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Female Mathematicians and Their Contributions

Female Mathematicians and Their Contributions

Be it consciously or subconsciously, women have mostly been viewed as the lesser competent sex in various fields, especially when it comes to the field of mathematics. But there were some, in fact, there are some who have surpassed all forms of barriers and excelled extraordinarily in this field. This Buzzle article honorably mentions some great female mathematicians and their contributions to this field.
Shalu Bhatti
Did You Know?
Maria Gaetana Agnesi, a renowned mathematician of the 18th century, was a child prodigy who could speak 7 different languages by the age of eleven. Later, when she was 12, she was diagnosed with a mysterious illness that was linked to her excessive studying.
While the world is invariably dominated by men, men who have always been the ones to make rules in the society, one cannot neglect the contribution of women in building a more defined world. Especially when we speak of the earlier times, where a woman's role was confined to looking pretty, raising a family, and taking care of the household, where they were hardly a part of something that was substantial, or lawmaking, there were a few of them who managed to make a mark in the world of men, who through their knowledge and intellect, forced the affluent and renowned society-makers to listen and acknowledge their views and findings.

Beginning from the early centuries, women have struggled not only to prove themselves, but also to be accepted by the general society as someone who is equally smart and competent as men. Since this article is about the contribution of women in mathematics, the following section gives you some of the many renowned women, who have inspired and paved way for many female aspirants who strive to contribute in this field.

List of Some Great Female Mathematicians

* Kindly note that this list is prepared in no particular order. The names mentioned herein are a few of the many women who have received great laurels in mathematical studies.

Some of these females were child prodigies, some were born in families with great academic achievements, while some had to struggle to become the inspiration that they are today to the countless aspirants who have to face obstacles in making a mark in society. We salute them for their determination, willpower, and their undefeated attitude towards achieving their goals.

Hypatia of Alexandria  
(born c. AD 350 - 370; died 415)

Hypatia was one of the earliest known female mathematicians in the world, known not only for her excellence in mathematics and astronomy, but also for the brutal death she suffered from the hands of the early Christians due to her pagan beliefs and political involvement. She was the daughter of a renowned Greek mathematician Theon Alexandricus. Being born to an educator, Hypathia herself had all the qualities that an ideal teacher should have. She was a great orator and people from all across the globe came to gain from her teachings.

Contributions and Achievements
✦ She edited the book On the Conics of Apollonius where she contributed on the ideas introduced by Apollonius on conic sections. It was through this that the development of concepts such as hyperbolas, parabolas, and ellipses took place later.

✦ Some sources also attribute her to be the inventor of hydrometer; however, it was invented before Hypatia and was already known at the time. Apart from editing the existing works of renowned mathematicians of the time, most of her works are believed to have been in collaboration with her father's work.

Maria Gaetana Agnesi
(16 May, 1718 - 9 January, 1799)

She was considered to be the first important female mathematician after Hypathia. As mentioned already, this Italian mathematician and philosopher was a child prodigy, who was known as the "Seven-Tongued Orator" at the age of eleven. She could fluently speak Italian and French by the age of 5, and by her eleventh birthday, she mastered Greek, Hebrew, Spanish, German, and Latin. By the time she was 14, she was studying ballistics and geometry. Her love and dedication for mathematics gained her a position at the University of Bologna as a professor.

Contributions and Achievements
✦ She is known for her detailed explanation of differential and integral calculus in her book 'Instituzioni analitiche ad uso della gioventù italiana',  translated as Analytical Institutions for the Use of Italian Youth in English, which was published in the year 1748 in Milan.

✦ She also gained fame for the curve called the "Witch of Agnesi", named after her. She wrote the equation of this curve, 'versiera' as it was previously known, which was originally studied and constructed by Pierre de Fermat and Guido Grandi. Her work was translated into English, where the word versiera, which seemed very similar to the word 'avversiera' (meaning 'the wife of the devil') got translated as the word 'witch', hence the curve came to be known as the Witch of Agnesi.

Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet
(17 December, 1706 - 10 September, 1749)

Émilie du Châtelet was a French mathematician and physicist who although lived a fairly short life, but lived it with full zest. She came from a background where the only skill for a girl to master was courting affluent men to gain a position in elite society. However, being brilliant at academics, her father supported her studies, especially her love for mathematics. In the midst of her social, family, and love life, she managed to engross herself in an in-depth study of mathematics and physics, in the company of renowned Frenchmen such as Voltaire and Pierre Louis de Maupertuis.

