The contributions of women to mathematics have often been overlooked or unacknowledged, but throughout history, many women have made groundbreaking advances that shaped our understanding of the field. From ancient times to the modern era, these mathematicians challenged gender norms, solved complex problems, and paved the way for future generations. At Oxford Summer Courses, we celebrate their achievements, inspiring the next wave of mathematicians to explore the beauty and logic of numbers.

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These 15 women mathematicians have transformed the field with their groundbreaking work and continue to inspire mathematicians around the world.

1. Hypatia of Alexandria (c. 360–415 AD)

Hypatia was a philosopher, mathematician, and astronomer in ancient Alexandria. She is one of the earliest known female mathematicians, celebrated for her work in teaching and expanding upon the mathematical knowledge of her time.

Famous works:

• Commentaries on Diophantus - Hypatia expanded on the works of the ancient Greek mathematician Diophantus, contributing to the study of algebra.
• Teaching Geometry and Astronomy - Hypatia taught mathematics and philosophy at the famous Library of Alexandria, preserving and disseminating the knowledge of Euclid and Ptolemy.

Awards and Legacy:

• Hypatia is regarded as one of the most influential female philosophers and mathematicians of the ancient world. Though none of her original works survive, her teachings played a vital role in keeping Greek mathematics alive during a turbulent time.

2. Émilie du Châtelet (1706–1749)

Émilie du Châtelet was a French mathematician, physicist, and philosopher. She is best known for her translation and commentary on Isaac Newton’s Principia Mathematica, making Newton’s ideas more accessible to French scientists.

Famous works:

• Translation of Newton’s Principia Mathematica - Her translation remains the standard French version of Newton’s work, and her commentaries helped clarify and expand on his theories.
• Work in Kinetic Energy - Du Châtelet’s contributions to the concept of kinetic energy laid the groundwork for later discoveries in physics.

Awards and Legacy:

• Though du Châtelet did not receive formal recognition during her lifetime due to her gender, her work remains influential, and she is now celebrated for her contributions to both mathematics and physics.

3. Ada Lovelace (1815–1852)

Ada Lovelace, the daughter of the poet Lord Byron, is often considered the world’s first computer programmer. Her work on Charles Babbage’s Analytical Engine, an early mechanical general-purpose computer, was groundbreaking.

Famous works:

• Notes on the Analytical Engine (1843) - Lovelace’s detailed notes on Babbage’s machine included what is considered the first algorithm intended to be processed by a machine, making her the first computer programmer.
• Concept of a Computing Machine - Lovelace foresaw that computers could go beyond calculations to manipulate symbols and even create music or art, an insight far ahead of her time.

Awards and Legacy:

• Lovelace is celebrated as a visionary in the field of computing, and Ada Lovelace Day, an international celebration of women in STEM, is named in her honour. Her contributions have been recognised posthumously, and her work continues to influence modern computer science.

4. Sofia Kovalevskaya (1850–1891)

Sofia Kovalevskaya was a Russian mathematician and the first woman to receive a doctorate in mathematics. Her work on partial differential equations and analysis earned her international recognition.

Famous works:

• Kovalevskaya’s Theorem - Her work in the field of partial differential equations led to the development of Kovalevskaya’s Theorem, which concerns the rotation of a rigid body around a fixed point.
• Mathematical Papers on Saturn’s Rings - Kovalevskaya published papers on the mechanics of Saturn’s rings, contributing to the field of celestial mechanics.

Awards and Legacy:

• Kovalevskaya became the first woman to hold a full professorship in northern Europe, and the Sofia Kovalevskaya Prize is awarded to outstanding mathematicians today. Her perseverance in a male-dominated field has made her an enduring symbol of excellence in mathematics.

5. Emmy Noether (1882–1935)

Emmy Noether is widely regarded as one of the most important mathematicians of the 20th century. Her work in abstract algebra and theoretical physics has had a lasting impact on both fields.

Famous works:

• Noether’s Theorem (1915) - This groundbreaking theorem established a fundamental relationship between symmetry and conservation laws in physics, a cornerstone of modern theoretical physics.
• Contributions to Abstract Algebra - Noether’s work laid the foundation for modern abstract algebra, particularly in the theory of rings, fields, and groups.

