Emmy Noether Essay
When thinking of mathematicians, usually people would envision a male rather than a female. However, this is false. Though many males have provided a vast amount of contributions to the mathematic field, numerous women have also played an immense role as well. Emmy Noether is one woman in the mathematic field who has contributed and transformed mathematics. Bettye Anne Case and Anne M. Leggett state, “Noether is indisputably among the greatest mathematicians of the twentieth century” (3). This is one of the reasons that interested me to learn more about this mathematical genius. I was also quite intrigued that Albert Einstein believed Emmy Noether to be the most significant female mathematician of all time. Emmy Noether was born on March 23, 1882 in the city of Erlangen, Germany into a Jewish family. Her full name is Amalie Emmy Noether however she preferred to be called by her middle name, Emmy. Max Noether and Ida Amalia Kaufman were Emmys parents. Emmys mother Ida was raised on an estate in Cologne, Germany in 1852. Ida was born into a wealthy family of wholesale merchants that were able to fund Ida and her ten brothers and sisters. Emmys father, Max Noether, was born in Mannheim,
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Germany in 1844. A well-off family of iron importers raised her father. At the age of fourteen, Max suffered from polio disease. Her father endured a long recovery however he did salvage most of his movement. Unfortunately, Max did not gain full control on one of his legs (Cooney, Miriam P., p. 125-126).
Ida and Max eventually married and had four children. Emmy was the oldest out of her three brothers, Fritz, Alfred, and Gustav. Two of her brothers unfortunately died at a young age leaving Emmy and her younger brother Fritz. Emmy Noethers family consisted of numerous mathematicians. Max, Emmys father, attended the University of Erlangen in 1868 where he received a Ph.D. in mathematics. Her father became known as an important algebraic geometrist. He eventually moved to Erlangen and by 1888 and became a professor at the University of Erlangen. Emmys younger brother, Fritz, became an applied mathematician (Cooney, Miriam P., p. 126).
From 1889-1897, Emmy attended the Städtischen Höheren Töchterschule in Erlangen (Cooney, Miriam P., p. 126). This was a school for girls. As a child, Emmy did not show any astonishing ability in mathematics as some would think. Instead she spent her days in school studying languages such as French and English. At the age of fourteen, girls were to learn household management, childcare, and religious instruction. While in school she also learned how to play an instrument, the piano. As years passed, Emmy wanted to become a certified teacher of French and English. For three years, Emmy attended a teachers training program (McGrayne, Sharon Bertsch, p. 68). In 1900, Emmy took the five-day Bavarian State examinations. She passed the strenuous examinations and was officially qualified to teach both French and English in schools for girls. However Emmy instead wanted to continue with her education and went to the University of Erlangen to study mathematics (Smith, Martha K). Emmy wanted to attend the university where her father went to school and taught, to follow in his footsteps.
Women were not allowed to gain credit or degrees from universities so it was an exceptionally difficult time for females. This was a time when women did not have the same rights that male students had. However, women were able to get permission from professors to sit in on their lectures. Many professors regrettably were not shy to refuse to admit women into their lectures (McGrayne, Sharon Bertsch, p. 68). In 1898, two years before Noether audited classes at the University of Erlangen, the Academic Senate declared that the admission of women of the university would “overthrow all academic order” (Cooney, Miriam P., p. 126). Noether was fortunate since she was able to ask friends and family who worked at the university to give her permission to sit in on lectures and they all agreed. During 1900-1902, only two students out of 986 students were women. Emmy sat in class lectures for two years. The lectures Emmy sat in on consisted of more foreign languages and her first mathematics course. This math class is where everything changed. On July 14, 1903 Emmy took and passed the entrance examination to the Bavarian universities.
At the age of twenty-one, Emmy entered into the University of Gottingen as an auditor for graduate school. Felix Klein administered the University of Gottingen. Felix Klein was a mathematician and a supporter of higher education for women. He was also a close friend of Emmys father, Max Noether, which assisted Emmy to audit classes at this university. Instead of learning languages as she had done for most of her schooling career, she brought it upon her self to only study mathematics. She attended this university for only one semester and then returned to the University of Erlangen in 1904 (McGrayne, Sharon Bertsch, p. 69). Women were now allowed to enroll into the University of Erlangen. Females were able to go to lectures, take examinations, and most importantly they were able to get the same education as men were. At the University of Erlangen, Emmy mainly studied with her father and his friend, Paul Gordan. Gordan was a renowned mathematician who advised Emmy when she wrote her thesis (Cooney, Miriam P., p. 127). In 1908, Emmy earned her Ph.D (Goldberg, Dave, p. 107).
