Wednesday, June 13, 2007

10 MATHEMATICIAN

1) Hypatia
philosopher, astronomer, and mathematician
Hypatia was the daughter of Theon of Alexandria who was a teacher of mathematics with the Museum of Alexandria in Egypt. A center of Greek intellectual and cultural life, the Museum included many independent schools and the great library of Alexandria.
Hypatia studied with her father, and with many others including Plutarch the Younger. She herself taught at the Neoplatonist school of philosophy. She became the salaried director of this school in 400. She probably wrote on mathematics, astronomy and philosophy, including about the motions of the planets, about number theory and about conic sections.
Hypatia corresponded with and hosted scholars from others cities. Synesius, Bishop of Ptolemais, was one of her correspondents and he visited her frequently. Hypatia was a popular lecturer, drawing students from many parts of the empire.
From the little historical information about Hypatia that survives, it appears that she invented the plane astrolabe, the graduated brass hydrometer and the hydroscope, with Synesius of Greece, who was her student and later colleague.
Hypatia dressed in the clothing of a scholar or teacher, rather than in women's clothing.

She moved about freely, driving her own chariot, contrary to the norm for women's public behavior. She exerted considerable political influence in the city.
Orestes, the governor of Alexandria, like Hypatia, was a pagan (non-Christian). Orestes was an adversary of the new Christian bishop, Cyril, a future saint. Orestes, according to the contemporary accounts, objected to Cyril expelling the Jews from the city, and was murdered by Christian monks for his opposition.
Cyril probably objected to Hypatia on a number of counts: She represented heretical teachings, including experimental science and pagan religion. She was an associate of Orestes. And she was a woman who didn't know her place. Cyril's preaching against Hypatia is said to have been what incited a mob led by fanatical Christian monks in 415 to attack Hypatia as she drove her chariot through Alexandria. They dragged her from her chariot and, according to accounts from that time, stripped her, killed her, stripped her flesh from her bones, scattered her body parts through the streets, and burned some remaining parts of her body in the library of Caesareum.
Hypatia's students fled to Athens, where the study of mathematics flourished after that. The Neoplatonic school she headed continued in Alexandria until the Arabs invaded in 642.
When the library of Alexandria was burned by the Arab conquerors, used as fuel for baths, the works of Hypatia were destroyed. We know her writings today through the works of others who quoted her -- even if unfavorably -- and a few letters written to her by contemporaries.
2) Elena Cornaro Piscopia


(June 5, 1646 - July 26, 1684)
mathematician, philosopher
(Elena Lucrezia Cornaro Piscopia)
first woman to earn a doctoral degree
The Cornaro family of Venice traced its heritage back to the Roman family of Cornelii. Ancestors included cardinals and popes. The castle Piscopia was given to the family by the husband of a (related) queen of Cyprus.
Elena Cornaro Piscopia was born in 1646 into this family. Her father was a public official who educated his children personally. A parish priest recognized Elena as a child prodigy when she was seven, and then she began to study with tutors in Latin, Greek, music, theology, and mathematics. She eventually learned Hebrew, Arabic, Chaldaic, and also French, English, and Spanish. She studied philosophy, and astronomy. Musically talented, by the time she was 17 years old she could sing, compose, and play such instruments as the violin, harp, and harpsichord.
Her achievements attracted the attention of many, including clerics, royals, and scientists. Many came to Venice to meet and speak with her.
Elena herself wanted to enter the Benedictine Order. She secretly practiced the disciplines of the Order and turned down marriage proposals, spending time serving the sick and the poor. But her father refused permission for her to enter the Order, and had her apply instead to the University of Padua.
Although some other women had studied science and math at the university level in Italy in her time, Elena Piscopia was the first to apply in theology. She studied there from 1672-1678, and in 1678, she received her master's and doctorate of philosophy degrees. The ceremony awarding her these degrees had to be held in the cathedral to accommodate the crowd that came to see her receive them.
Elena Piscopia became a lecturer in mathematics at the University, where she served until her early death in 1684.
She was honored after her death as a woman of learning. The University of Padua has a marble statue of her. Vassar College in New York has a stained glass window depicting her achievement.
Her achievement did not immediately open doors for many others, though. No other woman earned a doctorate at the University of Padua until the late twentieth century.
Maria Agnesi


