Vol.1 No.1 JulyDecember 2013ISSN: 23216530 

CONTRIBUTIONS OF WOMEN IN MATHEMATICSDori Lal Choudhary AbstractBehind every successful man there is a woman. But what about a successful woman that's also a mathematician? The answer is not so simple. The answer is inevitable determination and will power. It is a well known fact that a woman has a heart larger than a man, the courage more than a man to face the extreme conditions of their lives & support families besides having an outlook to let their determination of doing excellent in their chosen field, survive within themselves women have been great mathematicians probing their brains more efficient than millions of men in this world ever since the numerical values are known & mathematics came into existence, women had been wonderful mathematicians for they kept an account of distribution of food hunters & gatherers collected. How much for each? for how many days? Schedule for next hunting expedition, when the man changed from hunter to farmer, it was the woman staying behind making calculations of the time taken by a seed to become a seedling, a seedling transforming itself into a fully grown crop. The amount of time required for harvesting and the space needed for storage. For works such as managing a house, providing the essential amenities in a given budget involves mathematics. From the age of hunters & gatherers till today, when women have proven themselves to be successful astronauts, they have a wonderful sense of mathematics in them. No doubt they all still need a mention of their names & works because they are not as well known as Newton or Pythagoras or Lorentz. But as a matter of fact large segments of the world have their mental notion that mathematics is a field where women cannot contribute anything but even then they done some remarkable works. But from the history of mathematics, we find mention of women studying mathematics, developing new terms, concepts or ideas whether it was Pythagoras school of studies or the earlier works of Einstein. Let us now indulge ourselves to a world of same great female mathematicians who have changed the scenario of the field of mathematics by their amazing findings & contributions. IntroductionMathematics, in general, is not a wellknown group among scholars. However, women mathematicians are even less known. It is possible to read most histories of mathematics and find little or no mention of women mathematicians, even of the few these were. This article is therefore intended to trace the impact; some of these women have had, on the development of mathematics. However, firstly, why were these so few women mathematicians? It appears that the reason for this was that at (almost) every stage of their academic as well as nonacademic life, women faced many barriers, which men of far less ability did not have to face. For women, talent alone was not a sufficient criterion for success in mathematics. The women also needed to have driven and determination, not only to ignore role stereotypes but also to overcome the restrictions imparted on their education. It was not until these barriers were crossed that women were able to develop and enjoy their talents. The women that will be discussed in this article, all came from either academic or wealthy upper class families. Some of the women were from the French and English aristocracy and so had the benefits of outstanding mathematicians as teachers. This was important as education for girls was until very recently, nonexistent or very much restricted, as there was a great prejudice against women studying subjects like mathematics and science. These areas were considered to have male's sovereignty. However, even when women did receive the equivalence of a secondary education, Colleges were closed to them as it was believed that women were made for child rearing and that "brain work" may conflict with this function. The other discussed in this article are daughters of mathematicians. As they grew up they not only had access to mathematical texts, which was a crucial factor because this was a time when public libraries did not exist, but their talents were also recognized, developed and encouraged by their dedicated parents. However, "even with supportive parents and teachers, the traditional roles of wife, mother and home makers made study at advanced levels difficult." Husbands could also cause problems if they were opposed to their wife studying, and even when sufficient education was obtained by women to move to front of their professions, gaining professional employment was very difficult. But despite all the obstacles women have had to face in the past, women have still made a considerably large contribution to the development of mathematics. Perl believes that a closer look at the history of mathematics might also show that far more women that we realize did make significant contributions. For instance, we know that different historians notice, select and record different events and that for a long time it was considered improper for women to sign their own work. Therefore, he believes that when more historical research is done in their new area surprise may emerge. Women and MathematicsAccording to researchers, in