Emmy Noether is widely regarded as one of the most influential mathematicians in history. Albert Einstein described her as the most "significant" and "creative" female mathematician of her time, according to The New York Times.

Best known for developing Noether's theorem, she established a fundamental connection between symmetry in nature and conservation laws such as energy and momentum. The breakthrough became a cornerstone of modern physics and helped deepen scientists' understanding of Einstein's theory of relativity.

She developed an early interest in the subject but faced barriers because women were largely excluded from higher education in Germany. She initially audited university classes before earning a doctorate from the University of Erlangen, becoming only the second woman in Germany to receive a Ph.D. in mathematics.

Her talent earned the admiration of leading mathematicians David Hilbert and Felix Klein. In 1915, she joined the Mathematical Institute at the University of Göttingen, one of the world's leading centers for mathematics, where she worked with Hilbert and Klein on mathematical questions arising from Einstein's theory of general relativity.

When university administrators opposed her appointment because she was a woman, Hilbert defended her candidacy. "I do not see that the sex of the candidate is an argument against her," he said. "After all, we are a university, not a bathhouse."

Despite producing groundbreaking research, she spent years teaching without pay or an official academic title. Beyond Noether's theorem, she revolutionized abstract algebra through pioneering work in ring theory, group theory and number theory, helping unify several branches of mathematics.

With Einstein's support, she later earned a position at Bryn Mawr College in Pennsylvania, where she said she felt more appreciated than she had in Germany. However, only 18 months after arriving in the U.S., Noether underwent surgery for an ovarian cyst and died in 1935 at age 53.

Katherine Johnson

American mathematician Katherine Johnson. Photo courtesy of NASA

Born in White Sulphur Springs, West Virginia, in 1918, Johnson helped make some of NASA's most important early space missions possible through calculations that guided astronauts into orbit and supported missions to the moon.

A child prodigy, she entered high school at age 13 and graduated from West Virginia State College with highest honors at 18. In 1939, she became one of the first black students selected to integrate the graduate program at West Virginia University.

Johnson joined the National Advisory Committee for Aeronautics, NASA's predecessor, in 1953 as part of its segregated West Area Computing unit. She was among NASA's famed "human computers," mathematicians who performed complex calculations by hand before electronic computers became widely used.

Her expertise quickly earned her a place in the agency's Space Task Group. She worked on Alan Shepard's Freedom 7 mission in 1961, America's first human spaceflight, and helped verify the orbital calculations for astronaut John Glenn's Friendship 7 mission the following year, the first U.S. crewed mission to orbit Earth.

Although electronic computers had generated the flight calculations, astronauts remained cautious about relying entirely on the new machines. Before his launch, Glenn asked engineers to "get the girl", Johnson, to verify the numbers by hand, according to NASA. Johnson later recalled him saying: "If she says they're good, then I'm ready to go."

Her work later contributed to the Apollo program by helping synchronize the lunar lander with the command module orbiting the moon. During a 33-year career at NASA, she also worked on the space shuttle program and Earth-observing satellites while authoring or co-authoring 26 research reports.

Johnson retired in 1986. In 2015, she received the Presidential Medal of Freedom from former U.S. President Barack Obama. Her achievements later reached a global audience through the 2016 film "Hidden Figures," which highlighted the contributions of black female mathematicians to the U.S. space program.

Johnson died on Feb. 24, 2020, at age 101. NASA Administrator James Bridenstine said: "Our NASA family is sad to learn the news that Katherine Johnson passed away this morning at 101 years old. She was an American hero and her pioneering legacy will never be forgotten."

Cathleen Morawetz

Canadian mathematician Cathleen Morawetz. Photo courtesy of U.S.'s National Science and Technology Medals Foundation

Born in Toronto, Canada, in 1923, Cathleen Morawetz developed an early interest in mathematics under the influence of her father, physicist and mathematician John Lighton Synge, and later earned a doctorate from New York University under mathematician Richard Courant. She spent most of her career at NYU's Courant Institute of Mathematical Sciences, becoming its first female director in 1984.