Awards and Legacy:

• Noether’s contributions to mathematics were initially overlooked due to her gender, but today she is recognised as one of the greatest mathematicians of all time. The Noether Medal, awarded for achievements in mathematics, is named in her honour.

6. Mary Cartwright (1900–1998)

Mary Cartwright was a British mathematician who made significant contributions to the study of non-linear differential equations and chaos theory. She was one of the first to recognise the chaotic behaviour in certain mathematical systems.

Famous works:

• Cartwright-Littlewood Theorem - In collaboration with John Littlewood, Cartwright worked on non-linear differential equations, which later contributed to the development of chaos theory.
• Work on Radio Waves - Cartwright’s research was applied to the study of radio waves and radar during World War II.

Awards and Legacy:

• Cartwright was the first woman to serve as president of the London Mathematical Society and was awarded the De Morgan Medal in 1968. Her work on chaos theory has been influential in a wide range of scientific fields.

7. Dorothy Vaughan (1910–2008)

Dorothy Vaughan was an American mathematician and one of the first African-American women to work as a supervisor at NASA. She made significant contributions to the space programme, particularly in the early use of electronic computers.

Famous works:

• Work on the Space Programme - Vaughan contributed to the mathematical calculations that helped the United States achieve its first satellite launches and space missions.
• Fortran Programming - She became an expert in Fortran, one of the first high-level programming languages, and helped transition NASA’s computing work from manual to digital.

Awards and Legacy:

• Vaughan’s contributions were highlighted in the book and film Hidden Figures, which brought her pioneering work to a wider audience. She is remembered as a key figure in the success of the early space programme and a champion for women of colour in STEM fields.

8. Julia Robinson (1919–1985)

Julia Robinson was an American mathematician known for her work on Hilbert’s 10th Problem. Her contributions to number theory and mathematical logic had a profound impact on the field.

Famous works:

• Work on Hilbert’s 10th Problem - Robinson’s research helped solve Hilbert’s 10th Problem, a major question in number theory that had remained unsolved for decades.
• Contributions to Decision Problems in Mathematics - Robinson’s work in mathematical logic was influential in the development of algorithms and decision theory.

Awards and Legacy:

• Robinson was the first woman to be elected to the mathematical section of the National Academy of Sciences in the United States. Her work on Hilbert’s 10th Problem is considered one of the great achievements in mathematics, and the Julia Robinson Mathematics Festival was established in her honour.

9. Maryam Mirzakhani (1977–2017)

Maryam Mirzakhani was an Iranian mathematician and the first woman to win the prestigious Fields Medal, often referred to as the Nobel Prize of mathematics. Her work focused on the geometry of Riemann surfaces and their moduli spaces.

Famous works:

• Work on Hyperbolic Geometry - Mirzakhani made groundbreaking contributions to the understanding of the geometry and dynamics of Riemann surfaces and moduli spaces.
• Ergodic Theory - Her research in ergodic theory and complex geometry has had a lasting impact on the field.

Awards and Legacy:

• Mirzakhani received numerous honours throughout her career, culminating in the Fields Medal in 2014. Her untimely death at the age of 40 cut short a brilliant career, but her contributions to mathematics continue to influence the field today.

10. Shakuntala Devi (1929–2013)

Shakuntala Devi, known as the "Human Computer," was an Indian mathematician and writer who gained fame for her extraordinary mental calculation abilities. She demonstrated complex arithmetic abilities at a young age and became an international sensation for her mathematical prowess.

Famous works:

• World Record for Mental Calculation (1980) - Devi set a Guinness World Record for multiplying two 13-digit numbers in just 28 seconds.
• Writings on Mathematics - Devi wrote several books on mathematics and puzzles, including The Joy of Numbers and Figuring: The Joy of Numbers.

Awards and Legacy:

• Devi’s life and achievements were celebrated in the 2020 film Shakuntala Devi, which brought her remarkable abilities to a global audience. Her work in promoting mathematics and mental calculation continues to inspire people around the world.

11. Grace Hopper (1906–1992)

Grace Hopper was an American mathematician and computer scientist. She was one of the first programmers of the Harvard Mark I computer and developed the first compiler for a computer programming language, which led to the development of COBOL.

Famous works:

• Development of the First Compiler (1952) - Hopper’s compiler translated written language into machine code, revolutionising programming.
• COBOL Programming Language - Hopper played a key role in the development of COBOL, one of the earliest high-level programming languages that is still used in business and finance.

