Contributions To The Study Of Mathematics example essay topic

Abstract Women in the world of mathematics is a subject that people rarely hear about. The only time people do is if its a female math teacher. But what many do not know is that women have made extremely important contributions to the world of mathematics. Women have been documented to be involved in mathematics, since as early as the fifth century A.D. Women such as Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy Noether, Ruth Moufang and Sun-Yung Alice Chang. These women have lived through difficult times such as womens oppression, the French Revolution, World War I and II, which included Hitlers administration over womens schooling, and social prejudices.

This did not stop their yearning for math though. These women combined have earned many different awards, specifically ones usually given to men. They have conquered the biases people have had towards them and made what they do best count. Many of their theorems and equations are still used today, and some are even being perfected by others. It is important that the reader realizes that educating children about women in mathematics is important.

Many children think of mathematicians as men, and that is totally untrue. That thought could possibly contribute to the fact that women are less likely to enter the mathematics field compared to men. This is because they are not educated properly on the subject, and are not given the opportunity to excel. There are many more women in mathematics then mentioned above, but the ones named are very important to the field and children need to know that. By taking these 6 womens contributions and focusing on how they apply to the middle school curriculum would be very useful to any teacher. The children could each pick a female mathematician, and make a poste and do a presentation about their findings.

It could also be done as a group project. As long as the topic gets discussed and that the girls come out feeling like they could also get involved in mathematics. Womens Contributions to Mathematics In the world of mathematics, you rarely hear anything about women mathematicians. Although not much is said about women and math, there are many women mathematicians who have made significant contributions to the field.

From as early as 370 AD, women have been contributing to the study of equations, theorems, and even solving problems that have deemed themselves in the mathematical world as impossible. Because of the time period that these women lived, many were not recognized for their achievement; some were even banished or killed. Names such as Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy Noether, Ruth Moufang, and Julia Bowman Robinson may not be common to the everyday person. But to mathematicians around the world, especially women, they are a sign of achievement and determination in a field dominated by men. In order to make women recognized in the field of mathematics, educators need to spend time teaching their students that math is not just for males. Because of the contributions of the women named above, math exploration has been furthered and many questions have been answered, although some are still to this day unresolved.

Hypatia 370-415 AD Hypatia is the first, truly documented woman mathematician. Her works have given way to famous male mathematicians such as Newton, Descartes, and Leibniz. Raised in ancient Egypt during the time that Christianity started to take over many other religions, it was hard for Hypatia to study anything in an age where males dominated many fields of study. Hypatia was looked at, though, as a woman of strong character, and as a strong orator, astrologist, astronomist, and mathematician. Raised mostly by her father, Then, a known mathematician of the times, Hypatia gained a lot of knowledge at a young age. She studied under her fathers supervision, which gave her the wanting to know the unknown in mathematics.

Hyapthia made many contributions to the study of mathematics, her most famous being her work on conic sections. A conic section is when a person divides cones into different parts using planes. Because she edited a book written by Apollonius so well, her work survived all the way up until today. Her concepts later developed into what is today called, hyperbolas, parabolas, and ellipses. Hypatia died a very tragic death in 415 AD. Because she was a woman in the field of mathematics and science, many rumors were spread about her.

One of the Christian leaders named Cyril heard of these rumors and because he did not like the civil governor of Alexandria, where Hypatia lived, he made Hypatia a target. She was very respected and he knew that killing her would definitely hurt the city. On her way home one night, she was attacked by a mob and literally skinned with oyster shells. Some say she died for the love of mathematics (Adair, 1995). Maria Gaetana Agnesi 1718-1799 Maria Gaetana Agnesi was not really considered a mathematician in her time. But now that some people look back, she made a very significant contribution to the world of mathematics.

She practiced mathematics during the Renaissance in Italy. During this time, it was considered an honor to be an educated woman. So Maria was both looked up to and considered a prodigy by the time she was very young. This could be attributed to the fact that her father was an upstanding mathematician and professor in Milan, Italy. He often had lectures and seminars at his house for people to come and hear about math. She liked to listen to these lectures which may have sparked her interest in mathematics.

There are two accomplishments that Maria is accredited with. Her first is her book that she got published called Analytical Institutions, which was about integral calculus. Some say that it was originally written for her younger brothers, to aide them in math. Now that the book has been translated, many mathematicians are using her work and it is used as a textbook. Her second accomplishment is a curve called the Witch of Agnesi. Maria came up with the equation for this well known curve: y = a sqrt (a x-x x) /x.

