Hanna Neumann (1914-1971)
Hanna Neumann, author of the important monograph Varieties of Groups (1967), was born in Berlin, Germany. She studied mathematics at Berlin, notably with Bieberbach, Schmidt, and Schur. She actively opposed Nazism, avoiding the “political knowledge” part of the doctoral examination by taking the Staatsexamen in 1936. Her fiancé Bernhard Neumann, who was Jewish, had fled to Britain, where she married him in 1938. Under Olga Taussky-Todd, she received a D.Phil. from Oxford. She taught at Hull for twelve years, doing notable work on Hopf groups. In 1960-61, she, Bernhard, and their son Peter solved the problem of the structure of the semigroup of varieties of groups. In 1964 she took up the newly created chair in Pure Mathematics at the Australian National University, where she built a most distinguished department. An eminent algebraist and innovator in mathematics education, she was also a beloved teacher and mentor.
Image credit: Dr. Peter Neumann
Ada Lovelace (1815-1852)
Poetry comes in many forms. Lord Byron, father of Ada Lovelace, was a romantic poet. Lovelace translated Luigi Menabrea's notes on Charles Babbage's Analytical Engine, a proposed mechanical calculating device with storage. In her notes accompanying the translation, Lovelace made a number of striking observations. She noted that the Analytical Engine was a device for manipulating not just numbers, but symbols. Lovelace showed how to use the machine for calculating Bernoulli numbers, writing, in essence, the first computer program. Her tutor, the logician Augustus de Morgan, described Lovelace as creative and determined "to get beyond the current bounds of knowledge." Lovelace's work lay forgotten for almost a century, but was republished in 1953. In 1980, the U.S. Department of Defense named Ada, a new computer language, after Lovelace.
Courtesy of the National Portrait Gallery, London.
Grace Chisholm Young (1868-1944)In 1895, Grace Chisholm became the first woman to receive a doctorate in any field from a German university through coursework and a dissertation. Her Ph.D., Magna Cum Laude from the University of Göttingen, was supervised by Felix Klein. Educated at home, then at Girton College, Cambridge, she received the "equivalent" of a first-class degree on the Cambridge 1892 Mathematical Tripos, Part I. After receiving her doctorate, she married William Henry Young, a tutor at Girton. Together they wrote over 200 mathematical articles and several books that established their reputations, particularly in the field of real analysis. Her most famous result, later called the Denjoy-Young-Saks Theorem, concerns the derivatives of a real function. She completed a medical degree except for the internship, was fluent in six languages and brought up six children. In 1915 she was awarded the Gamble Prize from Girton for her essay on “Infinite derivatives”.
Image credit: Courtesy of Sylvia Wiegand
Mina Rees (1902-1997)
Mathematicians often claim that abstraction provides deep insights that enable the solution of hard problems; Mina Rees lived it. She received her doctorate at the University of Chicago in 1931 under the supervision of L.E. Dickson. She then became a professor at Hunter College. An algebraist by training, Rees was called to Washington during World War II to serve on the Applied Mathematics Panel of the National Defense Research Committee. She was central to the panel's effort of taking hard military problems (including fire control and resource allocation) and abstracting out their mathematical essence, then finding the mathematical expertise to solve it. After the war Rees was awarded the President's Certificate of Merit (U.S.) and the King's Medal for Service in the Cause of Freedom (U.K.). Later Rees headed the mathematics division of the Office of Naval Research, directing government support of research and demonstrating great foresight. In 1969, she was the founding president of the CUNY Graduate School and University Center, and became the first woman president of the American Association for the Advancement of Science in 1971.
Image credit: Courtesy CUNY Graduate Center Archives
Maria Agnesi (1718-1799)
The eldest child of a wealthy family, Maria Agnesi was first educated at home, then read l’Hôpital and Reyneau, and also discussed mathematics with Riccati. She was the first woman to publish a work in pure mathematics. Her Analytical Institutions (1748) was the most complete book-length treatment of algebra, analytic geometry, and calculus in the eighteenth century. The book was translated from Italian into English, with a curve’s name “la versiera” mistranslated as “witch,” resulting in the curve being called “the witch of Agnesi.” According to ideas prominent in the Catholic Enlightenment in Italy, mathematics, unlike other subjects, was thought to provide true knowledge, and there was space for a few talented women. Pope Benedict XIV offered Agnesi the chair of mathematics at the University of Bologna, though she did not accept the appointment. In 1752 she turned from mathematics to nursing work, and, ultimately, died in poverty.
Image credit: Courtesy of the Library of Congress.
Gabrielle du Châtelet (1706-1749)
Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet was married in 1725 to the Marquis du Châtelet. Her aristocratic background and beauty made it possible for her to meet mathematicians and learn mathematics. At various times she studied with Maupertuis, A.-C. Clairaut, and Samuel König. She charmed Voltaire, and lived with him for a number of years. She entered the Paris Academy of Sciences prize competition of 1737 with a paper on the nature and propagation of fire (Euler won). She collaborated with Voltaire on his éléments de la philosophie de Newton (1738), and published Institutions de physique, in 1740. She is best known for her French translation, with commentary, of Newton’s Principia, published after her death in 1759. For 250 years this was the only French translation. Du Châtelet was one of the few French women of this period to seriously develop a talent for mathematics and physics.
Image courtesy of Wikipedia Commons.
Dame Mary Cartwright (1900-1998)
Mary Lucy Cartwright was the first woman mathematician elected to the Royal Society of London. While at Cambridge University, under the supervision of G.H. Hardy and E.C. Titschmarsh, her thesis on zeros of integral functions generated a series of papers and eventually led to her book on integral functions. Although she did important work with Dirichlet series, Abel summation, analytic functions regular on the unit circle, integral functions, and cluster sets, she is best known for her work with Littlewood on van der Pol’s equation and nonlinear oscillators. Cartwright served as Mistress of Girton College and as president of the British Mathematical Association and the London Mathematical Society. She was a recipient of the Sylvester Medal from the Royal Society and the De Morgan Medal from the London Mathematical Society. She authored nearly 100 articles and books. She was a very effective administrator at Cambridge University and ambassador for several mathematical and scientific organizations. In 1969, Queen Elizabeth II elevated her to Dame Mary Cartwright, the female equivalent of a knighthood.
Courtesy of the Mistress and Fellows, Girton College, Cambridge
Caroline Herschel (1750-1848)
Caroline Herschel was born in Hanover, Germany. Her brother, astronomer William Herschel, discovered the planet Uranus in 1781. When William moved to England to become an organist, Caroline joined him. He taught her music, but also astronomy and mathematics. She began a career as a singer, but William’s need and her skill in applied mathematics led her to assist him by making calculations based on his observations. She systematically searched for comets and discovered eight between 1786 and 1797. She also discovered three new nebulae, including the companion to the Andromeda nebula. Her revised and updated version of Flamsteed’s star catalogue was published by the Royal Society in 1798. Later, while assisting William’s son John F. W. Herschel, she catalogued 2500 nebulae for which she received the Royal Astronomical Society's gold medal in 1828. She was named an honorary member of the Royal Society in 1835.
Image credit: Courtesy of the Museum of the History of Science, University of Oxford.