As fortunate as Emmy Noether was to become a mathematician, she was still living in a period that was hard for women to be thought of as equal. Due to her being a female, Emmy was unable to attain a regular or paid job. The University of Erlangen would not hire Emmy since it was against their policy to have professors who were women. From 1908 until 1915, Emmy worked without pay or title at the Mathematical Institute in her home, Erlangen. Emmy would assist her father and also carry out her research (Cooney, Miriam P., p. 127). Emmy soon began to be recognized. In 1908, Noether was acknowledged to join the Italian organization, Circolo Mathematico of Palermo. The following year, 1909, Noether was recognized to join the German Mathematical Union. She began to do public lectures talking about mathematics (Smith, Martha K).
Noether began to apply David Hilberts approach to algebra. David Hilbert was a mathematician who used highly abstract methods at Gottingen University. Hilbert and Klein recognized Emmy Noethers ability and they asked her to join their team. Noether moved to Gottingen in 1916. David Hilbert and Felix Klein were working alongside Albert Einstein. They were working together to develop a mathematical formulation of his general theory of relativity (McGrayne, Sharon Bertsch, p. 70). While at Gottingen University, Noether derived what is known as Noether’s (first) Theorem in 1915. It was then published it in 1918. Noether’s Theorem states, “Every symmetry corresponds to conserved quantity.” It discusses how momentum is conserved; it also explains and describes the conservation of spin, and on (Goldberg, Dave). Hilbert wanted Emmy to have a position at Gottingen University where she would be paid. Hilbert unfortunately was unable to convince faculty to pay Emmy. Instead he was able to allow Emmy to lecture however her lectures needed to be under his name (Cooney, Miriam P., p. 128).
Three years later, in 1919, Emmy finally began to receive a small salary. However she was the lowest paid faculty member at the university of Gottingen’s. Nevertheless, this did not discourage Emmy to continue doing what she loved. She could officially teach algebra, supervise dissertations, give examinations, and finally was allowed to lecture under her own name (Cooney, Miriam P., p. 128). In 1921, her father passed away. After her father’s death, Emmy turned algebra in a different direction. Emmy was “the leading founder of abstract algebra- now a major area in mathematics- and also worked in group theory, ring theory, group representatives, and number theory.” (McGrayne, Sharon Bertsch, p. 75). During 1921, Noether published the “Theory of Ideals in Rings”. This was one of her most important papers because it aided in the development of modern algebra. In the “Theory of Ideals in Rings”, Noether deals with Ideal theory and compares and contrasts concepts in abstract schemes (McGrayne, Sharon Bertsch, p. 75). In the years Noether spent at the University of Gottingen, she gathered followers who were known as “Noether boys”. These were no ordinary students. They were outstanding mathematicians. Emmy was always available for her students and shared her ideas and knowledge (Cooney, Miriam P., p. 128). In 1928-1929, Noether went to Moscow University to visit a professor.
During the years of 1924-1925, Noether taught a course on abstract algebra. She also led a seminar on algebraic geometry at the university. Around the 1930s Herman Weyl, a German mathematician, tried to get Emmy a better position at the University of Gottingen. This was because he was ashamed to have a higher position then Emmy knowing that she was the one who deserved a higher position (Cooney, Miriam P., p. 129). Weyl said, “In my Gottingen years, she was without doubt the strongest center of mathematical activity there, considering both the fertility of her scientific research program and her influence upon a large circle of pupils.” (McGrayne, Sharon Bertsch, p. 81). Unfortunately, he failed at his
attempt.
In 1932, Emmy received the Alfred Ackerman Teubner Memorial Prize. They recognized her for her advancement of the mathematical sciences. She received one hundred twenty dollars. Also in this same year, Emmy was invited to lecture at a general session of the International Mathematical Congress in Zurich. A year later, Hitler became chancellor of Germany on January 30 1933. The lives of Jewish individuals were changed radically. On April 7 1933 Emmy, along with other professors, received a notice that her right to teach has been withdrawn. This however did not stop or discourage Emmy from mathematics. Instead of teaching Emmy Noether would hold informal meetings to discuss mathematics. After Noether lost her right to teach, she along with many German-Jewish scientists and mathematicians had to leave the country of Germany. Many mathematicians and scientists found a new home in the United States of America. In the years 1933-1934 the Bryn Mawr College located in Pennsylvania, where Emmy was serving as a visiting professor, appointed Emmy a regular faculty position. Bryn Mawr College was an all girl college (Cooney, Miriam P., p. 129-131). A year later in April 1935, Emmy learned that she had a tumor. Surgery was needed to remove this tumor that impeded her health. Doctors however believed she was a risk because of her high blood pressure. On the fourth day of her recovery, with her temperature at 109 degrees, she slipped into unconsciousness. Emmy Noether passed away on April 14 1935. She was only 53 years old. While she was alive Emmy was not recognized for her work. After her death however, there were many recognitions of her brilliancy. On the fiftieth anniversary of Emmy receiving her doctoral degree, many of her own students gathered at the university of Erlangen to discuss the impact that she had on mathematics. Erlangen named a street after her in the year 1960. The American Mathematical Society celebrated Emmy’s 100th birthday with a conference at Bryn Mawr (Cooney, Miriam P., p. 131). Even though Emmy’s mathematical gift was not celebrated, as it should have been during her life, her impact and teachings will last forever.
