5 Pioneering Women in Mathematics

In 2019, Karen Uhlenbeck was honored as the first woman to receive the Abel Prize, the most prestigious award in mathematics (a field not covered by the Nobel Prize). This recognition celebrated Uhlenbeck's pioneering contributions to geometric partial differential equations and gauge theory, which form the mathematical foundation of theoretical physics.

Uhlenbeck's revolutionary discoveries have profound implications for particle physics, string theory, and general relativity. However, she is not the only renowned female mathematician. Let’s explore the lives of others, in chronological order.

1. Emmy Noether (1882-1935): Her Theorem Revolutionized Science

Ruth Gregory, a mathematician and cosmologist, once stated, "It is hard to overstate the importance of Noether's work in modern physics." While it may be challenging for non-experts to fully grasp, "Noether's theorem" stands as one of the monumental scientific discoveries of the 20th century, forming the bedrock for abstract algebra and theoretical physics.

Born in Germany in the late 1800s to a mathematician father, Emmy Noether faced gender-based barriers that prevented her from officially enrolling at the male-only university. Instead, she audited classes, passed all exams, and earned her undergraduate degree. She later obtained a Ph.D. at a more progressive institution but was still denied a teaching post.

In 1915, one year after Albert Einstein introduced his general theory of relativity, the young Noether—then an unpaid lecturer at the University of Göttingen—was called upon by a group of the world's foremost mathematicians to help resolve a problem with Einstein's groundbreaking theory of gravity. Unperturbed, she demonstrated why general relativity was consistent with the principle of energy conservation.

Three years later, Noether published her own revolutionary theorem, which established a mathematical connection between conservation laws and a concept called symmetry. Noether's theorem—which is not merely a theory but a mathematical proof—showed that every conservation law (such as energy, momentum, and angular momentum) is linked to an inherent symmetry in nature. This relationship had previously gone unrecognized by scientists.

With the mathematical framework provided by Noether's theorem, physicists went on to develop the Standard Model, which explains the interactions of the weak, strong, and electromagnetic forces. Today, Noether's theorem continues to aid in our understanding of phenomena like black holes and the mystery of dark matter.

2. Katherine Johnson (1918-2020): NASA's 'Human Computer'

Katherine Johnson, portrayed by Taraji P. Henson in the 2016 film "Hidden Figures," was a pioneer in many ways. Growing up as a black woman in segregated West Virginia, she overcame racial barriers in both education and career, becoming a crucial figure in the success of the early American space program, including John Glenn's 1962 orbital mission.

Gifted in mathematics from a young age, Johnson excelled in school, earning an early graduation from the historically black West Virginia State College. After teaching at black public schools for several years, she was invited to integrate West Virginia University's graduate programs in 1939. Although she accepted the challenge, she left the program when she and her husband decided to start a family.

For the next decade, Johnson stayed home to raise her three daughters, as was customary for many women of her era. Her life took a turn when a relative informed her about the all-black computing department at what was then the National Advisory Committee for Aeronautics (NACA) in 1952. Johnson and her family relocated to Virginia, where she quickly made an impression with her speed and precision in calculations at the Langley research facility.

Known as one of NASA's "human computers," Katherine Johnson performed critical computations for trajectory analysis and orbital paths of near-Earth satellites. Her pivotal moment occurred during the last-minute preparations for John Glenn's Friendship 7 mission, America's first manned orbital flight. Glenn, concerned about relying on early computers, instructed his engineers to "get the girl" to run the calculations by hand. "If she says they're good," Johnson recalled Glenn saying, "then I'm ready to go."

In 2015, President Barack Obama honored 97-year-old Katherine Johnson with the Presidential Medal of Freedom. In 2018, NASA celebrated her 100th birthday. Johnson passed away in 2020.

3. Cathleen Morawetz (1923-2017): Ingenious Problem-Solver

While many mathematicians prefer to explore abstract concepts and theoretical frameworks, Cathleen Morawetz, a Canadian mathematician, focused on applying her mathematical expertise to solve challenging real-world problems in physics.