Awards and Legacy:

• Hopper received numerous awards for her pioneering work in computer science, including the National Medal of Technology. The Grace Hopper Celebration of Women in Computing, an annual conference, is named in her honour, recognising her groundbreaking contributions to the field.

12. Karen Uhlenbeck (1942– )

Karen Uhlenbeck is an American mathematician who made significant contributions to geometric analysis and mathematical physics. She was the first woman to be awarded the prestigious Abel Prize for her pioneering work.

Famous works:

• Work on Minimal Surfaces - Uhlenbeck’s work on variational problems, particularly in the study of minimal surfaces, has had a profound impact on differential geometry.
• Gauge Theory - Her contributions to gauge theory in mathematical physics have influenced developments in both mathematics and theoretical physics.

Awards and Legacy:

• Uhlenbeck was awarded the Abel Prize in 2019, marking the first time a woman had received this honour. Her research continues to shape modern mathematics, and she is recognised as one of the most influential mathematicians of her generation.

13. Ada Yonath (1939– )

Ada Yonath is an Israeli crystallographer and biochemist who made groundbreaking discoveries in the field of ribosome research. Though primarily a biochemist, her work relies heavily on mathematical models and crystallography.

Famous works:

• Ribosome Structure - Yonath’s research revealed the structure of ribosomes, which play a crucial role in translating genetic information into proteins.
• Work in Crystallography - Yonath’s work in developing innovative methods of crystallography has made a significant impact in structural biology.

Awards and Legacy:

• Yonath was awarded the Nobel Prize in Chemistry in 2009 for her work on the structure and function of ribosomes. Her research continues to impact medicine and biochemistry, showcasing the important role of mathematics in solving complex biological problems.

14. Ingrid Daubechies (1954– )

Ingrid Daubechies is a Belgian mathematician known for her contributions to the field of wavelets, which have applications in image compression and signal processing. Her work has had a lasting impact on both mathematics and applied science.

Famous works:

• Wavelets in Signal Processing - Daubechies developed new wavelet transforms that are widely used in data compression, such as in JPEG 2000 for image files.
• Mathematical Models for Image Processing - Her research has contributed to advancements in medical imaging, data compression, and communication technologies.

Awards and Legacy:

• Daubechies was the first woman to serve as president of the International Mathematical Union and was awarded the L’Oréal-UNESCO Award for Women in Science in 2019. Her work has transformed applied mathematics and continues to influence fields ranging from computer science to medical diagnostics.

15. Joan Birman (1927– )

Joan Birman is an American mathematician whose work in topology, specifically braids and knot theory, has influenced both pure mathematics and applications in fields like DNA research and statistical mechanics.

Famous works:

• Birman-Murakami-Wenzl Algebra - Birman’s work in algebra has applications in both knot theory and quantum physics.
• Knot Theory - Her research into knot theory has impacted areas such as the study of DNA replication and quantum computing.

Awards and Legacy:

• Birman received the Chauvenet Prize and was inducted into the American Academy of Arts and Sciences. Her contributions to knot theory and topology have made her one of the leading figures in her field, and her work continues to influence modern mathematical research.

How did the personal experiences and backgrounds of these famous women mathematicians influence their contributions to the field?

Many of these mathematicians overcame personal and professional challenges to achieve recognition in a male-dominated field. For example, Ada Lovelace’s background in poetry and the sciences helped her foresee the future applications of computing, while Maryam Mirzakhani’s upbringing in post-revolutionary Iran inspired her to push the boundaries of mathematical discovery.

What challenges did these women mathematicians face during their careers, and how did they overcome them?

Many of these mathematicians faced significant obstacles due to their gender. For example, Emmy Noether struggled to gain recognition and formal employment despite her revolutionary contributions to algebra, while Sofia Kovalevskaya had to travel outside of Russia to receive formal education. Despite these challenges, they persevered and made lasting contributions to mathematics.

How did the contributions of these women mathematicians impact broader scientific and technological movements?

The work of these mathematicians has had a profound impact not just on mathematics but on a wide range of scientific and technological fields. From Grace Hopper’s role in developing computer programming languages to Ingrid Daubechies’ contributions to image processing, their innovations continue to shape modern technology and science.

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