Germany in 1844. A well-off family of iron importers raised her father. At the age of fourteen, Max suffered from polio disease. Her father endured a long recovery however he did salvage most of his movement. Unfortunately, Max did not gain full control on one of his legs (Cooney, Miriam P., p. 125-126).
Ida and Max eventually married and had four children. Emmy was the oldest out of her three brothers, Fritz, Alfred, and Gustav. Two of her brothers unfortunately died at a young age leaving Emmy and her younger brother Fritz. Emmy Noethers family consisted of numerous mathematicians. Max, Emmys father, attended the University of Erlangen in 1868 where he received a Ph.D. in mathematics. Her father became known as an important algebraic geometrist. He eventually moved to Erlangen and by 1888 and became a professor at the University of Erlangen. Emmys younger brother, Fritz, became an applied mathematician (Cooney, Miriam P., p. 126).
From 1889-1897, Emmy attended the Städtischen Höheren Töchterschule in Erlangen (Cooney, Miriam P., p. 126). This was a school for girls. As a child, Emmy did not show any astonishing ability in mathematics as some would think. Instead she spent her days in school studying languages such as French and English. At the age of fourteen, girls were to learn household management, childcare, and religious instruction. While in school she also learned how to play an instrument, the piano. As years passed, Emmy wanted to become a certified teacher of French and English. For three years, Emmy attended a teachers training program (McGrayne, Sharon Bertsch, p. 68). In 1900, Emmy took the five-day Bavarian State examinations. She passed the strenuous examinations and was officially qualified to teach both French and English in schools for girls. However Emmy instead wanted to continue with her education and went to the University of Erlangen to study mathematics (Smith, Martha K). Emmy wanted to attend the university where her father went to school and taught, to follow in his footsteps.
Women were not allowed to gain credit or degrees from universities so it was an exceptionally difficult time for females. This was a time when women did not have the same rights that male students had. However, women were able to get permission from professors to sit in on their lectures. Many professors regrettably were not shy to refuse to admit women into their lectures (McGrayne, Sharon Bertsch, p. 68). In 1898, two years before Noether audited classes at the University of Erlangen, the Academic Senate declared that the admission of women of the university would “overthrow all academic order” (Cooney, Miriam P., p. 126). Noether was fortunate since she was able to ask friends and family who worked at the university to give her permission to sit in on lectures and they all agreed. During 1900-1902, only two students out of 986 students were women. Emmy sat in class lectures for two years. The lectures Emmy sat in on consisted of more foreign languages and her first mathematics course. This math class is where everything changed. On July 14, 1903 Emmy took and passed the entrance examination to the Bavarian universities.
At the age of twenty-one, Emmy entered into the University of Gottingen as an auditor for graduate school. Felix Klein administered the University of Gottingen. Felix Klein was a mathematician and a supporter of higher education for women. He was also a close friend of Emmys father, Max Noether, which assisted Emmy to audit classes at this university. Instead of learning languages as she had done for most of her schooling career, she brought it upon her self to only study mathematics. She attended this university for only one semester and then returned to the University of Erlangen in 1904 (McGrayne, Sharon Bertsch, p. 69). Women were now allowed to enroll into the University of Erlangen. Females were able to go to lectures, take examinations, and most importantly they were able to get the same education as men were. At the University of Erlangen, Emmy mainly studied with her father and his friend, Paul Gordan. Gordan was a renowned mathematician who advised Emmy when she wrote her thesis (Cooney, Miriam P., p. 127). In 1908, Emmy earned her Ph.D (Goldberg, Dave, p. 107).
As fortunate as Emmy Noether was to become a mathematician, she was still living in a period that was hard for women to be thought of as equal. Due to her being a female, Emmy was unable to attain a regular or paid job. The University of Erlangen would not hire Emmy since it was against their policy to have professors who were women. From 1908 until 1915, Emmy worked without pay or title at the Mathematical Institute in her home, Erlangen. Emmy would assist her father and also carry out her research (Cooney, Miriam P., p. 127). Emmy soon began to be recognized. In 1908, Noether was acknowledged to join the Italian organization, Circolo Mathematico of Palermo. The following year, 1909, Noether was recognized to join the German Mathematical Union. She began to do public lectures talking about mathematics (Smith, Martha K).