The way to generate the curve is xy 2 = a 2 (a-x) (Golden & Hanzsek-Brill, no date) The reason why it is called the Witch of Agnesi is because the man who translated the name of the curve may have mistranslated the Latin word versi era. It can either mean to turn or the wife of the devil. This curve is very useful in the field of mathematics; even Fermat studied this curve. Fermat also made the famous problem called Fermats Last Theorem, which famous female mathematician Sophie Germain studied (Unlu, 1995). Sophie Germain April 1, 1776-June 27, 1831 Sophie Germain, was born right before the French Revolution. She was born into the middle class, and this meant that she had to hide her identity in order to practice math.

The middle class was not supportive of women studying math, therefor much of her work is done under her pseudonym M. Leblanc. Because of the Revolution, Sophie had to spend many days in her house, for fear of being killed in a revolt. She was intrigued by the story of Archimedes and how he got killed because he would not respond to a soldier while looking at a math problem. Some people think this is why Sophie choose to study mathematics.

Sophie Germain studied under famous mathematician of the time, Carl Friedrich Gauss. Gauss was really into number theory and Fermats Last Theorem. Fermats Last Theorem is closely related to the Pythagorean theorem. Instead of using x 2+y 2 = z 2, Pierre de Fermat used x, y, and z raised to powers of 3, 4, 5, etc. Many think that this problem was unsolvable, but Fermat said that he had proof it could work. The mystery is though, that Fermat never wrote down his solution.

It was up to future mathematicians to find the solution that Fermat claimed. Sophie was up to the challenge, and in a letter to Gauss, written in 1808 she came up with a calculation that said something about several solutions. Fermats theory says there are no positive integers such that for n 2. But Sophie proved in her theorem that if x, y, and z are to the fifth power than n has to be divisible by five. Sophie said that this would work only with what are now called Germain primes. Germain primes are primes such that when you take a prime, multiply it by two, and then add one, your answer will be prime.

Some Germain primes are 2, 3, 5, 11, 23 and 29 (Singh, no date). In 1825, she proved, that for the first part of Format Last theorem, these primes would work. There are many other mathematicians that have followed up on Sophie work on Fermats Last Theorem. Number theorist, Euler and Lagrange, proved that if p = 3 is prime, 2 p+1 is also prime if and only if 2 p+1 divides 2 p-1. In 2000, famous number theorist, Henri Lipchitz, found an easier way to determine a Germain prime. He says that if p = 5 is prime, q = 2 p+1 is also prime if and only if q divides 3 p-1.

It turns out though in 1994, Andrew Wiles, a researcher at Princeton, claimed to have proof of the theorem. His manuscripts have been reviewed and it is among the majority that he has proved it (Swift, 1997) Emmy Noether March 23, 1882-April 14, 1935 Still in the late 1800's, it was not proper or allowed for a woman to go to college. Emmy Noether became one of these women, when she was denied enrollment at the University of Erlangen. They did allow her, though, to sit in on two years of math classes and take the exam that would let her be a doctoral student in math. She passed the test and after going for five more years, she was given a diploma. After graduation, Emmy decided to take up teaching, but the university would not hire her because she was a woman.

So she decided to work along side her father, who at the time was a professor at the university. Emmy Noether's first piece of work was finished in 1915. It is work in theoretical physics, sometimes called the Noether's Theorem, which proves a relationship between symmetries in physics and conservation principles. This basic result in the general theory of relativity was praised by Einstein, where he commended Noether on her achievement. During the 1920's Noether did foundational work on abstract algebra, working in group theory, ring theory, group representations, and number theory. During the time that she was a teacher, Germany was involved in WWI and WWII.

Because of the war, and since Noether was a Jew, she was forced out of Germany and went to live in the United States (Emmy Noether, no date). While in the United States, Noether taught at an all girls college. Her students loved her and many followed her teachings. Some say that they way she taught was phenomenal. She was clear and used many different methods of teaching so that her students could understand math easier. She was praised by Einstein constantly on her theory of relativity.

Albert Einstein paid her a great tribute in 1935: "In the judgement of the most competent living mathematicians, (Emmy) Noether was the most significant creative mathematical genius thus far produced since the higher education of women began". Throughout her career she worked with many mathematicians such as Emanuel Lasker, Bartel van der Warden, Helmut Hasse and Richard Brauer. Twice Noether was invited to address the International Mathematical Congress (1928, 1932). In 1932 she received the Alfred Ackermann-Teu bner Memorial Prize for the Advancement of Mathematical Knowledge.