Contributions and Achievements
✦ She is primarily known for her book, Institutions du Physique, which was published in the year 1740.

✦ Her translation of Newton's Principia Mathematica, along with her commentary, is till date considered to be the best French translation of this book. It was published ten years after her death.

Marie-Sophie Germain
(1 April, 1776 - 27 June, 1831)

A truly inspirational French woman who overcame all odds to achieve fame/recognition as a true mathematician! She was self-taught, introduced to this subject by the story of Archimedes' death that she read in her father's library. She was intrigued by the thought that how could geometry be so interesting that Archimedes ignored his death but not the subject? This sparked her curiosity, and even when her own family did everything to prevent her from studying, through her dedication and passion she compelled them to allow her to learn. Because she was a woman, she would submit her analysis papers under a man's name, M. LeBlanc, but when her teacher impressed by the paper insisted on meeting her, it was then that her true identity came forth. She continued to learn under the tutelage of renowned mathematicians of the time including Joseph-Louis Lagrange, Adrien-Marie Legendre, and Carl Friedrich Gauss.

Contributions and Achievements
✦ She became the first woman to win a prize from the Paris Academy of Sciences for her paper on elasticity theory, 'Recherches sur la théorie des surfaces élastiques', in 1816. She was also the first woman to attend the sessions of the Academy of Sciences', which was otherwise accessible by only male members and their wives.

✦ She is mainly acknowledged for her work in number theory, but also contributed in proving Fermat's Last Theorem, which played a crucial role in understanding and exploring this topic even after many centuries.

✦ Because she was self-taught, the University of Göttingen gave her an honorary degree for her work and potential, as recommended by her former tutor Gauss. However, it was received six years after her death from a long battle with breast cancer.

Augusta Ada King, Countess of Lovelace
(10 December, 1815 - 27 November, 1852)

Born as Augusta Ada Byron, the only legit daughter of Lord Byron, this English mathematician achieved quite a lot of fame and recognition for her analytical and computing abilities. In fact, she is widely known as the world's first computer programmer. Her mother discouraged her to learn literature as she feared that Ada too, may turn out to be reckless and emotionally unstable as her father, with whom she separated soon after Ada's birth. However, Ada showed great interest in becoming an analyst and a metaphysician, and was highly intelligent and farsighted for her time. In fact, when she heard of Charles Babbage's idea of inventing a calculating engine, she was the only one who believed that computers could do more than just calculating. Babbage called her The Enchantress of Numbers.

Contributions and Achievements
✦ It was she who suggested Babbage to write a plan where the 'Analytical Engine' could calculate Bernoulli numbers, which later on developed as the very first 'computer program'. This is the reason why the U.S. Department of Defense named a software language of theirs, as 'Ada' in the year 1979.

✦ She translated the memoir of Italian mathematician Luigi Menabrea on Babbage's machine, the Analytical Engine. She also included her own notes explaining the functioning of the Analytical Engine. Her notes were lengthier than the original translation!

Sofia Vasilyevna Kovalevskaya
(January 15, 1850 - February 10, 1891)

She was the first Russian woman to be recognized as a mathematician. Sofia's interest in mathematics began when she observed her room's wallpaper that had calculus notes of her father. These papers were put on the wall for there was a shortage of wallpaper. Her passion for studies was such that she even agreed to marry, for a young and unmarried woman in those times was not allowed to travel alone to outside place, the nearest university being in Switzerland. She had to leave her homeland, Russia, to fulfill her dreams of becoming a teacher, for women there were not allowed to become lecturers in universities. Yet, after going through many hardships, she managed to attain a Ph.D. from the University of Gottingen, became a lecturer at the University of Stockholm, and won the Prix Bordin from the French Academy of Sciences.

Contributions and Achievements
✦ She is best known for the Cauchy-Kovalevskaya Theorem, which was proven by French mathematician Augustin Cauchy in 1842. However, it was Sofia who simplified his method of proof and gave it a final result in the year 1875.

✦In her paper 'Sur Le Probleme De La Rotation D'Un Corps Solide Autour D'Un Point Fixe', Sofia discovered what came to be known as the Kovalevskaya Top. It is an example of integrable rigid body motion.

✦ In her lifetime, she published ten papers in mathematics and mathematical physics. Most of her work was groundbreaking and paved the way for many future discoveries.