Much of her research focused on understanding how waves behave, from sound and light to airflow around aircraft. Her work helped scientists better understand how waves move around objects and dissipate over time, leading to advances in aerodynamics, acoustics and optics.

Among her most influential contributions was research showing that aircraft wings could not completely eliminate shock waves under real-world conditions, helping engineers develop designs that minimized their effects instead.

Morawetz was also a dedicated mentor to younger mathematicians and an advocate for women in science. In 1998, she became the first female mathematician to receive the National Medal of Science, the highest scientific honor in the U.S. She was also named Outstanding Woman Scientist by the Association for Women in Science, served as president of the Association for Women in Mathematics and received a Guggenheim Fellowship.

She died in Manhattan, New York, in 2017 at age 94.

Karen Uhlenbeck

American mathematician Karen Uhlenbeck. Photo courtesy of the U.S.'s Institute for Advanced Study

In 2019, Uhlenbeck became the first and only woman to receive the Abel Prize, often referred to as "math's Nobel" prize.

Her research on geometric equations and gauge theory helped advance both mathematics and theoretical physics, contributing to fields including particle physics and string theory. The Abel Prize committee recognized her for "her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics," according to CBS News.

Hans Munthe-Kaas, chair of the Abel committee, said her work had "dramatically changed the mathematical landscape."

Born in Cleveland, Ohio, in 1942, she developed a love of reading as a child, which sparked her interest in science and mathematics. She later studied at New York University's Courant Institute and earned a doctorate from Brandeis University in 1968.

After receiving her Ph.D. Uhlenbeck taught at MIT and UC Berkeley, but encountered many obstacles to getting hired as a full-time faculty member, according to The National Science and Technology Medals Foundation. She was told "that people didn’t hire women, that women were supposed to go home and have babies." "So the places interested in my husband — MIT, Stanford, and Princeton — were not interested in hiring me," she said.

Despite those challenges, she built a distinguished research career. She received a MacArthur Fellowship in 1983 and joined the University of Texas at Austin as a professor in 1987, remaining there for more than three decades.

Beyond her research, Uhlenbeck has been a prominent advocate for women in mathematics and science. She helped establish programs designed to support female mathematicians and encourage young people to pursue careers in the field.

Maryam Mirzakhani

Iranian mathematician Maryam Mirzakhani. Photo courtesy of Stanford University

Mirzakhani became the first woman and the first Iranian to win the Fields Medal in 2014, breaking a barrier that had stood since the award's creation nearly eight decades earlier.

Often described as the highest honor in mathematics for young researchers, the Fields Medal is awarded every four years by the International Mathematical Union (IMU) to up to four mathematicians under the age of 40. Before Mirzakhani's victory, all 52 recipients had been men.

She received the award for her outstanding contributions to understanding the dynamics and geometry of Riemann surfaces and their moduli spaces, IMU said. Her work centered on geometry and dynamical systems, especially the properties and symmetries of curved surfaces such as spheres and doughnut-shaped forms. Though theoretical, it also had applications in physics and quantum field theory.

"It was bound to happen," Ingrid Daubechies, a former president of the IMU, told Scientific American in 2017. "There are excellent young women mathematicians. Many times they have been on the short, short list, but it had so far not happened. I was very, very happy that it happened on my watch."

Born in Tehran on May 3, 1977, Mirzakhani initially dreamed of becoming a writer before discovering a passion for mathematics in high school. She went on to win gold medals at the International Mathematical Olympiads in 1994 and 1995, earning a perfect score in the latter competition.

After receiving a bachelor's degree from Sharif University of Technology in Iran, Mirzakhani completed her Ph.D. at Harvard University, where she conducted pioneering research in geometry. She later taught at Princeton University before joining Stanford University in 2008.

Known for her patient and methodical approach to solving difficult mathematical problems, Mirzakhani earned international recognition for research that expanded understanding of geometric structures and curved spaces.

Her work helped establish her as one of the leading mathematicians of her generation. Mirzakhani was still pursuing new research when she died from cancer on July 17, 2017, at age 40. She continued working until shortly before her death and was survived by her husband, Jan Vondrák, and their daughter, Anahita.