It is said that her greatest work was that of abstract algebra (Taylor, 1995). Ruth Moufang January 10, 1905-November 26, 1977 Like the Nazis refused Emmy Noether the right to teach, Ruth Moufang was also denied the right. Because of this, Ruth Moufang decided to enter the field of industrial mathematics, and work on the elasticity theory. She was the first German woman to have a doctorate in this field. Ruth Moufang published one famous paper on group theory. This paper was first written based on the writings of Hilbert.

Ruths most famous teachings were on number theory, knot theory, and the foundations of geometry. She also is famous for what we call today, Moufang planes and Moufang loops. Moufang loops are a class of loops which arise naturally in many other fields such as finite group theory and algebraic geometry (OConner & Robertson, 1996). Sun-Yung Alice Chang March 24, 1948-present Sun-Yung was born in Ci-an, China. During research, no information was found on the time period when she was born. What was found though is an abundance of information on her college life and what her contributions to mathematics were.

Sun Yung Chang received her doctorate in mathematics from University of California. She then went to teach college math at UCLA. Currently, she still teaches at UCLA, but since she started many things have happened to her. Her greatest accomplishment is when she received the Ruth Lyttle Satter prize for her contributions to mathematics over the last five years. She was awarded the prize for her contributions to partial differential equations and on Riemannian manifolds. The study of manifolds having a complete Reimannian Metric is called Reimannian geometry (Weisstein, 1996-2000).

This is a topic that Sun-Yung studied a lot. Sun-Yang says, in her speech at the American Mathematical Society, Following the early work of J Moser and influenced by the work of T Aubin and R Schoen on the Yama be problem, P. Yang and I have solved the partial differential equation of Gaussian / scalar curvatures on the sphere by studying the extremal functions for certain variation functionals. We have also applied this approach in conformal geometry to the iso spectral compactness problem on 3-manifolds when the metrics are restricted in any given conformal class. More recently we have been studying the extremal metrics for these functionals. We are working to derive further geometric consequences. This latter piece of work is a natural extension of the earlier work by Osgood-Phillips-Sar nak on the log-determinant functional on compact surfaces.

(OConner & Robertson, 1998, p. 2) Sung-Yung is already considered to be a great mathematician, even though she says there is still work to be done. Women in Mathematics connected to the Middle School Curriculum In Sun-Yung speech, given at the acceptance of her award in 1995 she states, Since the Satter Prize is an award for women mathematicians, one cannot help but to reflect on the status of women in our profession now. Compared to the situation when I was a student, it is clear that there are now many more active women research mathematicians. I can personally testify to the importance of having role models and the companionship of other women colleagues. However, I think we need even more women mathematicians to prove good theorems and to contribute to the profession. (OConner & Robertson, 1998, p. 2) This is exactly why this topic needs to be discussed in the middle grades.

Girls need to know that mathematics is not only for men. Young girls may be less apt to go into the field of mathematics based on the biases that have been going for years. Teachers need to tell about the importance of mathematical skills for both boys and girls, and also need to plan activities centered around women in mathematics. By talking to young girls in middle school about female mathematicians, educators could possibly ignite a flame, under possibly, another great female mathematician. Although many do not think of women as mathematicians, there are many women who have proved themselves in the mathematical world. Through their theorems and problem solving, these women have furthered the world of mathematics, for others to someday conquer.

Bibliography

Adair, G. (1995).
Hypatia. Agnes Scott College [Online]. Available: web [1 March 2000].
Emmy Noether (no date). [Online]. Available: web ml [5 March, 2000].
Golden & Hanzsek-Brill. (no date). Investigation of the Witch Curve. [Online]. OConner, J.J., & Robertson, E.F. (1996).
Ruth Moufang. [Online]. Available: web [24 February 2000].
OConner, J.J., & Robertson, E.F. (1998).
Sun-Yung Alice Chang. [Online]. Available: web [6 March 2000].
Singh, Simon. (no date). Maths Hidden Women. [Online]. Swift, Amanda. (revised in 1997).
Sophie Germain. Taylor, Mandie. (1995).
Emmy Noether. Available: web [2 February 2000].
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Maria Gaetana Agnesi. Weisstein, Eric. (1996-2000).
Riemannian Geometry. Wolfram Research Inc. [Online]. Available: web [7 March 2000].
Bibliography References Adair, G. (1995).
Hypatia. Ruth Moufang. [Online]. Singh, Simon. (no date). Sophie Germain. Taylor, Mandie. (1995).
Emmy Noether. Unlu, Elif. (1995).