Hertha Marks Ayrton
(April 28, 1854 - August 23, 1923)

Born as 'Phoebe Sarah Marks', she changed her name to Hertha during her teens, after an eponymous heroine of a Swinburne  poem that profoundly criticized organized religious beliefs, as Phoebe herself was an agnostic. This English mathematician paved her way from being the daughter of a seamstress to becoming the recipient of the Royal Society's prestigious Hughes Medal  for her discovery in physical sciences. After passing the Mathematical Tripos  in 1880, and receiving her B.Sc. degree from the University of London, she taught mathematics to children. In her career, she devised and solved mathematical problems, a majority of which were published in the Mathematical Questions and  Their Solutions  from the "Educational Times". She also was a renowned inventor and physicist.

Contributions and Achievements
✦ In 1884, she invented a line-divider, a draftsman's device that could divide a line equally in different parts, and also enlarge or reduce the figures. Including this, she registered 26 patents in her lifetime; five on mathematical dividers, 13 on arc lamps and electrodes, and the remaining on the propulsion of air.

✦ In 1899, she became the first woman to read her own paper, titled "The Hissing of the Electric Arc", before the Institution of Electrical Engineers (IEE). Soon, she was elected as the first female member of the IEE.

✦ She was also the first woman to read a paper before the Royal Society. In 1904, she read her paper titled "The Origin and Growth of Ripple Marks" which was later published in the Proceedings of the Royal Society.

✦ For her work and research on electric arc and sand ripples, she was bestowed the Hughes Medal by the Royal Society in 1906. She is one of the only two women that have been given this honor so far.

Mary Fairfax Somerville
(26 December, 1780 - 28 November, 1872)

Mary Somerville was born at a time when it was considered that women did not possess the intellect or capacity required to understand subjects such as math and science. This Scottish mathematician and science writer was hardly given a chance to receive education due to her gender, but she did manage to teach herself in the long run, with some unofficial help from her uncle and her brother's tutor. After the death of her first husband, who didn't consider much of her intellectual and academic interests, she got the freedom to pursue her studies, which continued after her second marriage to Dr. William Somerville, a supportive and understanding partner who admired her for her academic abilities. With the freedom to learn, she achieved great honors during her lifetime for her work in mathematics and science. Even till her old age (she died at the age of 92), she continued to "read books on the higher algebra for four or five hours in the morning, and even to solve problems", as stated in her autobiography.

Contributions and Achievements
✦ She gained fame after the successful translation of Laplace's Mécanique Céleste. Titled 'The Mechanism of the Heavens, this work is considered as her most famous mathematical writing ever.

✦ She was the first female to be nominated as the member of the Royal Astronomical Society, jointly along with Caroline Herschel.

✦ It was her writing involving the discussion of a hypothetical planet perturbing Uranus, in the 6th edition of On the Connexion of the Physical Sciences (1842) that influenced John Couch Adams and led him to discover Neptune.

✦ In 1848, she published, Physical Geography, when she was 69 years old. This was her most successful book till that time, and was widely used in schools and universities for half a century.

✦ She was the recipient of the 'Victoria Medal' of the Royal Geographical Society in the year 1869. In fact, William Whewell coined the term "scientist" when he was reviewing her work, 'On the Connexion of the Sciences', in 1834.

Amalie Emmy Noether
(23 March, 1882 - 14 April, 1935)

Described by renowned scholars including Albert Einstein, Jean Dieudonné, Pavel Alexandrov, and Norbert Wiener as the most important woman in mathematical history, this German-born mathematician gave some irreplaceable contributions in the field of math and physics, which, as experts say, were groundbreaking, revolutionary, and beyond comparison. She was the daughter of a noted mathematician himself, Max Noether. Although she wasn't quite passionate about the subject initially, it was only at the age of 18 that she decided to pursue her studies in math. In spite of being the daughter of a mathematician who was also a lecturer at the University of Erlangen, she wasn't allowed to attend full-time classes because she was a woman. However, she was allowed to audit the classes. She obtained her doctorate from the university but couldn't find a teaching job because of her gender. She did teach under the name of her father and other male professors, but was never paid for her work by the university until 7 years later when she proved her worth and gained a teaching position. She was a kind and compassionate teacher and most of the time, her students were called, The Noether Boys.