Noether began to apply David Hilberts approach to algebra. David Hilbert was a mathematician who used highly abstract methods at Gottingen University. Hilbert and Klein recognized Emmy Noethers ability and they asked her to join their team. Noether moved to Gottingen in 1916. David Hilbert and Felix Klein were working alongside Albert Einstein. They were working together to develop a mathematical formulation of his general theory of relativity (McGrayne, Sharon Bertsch, p. 70). While at Gottingen University, Noether derived what is known as Noether’s (first) Theorem in 1915. It was then published it in 1918. Noether’s Theorem states, “Every symmetry corresponds to conserved quantity.” It discusses how momentum is conserved; it also explains and describes the conservation of spin, and on (Goldberg, Dave). Hilbert wanted Emmy to have a position at Gottingen University where she would be paid. Hilbert unfortunately was unable to convince faculty to pay Emmy. Instead he was able to allow Emmy to lecture however her lectures needed to be under his name (Cooney, Miriam P., p. 128).
Three years later, in 1919, Emmy finally began to receive a small salary. However she was the lowest paid faculty member at the university of Gottingen’s. Nevertheless, this did not discourage Emmy to continue doing what she loved. She could officially teach algebra, supervise dissertations, give examinations, and finally was allowed to lecture under her own name (Cooney, Miriam P., p. 128). In 1921, her father passed away. After her father’s death, Emmy turned algebra in a different direction. Emmy was “the leading founder of abstract algebra- now a major area in mathematics- and also worked in group theory, ring theory, group representatives, and number theory.” (McGrayne, Sharon Bertsch, p. 75). During 1921, Noether published the “Theory of Ideals in Rings”. This was one of her most important papers because it aided in the development of modern algebra. In the “Theory of Ideals in Rings”, Noether deals with Ideal theory and compares and contrasts concepts in abstract schemes (McGrayne, Sharon Bertsch, p. 75). In the years Noether spent at the University of Gottingen, she gathered followers who were known as “Noether boys”. These were no ordinary students. They were outstanding mathematicians. Emmy was always available for her students and shared her ideas and knowledge (Cooney, Miriam P., p. 128). In 1928-1929, Noether went to Moscow University to visit a professor.
During the years of 1924-1925, Noether taught a course on abstract algebra. She also led a seminar on algebraic geometry at the university. Around the 1930s Herman Weyl, a German mathematician, tried to get Emmy a better position at the University of Gottingen. This was because he was ashamed to have a higher position then Emmy knowing that she was the one who deserved a higher position (Cooney, Miriam P., p. 129). Weyl said, “In my Gottingen years, she was without doubt the strongest center of mathematical activity there, considering both the fertility of her scientific research program and her influence upon a large circle of pupils.” (McGrayne, Sharon Bertsch, p. 81). Unfortunately, he failed at his
attempt.
In 1932, Emmy received the Alfred Ackerman Teubner Memorial Prize. They recognized her for her advancement of the mathematical sciences. She received one hundred twenty dollars. Also in this same year, Emmy was invited to lecture at a general session of the International Mathematical Congress in Zurich. A year later, Hitler became chancellor of Germany on January 30 1933. The lives of Jewish individuals were changed radically. On April 7 1933 Emmy, along with other professors, received a notice that her right to teach has been withdrawn. This however did not stop or discourage Emmy from mathematics. Instead of teaching Emmy Noether would hold informal meetings to discuss mathematics. After Noether lost her right to teach, she along with many German-Jewish scientists and mathematicians had to leave the country of Germany. Many mathematicians and scientists found a new home in the United States of America. In the years 1933-1934 the Bryn Mawr College located in Pennsylvania, where Emmy was serving as a visiting professor, appointed Emmy a regular faculty position. Bryn Mawr College was an all girl college (Cooney, Miriam P., p. 129-131). A year later in April 1935, Emmy learned that she had a tumor. Surgery was needed to remove this tumor that impeded her health. Doctors however believed she was a risk because of her high blood pressure. On the fourth day of her recovery, with her temperature at 109 degrees, she slipped into unconsciousness. Emmy Noether passed away on April 14 1935. She was only 53 years old. While she was alive Emmy was not recognized for her work. After her death however, there were many recognitions of her brilliancy. On the fiftieth anniversary of Emmy receiving her doctoral degree, many of her own students gathered at the university of Erlangen to discuss the impact that she had on mathematics. Erlangen named a street after her in the year 1960. The American Mathematical Society celebrated Emmy’s 100th birthday with a conference at Bryn Mawr (Cooney, Miriam P., p. 131). Even though Emmy’s mathematical gift was not celebrated, as it should have been during her life, her impact and teachings will last forever.