age nine and thirteen, girls score slightly higher than boys in mathematics proficiency tests that assess visualization skills, but by the age of seventeen, girls do lag behind boys. However, this different is only about 1 per cent. The National Assessment of Educational Progress (NAEP)  1997 study revealed that female high school seniors were more likely those male seniors to say that they didn't take additional mathematics because of poor performance in the subject matter, although no significant differences existed between their performance and that of their male peers. Since fewer girls take advanced mathematics course, the result that males in general outscore female by nearly fifty points on the SAT in not surprising. Support for Women in MathematicsNot all men of the past believed that women had to be prevented from studying Mathematics, For example, H.J Mozons, actually a catholic priest named J.A Zahm, urged women to join the scientific enterprise and there by unleash half the energies of humanity. The genius of Zahm, lay in including science and mathematics in the mainstream of college curriculum. In his remarkable work women in science, he writes, "Women's long struggle for complete intellectual freedom is almost ended, and certain victory is already in sight. (1991, p. xv)."At the time, the intellectual ability of women was wide maligned, especially when it comes to mathematics. Leibniz, the coinventor of calculus, supported women in a de facto way. He argued that because women had an abundance if leisure time, they could better cultivate mathematics that men since had to worry about so many other worldly things. Other people believed that women had an edge in philosophy they were by nature curious and more dietary those men. In past generations, most women who made it through the barriers to certain in Mathematics were encouraged by their fathers  who were themselves, in the profession. Women's Continued ExclusionThroughout the twentieth century, women have had to swim against the tide to find their place in sea of science and mathematical scholars. Even in the 1950's women were not permitted into the physics building at Harvard or Princeton universities. Although overt discrimination was no longer prevalent, covert discrimination had not disappeared. Gender discrimination does not begin at the level of higher education. The Nature and Gender of MathematicsIronically, although the doors of mathematics were long closed to women, the discipline of mathematics is considered by many to be the queen of science. In this view, she is somewhat superior unto herself and does not need others to validate her existence. Here she exists more as an art form than as technological enterprise. However, Mathematics has also been perceived as the servant of science, that is, as the quantitative handyman who supplies the tools and the framework for other discipline. Encouraging Young Women to Enter MathematicsSuch programmes that target women as the Mentoring Programmes for women in Mathematics at the institute of Advanced Studies (IAS) and women in the science and Engineering (WISE) Institute at Pennsylvania state university, as well as programmes geared to precollege women are making difference by furnishing young women with role models and offering support for women who find themselves in a predominantly male profession. Early success in mathematics is important, both a firm foundation in basic principles is necessary before more complex material can be mastered and because early success can keep young people interested in these fields. The women of NASA interactive project is another example of a programme designed to showcase outstanding women in Mathematics and demonstrate how these women balance personal and professional responsibilities. The main components of the project are profiles of these women and the weekly web chats for women in the sciences. Participants can communicate with a featured mentor during the chats. The profiles and archived chats are rich sources of information about NASAwomen and their work. Now, that legal issue is being resolved, the culture of Mathematics must also change. The attitude those women are less capable of mathematical thinking than men needs to be visible, to openly display their passion for their chosen profession. They need to carry their understanding of mathematics into their communities and society at large. They should also be a role models and sources of encouragement for younger girls and women. As Wertheim has said, "the time has come for a mathematically based science envisioned and practical equally by both sexes." The Evolving Role of Women in MathematicsManilyn K. Simon lives Wendell Holmes Proclaimed that history lands a perspective to the way in which we view ourselves and our future. Through most of the history of mathematics, women have been persona non grata. According to Wertheim (1995) the battles that women have faced to break into mathematics parallel the battles that they have faced to back into clergy. Even today, the notion that mathematics is masculine pursuit persists, and many can readily cite with examples of people whom they know to illustrate this point. From the age of hunters & gatherers till today, when women have proven themselves to be successful astronauts, they have a wonderful sense of mathematics in them. No doubt they all still need a mention of their names & works because they are not as well known as Newton or Pythagoras or Lorentz. But as a matter of fact a large segment of the world has their mental notion that mathematics is a field where women cannot contribute anything but even then they done some remarkable works. But from the history of mathematics, we find mention of women studying mathematics, developing new terms, concepts or ideas whether it was Pythagoras school of studies or the earlier works of Einstein. Let us now indulge ourselves to a world of great female mathematicians who have changed the scenario of the field of mathematics by their amazing findings & contributions. Remarkable Female MathematiciansThe majority of mathematicians are male, although more women have entered mathematics since World War II. Women are still a small minority of notables in mathematics and neighboring branches of science such as physics. Here are some of those remarkable mathematicians: Hypatia, the daughter of the wellknown mathematician and astronomer Theon, became the last early Greek mathematician. She was also an inventor. She lived in Alexandria in Egypt from 370 to 415 and lectured at the University of Alexendria on geometry, astronomy, simple mechanics, Philosophy and algebra, attracting student from all over the world. In mathematics, her main interest was Algebra where she built on the work of another Alexandrian mathematician Diaphantus a founder of modern algebra. She also wrote about conic sections. Emy Noether's main contribution to mathematics was the formulation of development of the concept of primary ideas. She also investigated the structure of noncommutative algebra. Noether was born in the south German university known of Erlangen on March 23, 1882. At her enrolment at the university, she as one of the only two women among 1000 students. A doctorate was awarded to her in 1907. From 1916 to 1933, she worked at the University of Gottingen as a teacher of algebra. Her main contribution to mathematics was the building up of investigation of the structure of noncommutative algebra in 1933; Noether left Germany for the United States where she became a University Lecturer. Sonya Kovalevskaya was a Russian lady. She attended lectures at the University of Heidelberg in Germany and studied privately with German Mathematicians weirstrass in Berlin. Four years of work resulted in three outstanding research papers, including one of partial differential equations. They earned her a doctorate from the University of Gottingen. In 1883, she became the first women lecturer at the newly established University of Stockholm. Her greatest achievement was winning the Prix Bordin, awarded by the French Academy of science for her paper'on the rotation of a solid body about a fixed point." Kovalevskaya worked on complex analysis and generalized the work done by Euler, Poisson and Lagrange, using hyperelliptic integrals to solve differential equations of motion. She also wrote plays, poems, novels and an autobiography. One of a family of 20 children, Maria Gaetana Agnesi was born on May 16, 1718 in the Italian town of Bologna where the father was Professor of Mathematics. A highly gifted child Agnesi became fluent in several language and while still in her teens was able to take part in abstract mathematical and philosophical discussions. Published in 1748, Agnesi's two volumes work "Analytical Institutional on algebra and differential and integral calculus brought together material from many source in a variety of languages. It also includes methods and generalization of her own. A model of clarity, it became a mathematics textbook in several languages. The2 curve called the witch of Agnesi is named after her. It has the equation x2y = a (ay). Although she did not discover this curve, she worked with it in the analytical geometry section of her book. She devoted the second half of her long for the sick and the poor.She died in Bologna on January 9 1799. Mary Fairfax Sommer ville Mary Fairfax Sommer ville was born in Scotland on 26th December, 1780 and became a popular influential writer on science and mathematics when interest in the subject among the general public was high. Her first book "Mechanism of the Heaven's" a translation and popularized account of leplace;s celestial Mechanics became a widely used textbook for students of higher mathematics and astronomy. She also wrote monographs on mathematical subjects. Recognition of her work came in the form of a pension from the king of England and she was one of the first women elected to membership of the RoyalAstronomical Society. Vasilyevna Kovalevskaya was the first major Russian female mathematician, responsible for important original contributions to analysis, differential equations and mechanics, and the first woman appointed to a full professorship in Northern Europe. Sonia Kovalevsky High School Mathematics Day is a grantmaking program of the Association for Women in Mathematics, funding workshops across the United States which encourages girls to explore