Contributions and Achievements
✦ She is known for her revolutionary work in theoretical physics and abstract algebra (with special focus to rings, groups, and fields). The theorem named after her, Noether's Theorem successfully explains the relationship between conservation laws and symmetry.

✦ The term Noetherian Ring was coined in her honor, arising from her publication, Idealtheorie in Ringbereichen, which was called "revolutionary" by renowned algebraist Irving Kaplansk. Her findings changed the approach of abstract algebra!

✦ Her contribution in mathematics were highly significant. She worked on theories of algebraic invariants and number fields, calculus of variations, noncommutative algebras, hypercomplex numbers, and algebraic topology. She also developed the theory of ideals in commutative rings.

✦ She won the Ackermann-Teubner Memorial Award, along with Emil Artin for their contributions to mathematics. She also taught many renowned future mathematicians including Grete Hermann, Ernst Witt, and Max Deuring.

Dame Mary Lucy Cartwright DBE FRS
(17 December, 1900 - 3 April, 1998)

She is one of the most successful British mathematician, who, through her mathematical findings and publishing, gained varied accolades of the highest degrees. She was the first woman to obtain a final degree in mathematics at Oxford. After graduating, she taught mathematics for four years to school children and then pursued her studies further in the subject at Oxford, under the guidance of famous mathematicians, G. H. Hardy and E. C. Titchmarsh. She became the Director of Studies in Mathematics at Girton College in 1936 after holding the post of a lecturer in this college. In her career, she published more than 100 papers on topics such as classical analysis, differential equations, and related topological problems.

Contributions and Achievements
✦ She is best known for Cartwright's theorem, named after her, which "gave an estimate for the maximum modulus of an analytic function which takes the same value no more than p times in the unit disc."

✦ In the year 1945, she simplified Charles Hermite's elementary proof of the irrationality of π. Her collaboration with famous mathematician J. E. Littlewood, in the 1940s, helped find the solution to the Van der Pol equation and eventually paved the way for the discovery of many of the phenomena that later came to be known as "chaos".

✦ She became the President of the London Mathematical Society in the year 1951, the first woman holding this title.

✦ She was the first female mathematician to be elected as a Fellow of the Royal Society (FRS), in the year 1947. She was also the first female to be awarded the Sylvester Medal of the Royal Society in 1964. In 1968, she received the De Morgan Medal of the London Mathematical Society, and in 1969, she was honored by the Queen and became 'Dame Mary Cartwright', Dame Commander of the Order of the British Empire.

Euphemia Lofton Haynes
(September 11, 1890 - July 25, 1980)

Born as Martha Euphemia Lofton, she was a brilliant student with a love for mathematics. This African-American mathematician pursued her studies even after her marriage, as a result of which she earned a Ph.D. from the Catholic University of America, her dissertation being on "The Determination of Sets of Independent Conditions Characterizing Certain Special Cases of Symmetric Correspondences". She gave 47 years of her life to the field of education, teaching mathematics and English in schools and colleges, and playing an evident role in the integration of the public schools in D.C.

Contributions and Achievements
✦ She was the first African-American woman to have earned a Ph.D. in mathematics.

✦ She was also the first female to chair the District of Columbia School Board.

✦ After her death, she left USD 700,000 to the Catholic University of America. These funds were used to establish and support the Euphemia Lofton Haynes Chair in the Department of Education and to support a loan fund for needy students in the School of Education.

Marjorie Lee Browne
(September 9, 1914 - October 19, 1979)

Yet another brilliant mathematician of the African-American descent, Marjorie Lee Browne dedicated her knowledge and her personal earnings to help other gifted and talented African-American students to thrive and learn. Similarly how her father, who was a railway postal clerk but was gifted in math, encouraged her to study the subject. After completing her high-school studies, she majored in mathematics and graduated cum laude, in the year 1935 from Howard University. She also earned her Ph.D. in the year 1949 from the University of Michigan; this was one of the very few universities that accepted African-American students in the United States at the time. After her Ph.D., she joined the North Carolina College (now North Carolina Central University (NCCU)), and contributed 30 years of her life teaching and researching in this institution. She also served as the head of the department from 1951 to 1970. Her work mainly focused on topology, linear and matrix algebra. Her work also showcased simple evidences of topological properties significance and relations between classical groups.

Contributions and Achievements
✦ After Euphemia Haynes, Browne and Evelyn Boyd Granville, were the next African-American women to have earned a Ph.D. in mathematics.

