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.

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.

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

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.

## Maria Gaetana Agnesi

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.

## Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet

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.

## Marie-Sophie Germain

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.

## Augusta Ada King, Countess of Lovelace

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.

## Sofia Vasilyevna Kovalevskaya

## Hertha Marks Ayrton

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.

## Mary Fairfax Somerville

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.

## Amalie Emmy Noether

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.

## 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.

## Euphemia Lofton Haynes

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.

## Marjorie Lee Browne

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.

## Julia Bowman Robinson

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.

## Alexandra Bellow

## Shafi Goldwasser

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.

## Maryam Mirzakhani

(May 3, 1977, Tehrān, Iran — July 14, 2017, Palo Alto, California, U.S.)

Iranian mathematician who became (2014) the first woman and the first Iranian to be awarded a Fields Medal. The citation for her award recognized “her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.”

While a teenager, Mirzakhani won gold medals in the 1994 and 1995 International Mathematical Olympiads for high-school students, attaining a perfect score in 1995. In 1999 she received a B.Sc. degree in mathematics from the Sharif University of Technology in Tehrān. Five years later she earned a Ph.D. from Harvard University for her dissertation Simple Geodesics on Hyperbolic Surfaces and Volume of the Moduli Space of Curves. Mirzakhani served (2004–08) as a Clay Mathematics Institute research fellow and an assistant professor of mathematics at Princeton University. In 2008 she became a professor at Stanford University.

Mirzakhani’s work focused on the study of hyperbolic surfaces by means of their moduli spaces. In hyperbolic space, in contrast to normal Euclidean space, Euclid’s fifth postulate (that one and only one line parallel to a given line can pass through a fixed point) does not hold. In non-Euclidean hyperbolic space, an infinite number of parallel lines can pass through such a fixed point. The sum of the angles of a triangle in hyperbolic space is less than 180°. In such a curved space, the shortest path between two points is known as a geodesic. For example, on a sphere the geodesic is a great circle. Mirzakhani’s research involved calculating the number of a certain type of geodesic, called simple closed geodesics, on hyperbolic surfaces.

Her technique involved considering the moduli spaces of the surfaces. In this case the modulus space is a collection of all Riemann spaces that have a certain characteristic. Mirzakhani found that a property of the modulus space corresponds to the number of simple closed geodesics of the hyperbolic surface.

Source: www.buzzle.com , Encyclopedia Britannica - Martin L. White