mathematics. The lunar crater Kovalevskaya is named in her honour. Agnes Sime Baxter (Hill) was a Canadianborn mathematician. She studied at Dalhousie University, receiving her BA in 1891, and her MA in 1892 and received her Ph.D. from Cornell University in 1895; her dissertation was "On Abelian integrals, a resume of Neumann's 'Abelsche Integrele' with comments and applications." She received multiple awards at graduation, including the Sir William Young Medal for highest standing in mathematics and mathematical physics. On the completion of her thesis, "On Abelian integrals, a resume of Neumann's 'Abelsche Integrele' with comments and applications," she became the second Canadian woman and the fourth woman on the North American continent to receive a Ph. D. in mathematics. Mileva Maric was one of the first women to study mathematics and physics in Europe. The question whether (and if so, to what extent) Mariæ contributed to Einstein's early work, and to the Annus Mirabilis Papers in particular, has been the subject of some debate. Dmae Mary Lucy Cartwright was a leading 20thcentury British mathematician. Her theorem, now known as Cartwright's theorem, gives an estimate for the maximum modulus of an analytic function that takes the same value no more than p times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by LarsAhlfors for conformal mappings. She anticipated Ivan Niven's elementary proof of the irrationality of ð. Her version of the proof was published in an appendix to Sir Harold Jeffreys' book Scientific Inference. Shakuntla Devi is a renowned and much venerated Indian Mathematician who isconsideredthas a genius and is popularly known as the Human Computer. She was born on 4 November, 1939 in Bengaluru in a wellknown Brahmin Priest family. She did card tricks with her father when she was only three. By the age of five she became an expert in Complex mental arithmetic and was recognized as a Child prodigy. Shakuntla extracted the 23rd root of a 201 digit number mentally, 12 seconds faster than the Univac 1108. It was her passionate interest in exploring and increasing the learning capacity of the human mind that led her to build up the concept of mind dynamics. In year 1997, Shakuntala Devi mentally solved the 23rd root of 201 digit number without any help from mechanical aid. In 1980, 18th June she solved the multiplication of 13 digit number 7686369774870 and2465099745779 picked up by the computer in science department of imperial College, London. She also solved that question in a flash and took 28 seconds to solve the entire problem, and her answer was 18947668177995426773730. This amazing incident helped her get a place in Guinness Book of World Record. Bhama Srinivasan (1935), born in Madras. She is a mathematician known for her work in the representation theory of finite groups. Her contributions were honored with the 1990 Noether Lecture. She had professorship of mathematics at the University of Illinois at Chicago, Ecole Normale Superieure in Paris, University of Essen in the Federal Republic of Germany, Sydney University in Australia, and the Science University of Tokyo in Japan. She served as president of the Association for women in Mathematics from 1981 till 1983. She earned her Ph.D. in 1960 with her dissertation Problem on Modular Representation of finite groups. She worked on the invasion of Geometry into finite group theory. She served as the editor of the Proceedings of the AMS(198387), Communications in Algebra(197884), and Mathematical Surveys and Monographs (199193). Lilavati was a veteran Indian Mathematician. Many of the problems are addressed to Lilavati herself who must have been very bright young women, for example "oh! lilavati, intelligent girl, if you understand addition and subtraction, tell me the sum of the amounts 2,5,32,,193,18,10, and 100, as well as (the remainder of ) those when subtracted from 1000," and fawn  eyed lilavati, tell me, how much is the number [resulting from] 135 multiplied by 12, if you understand multiplication by separate part and by separate digits. And tell me, beautiful one, how much is that Product divided by the same multiplication?" ConclusionNow, after checking the above great women talents all around the world in the field of mathematics, it is now clear that instead of having sex discrimination, social pressure, drawbacks of our customs and rituals, overburdened family responsibilities and household activities women are not behind in any field neither in past nor in present and they are competing males in every field. At, last we can say that there is always a woman who bears almost all responsibility for meeting basic needs of the family, yet are systematically denied the resources, information and freedom of action they need to fulfill this responsibility. The vast majority of the world's poor are women. Twothirds of the world's illiterates are female. Of the millions of school age children not in school, the majority are girls. Studies show that when women are supported and empowered, all of society benefits. Their families are healthier, more children go to school, agricultural productivity improves and incomes increase. In short, communities become more resilient. Refereces