✦ Dr. Browne became the first to receive the W.W. Rankin Memorial Award for Excellence in Mathematics Education, in the year 1975. The award states the following, "She pioneered in the Mathematics Section of the North Carolina Teachers Association, helping to pave the way for integrated organizations."

✦ She gauged the crucial need of computer science early on. Which is why she wrote a USD 60,000 grant to IBM, in the year 1960, to bring a computer to NCCU. It was one of the very first computers in academic facilities, and most likely the first at a historically black school.

Julia Bowman Robinson
(December 8, 1919 - July 30, 1985)

A truly admirable and inspirational American mathematician, who irrespective of her health issues and insecurities, managed to achieve honors that no other American woman had achieved. She contracted scarlet fever and rheumatic fever during childhood, as a result of which, most of her childhood was spent in isolation. She graduated from San Diego High in 1936 with honors in mathematics and science courses. She also won the Bausch-Lomb Medal for all-around excellence in science. She received her B.A. degree in the year 1940, and her Ph.D. in 1948 from the University of California at Berkeley. Mathematics was not only a passion for her, but a treatment that helped her come out of depression when she was unable to conceive due to health issues. Her husband, renowned mathematician Raphael Mitchel Robinson, helped her regain her interest in mathematics to overcome her grief.

Contributions and Achievements
✦ She was the first woman mathematician to be elected in the United States National Academy of Sciences, in 1975.

✦ She is best known for her work on Hilbert's Tenth Problem that comes under Diophantine analysis, and Decidability. She also worked for the Office of Naval Research on a problem in hydrodynamics.

✦ She was also the first female officer in the American Mathematical Society, and after four years, she ended up becoming the first woman president of the the society. She was also the recipient of the MacArthur Foundation Prize Fellowship of USD 60,000 for five years, in the year 1983.

Alexandra Bellow
(August 30, 1935 - )

Alexandra Bellow is a famous mathematician from Romania, who was working as a full-time professor at the Northwestern University until her retirement in the year 1998. Her career was highly illustrious and she is well-known for her mathematical work, mainly in ergodic theory. She graduated in the year 1957 from the University of Bucharest, and received her Ph.D. from Yale in 1959. She is the wife of the famous mathematician Alberto Calderón who is no longer with us. Her ex-husband was the famous Nobel Prize recipient Saul Bellow who is known for his literary works.

Contributions and Achievements
✦ Throughout her career, she has contributed immensely to the fields of ergodic theory, probability, and analysis.

✦ She also contributed to the editorial boards of The Transactions of the American Mathematical Society, the Annals of Probability, and Advances in Mathematics.

✦ She published various papers throughout her career and is the recipient of awards such as Fairchild Distinguished Scholar Award and Humboldt Prize.

Shafi Goldwasser
(1958 - )

Shafrira Goldwasser is an Israeli-American computer scientist who is currently a professor at the Massachusetts Institute of Technology, teaching electrical engineering and computer science. She is also the Professor of Mathematical Sciences at the Weizmann Institute of Science, Israel. She has worked magnificently in areas including complexity theory, computation number theory, cryptography, and her work with zero-knowledge proofs is highly acknowledged. Her husband, computer scientist Nir Shavit, is also a Gödel Prize winner like herself.

Contributions and Achievements
✦ She is the first recipient of the RSA Professorship, which she received in the year 1997.

✦ She has won the Gödel Prize twice in theoretical computer science. First in 1993 for The knowledge complexity of interactive proof systems, and in 2001 for Interactive Proofs and the Hardness of Approximating Cliques.

✦ She has won many other awards, a few among them are: ACM Grace Murray Hopper Award, RSA Award in Mathematics for outstanding mathematical contributions to cryptography, Benjamin Franklin Medal in Computer and Cognitive Science, and the Turing Award for her work in the field of cryptography, along with Silvio Micali.

Due to time and space constraints, we had to omit many illustrious names. Yet, we believe that each and every woman mathematician, irrespective of the fact of being included in this list or not, is an inspiration to one and all, especially those women and girls who have been told that mathematics and science are not suitable fields for women to thrive. The aforementioned list is a fragment of proof that makes it evident that women too are as capable when it comes to providing a substantial contribution in complex subjects such as mathematics and computer sciences. Gender never stops you from achieving, it's only your attitude that decides your winning or losing. These women never gave up, never doubted their abilities even when their own family did, and as a result, they are remembered and honored by one and all for their achievements.