Similar to Noether, Morawetz's father was an accomplished mathematician and physicist. Interestingly, she was mentored at New York University (NYU) by Richard Courant, who was also one of Noether's mentors in Göttingen. After earning her Ph.D., Morawetz dedicated her entire career to research and teaching at NYU, where she became the first female director of the Courant Institute of Mathematical Sciences.

Morawetz is best known for her contributions to wave propagation, particularly the 'Morawetz inequality' and 'Morawetz estimate.' In 1956, she became the first to prove that no aircraft airfoil design could entirely eliminate shock waves at supersonic speeds. This discovery helped engineers design wings that minimized shock waves instead of trying to eradicate them completely. Her later work focused on nonlinear wave scattering by obstacles, making significant strides in hyperbolic and mixed-type partial differential equations, which engineers use to model interactions involving various types of waveforms.

Beyond her remarkable intellectual abilities, Morawetz was a devoted mentor to female mathematicians at NYU. Among her many accolades, she received the National Medal of Science in 1998, becoming the first female mathematician to be honored with this prestigious award.

4. Karen Uhlenbeck (1942- ): First Woman to Win the 'Nobel' of Math

As a young girl, Karen Uhlenbeck developed a love for reading, which sparked her interest in science. She pursued her studies at NYU's Courant Institute and earned her Ph.D. from Brandeis University in 1968. Reflecting on her job search, she recalls, 'The places interested in my husband — MIT, Stanford, and Princeton — were not interested in hiring me.' While these institutions attributed their decisions to 'nepotism rules,' Uhlenbeck suspected that her gender played a role.

In 1983, Uhlenbeck was awarded a MacArthur Prize Fellowship, and in 1987, she became a professor at the University of Texas at Austin, where she spent three decades. Her research focused on geometric partial differential equations and gauge theory, contributing significantly to the advancement of string theory and particle physics. Her groundbreaking work in the intersection of mathematics and physics led her to receive the Abel Prize in 2019, becoming the first woman to earn this prestigious award.

Not only is Uhlenbeck celebrated as 'one of the most important mathematicians of the 20th century,' but she is also a passionate advocate for increasing the representation of women in mathematics. She has initiated multiple programs to encourage both women and children to engage more deeply with the field of mathematics.

5. Maryam Mirzakhani (1977-2017): Math Star Extinguished Too Soon

At the age of 37 in 2014, Maryam Mirzakhani made history by becoming the first woman and the first Iranian to receive the Fields Medal, one of the highest honors in mathematics, awarded every four years to exceptional mathematicians under the age of 40. Sadly, Mirzakhani passed away in 2017 after a brave fight with breast cancer.

Raised in Tehran during the Iran-Iraq war, Mirzakhani graduated from Sharif University before earning her Ph.D. from Harvard University. At Harvard, she delved into the geometry of hyperbolic surfaces, studying complex shapes such as theoretical donut-like objects and other intricate topics in mathematics.

When asked to explain her research in simpler terms, Mirzakhani shared with The Guardian, 'Most problems I work on are related to geometric structures on surfaces and their deformations. Specifically, I'm interested in understanding hyperbolic surfaces. Sometimes, the properties of a fixed hyperbolic surface can be better understood by studying the moduli space that parameterizes all hyperbolic structures on a given topological surface.'

Got all that?

Mirzakhani, renowned for her meticulous and persistent method in tackling intricate theoretical challenges, was charting thrilling new territories when her journey was tragically cut short. Her groundbreaking achievement of the Fields Medal is a beacon of inspiration, urging the next generation of female mathematicians to follow in her trailblazing footsteps.

"While not everyone is meant to be a mathematician, I strongly believe many students never give mathematics the opportunity it deserves," Mirzakhani shared in the same interview. "I struggled with math for several years during middle school; I simply wasn’t interested in engaging with it. Without passion, mathematics can seem meaningless and cold. The true elegance of mathematics only reveals itself to those who approach it with patience."

Explore more about the role of women in mathematics in "Power in Numbers: The Rebel Women of Mathematics" by Talithia Williams. Mytour suggests related titles based on books we think you'll enjoy. If you decide to make a purchase, we'll earn a small commission from the sale.