(May 16, 1718 - January 9, 1799)
mathematician, philosopher, philanthropist
Maria Gaetana Agnesi, Maria Gaëtana Agnesi
• wrote first mathematics book by a woman that still survives
• first woman appointed as a mathematics professor at a university
Maria Agnesi's father was Pietro Agnesi, a wealthy nobleman and a professor of mathematics at the University of Bologna. It was normal in that time for the daughters of noble families to be taught in convents, and to receive instruction in religion, household management and dressmaking. A few Italian families educated daughters in more academic subjects; a few attended lectures at the university or even lectured there.
Pietro Agnesi recognized the talents and intelligence of his daughter Maria. Treated as a child prodigy, she was given tutors to learn five languages (Greek, Hebrew, Latin, French and Spanish) and also philosophy and science.
The father invited groups of his colleagues to gatherings at their home, and had Maria Agnesi present speeches to the assembled men. By age 13, Maria could debate in the language of the French and Spanish guests, or she could debate in Latin, the language of the educated. She didn't like this performing, but she could not persuade her father to let her out of the task until she was twenty years old.
In that year, 1738, Maria Agnesi assembled almost 200 of the speeches she had presented to her father's gatherings, and published them in Latin as Propositiones philosphicae -- in English, Philosophical Propositions. But the topics went beyond philosophy as we think of the topic today, and included scientific topics like celstial mechanics, Isaac Newton's gravitation theory, and elasticity.
Pietro Agnesi married twice more after Maria's mother died, so that Maria Agnesi ended up the eldest of 21 children. In addition to her performances and lessons, her responsibility was to teach her siblings. This task kept her from her own goal of entering a convent.
Also in 1783, wanting to do the best job of communicating up-to-date mathematics to her younger brothers, Maria Agnesi began to write a mathematics textbook, which absorbed her for ten years.
The Instituzioni Analitiche was published in 1748 in two volumes, over one thousand pages. The first volume covered arithmetic, algebra, trigonometry, analytic geometry and calculus. The second volume covered infinite series and differential equations. No one before had published a text on calculus that included the methods of calculus of both Isaac Newton and Gottfried Liebnitz.
Maria Agnesi brought together ideas from many contemporary mathematical thinkers -- made easier by her ability to read in many languages -- and integrated many of the ideas in a novel way that impressed the mathematicians and other scholars of her day.
As recognition of her achievement, in 1750 she was appointed to the chair of mathematics and natural philosophy at the University of Bologna by an act of Pope Benedict XIV. She was also recognized by the Hapsburg Empress Maria Theresa of Austria.
Did Maria Agnesi ever accept the Pope's appointment? Was it a real appointment or an honorary one? So far, the historical record does not answer those questions.
Maria Agnesi's name lives on in the name that English mathematician John Colson gave to a mathematical problem -- finding the equation for a certain bell-shaped curve. Colson confused the word in Italian for "curve" for a somewhat similar word for "witch," and so today this problem and equation still carries the name "witch of Agnesi."
Maria Agnesi's father was seriously ill by 1750 and died in 1752. His death released Maria from her responsibility to educate her siblings, and she used her wealth and her time to help those less fortunate. She established in 1759 a home for the poor. In 1771 she headed up a home for the poor and ill. By 1783 she was made director of a home for the elderly, where she lived among those she served. She had given away everything she owned by the time she died in 1799, and Maria Agnesi was buried in a pauper's grave.
Sophie Germain


(April 1, 1776 - June 27, 1831)
mathematician, number theorist, mathematical physicist
Marie-Sophie Germain, Sophia Germain, Sophie Germaine
• first woman not related to a member by marriage to attend Academie des Sciences meetings
• first woman invited to attend sessions at the Institut de France
Sophie Germain's father was Ambroise-Francois Germain, a wealthy middle class silk merchant and a French politician who served in the Estates Général and later in the Constituent Assembly. He later became a director of the Bank of France. Her mother was Marie-Madeleine Gruguelu, and her sisters, one older and one younger, were named Marie-Madeleine and Angelique-Ambroise. She was known simply as Sophie to avoid confusion with all the Maries in the household.
When Sophie Germain was 13, her parents kept her isolated from the turmoil of the French Revolution by keeping her in the house. She fought boredom by reading from her father's extensive library. She may also have had private tutors during this time.
A story told of those years is that Sophie Germain read the story of Archimedes of Syracuse who was reading geometry as he was killed -- and she decided to commit her life to a subject that could so absorb one's attention.
After discovering geometry, Sophie Germain taught herself mathematics, and also Latin and Greek so that she could read the classical mathematics texts. Her parents opposed her study and tried to stop it, so she studied at night. They took away candles and forbid nighttime fires, even taking her clothes away, all so that she could not read at night. Her response: she smuggled candles, she wrapped herself in her bedclothes. She still found ways to study. Finally the family gave in to her mathematical study.
In the eighteenth century in France, a woman was not normally accepted in universities. But the École Polytechnique, where exciting research on mathematics was happening, allowed Sophie Germain to borrow the lecture notes of the university's professors. She followed a common practice of sending comments to professors, sometimes including original notes on mathematics problems as well. But unlike male students, she used a pseudonym, "M. le Blanc" -- hiding behind a male pseudonym as many women have done to have their ideas taken seriously.
Beginning this way, Sophie Germain corresponded with many mathematicians and "M. le Blanc" began to have an impact in turn on them. Two of these mathematicians stand out: Joseph-Louis Lagrange, who soon discovered that "le Blanc" was a woman and continued the correspondence anyway, and Carl Friedrich Gauss of Germany, who eventually also discovered that he'd been exchanging ideas with a woman for three years.
Before 1808 Germain mainly worked in number theory. Then she became interested in Chladni figures, patterns produced by vibration. She anonymously entered a paper on the problem into a contest sponsored by the French Academy of Sciences in 1811, and it was the only such paper submitted. The judges found errors, extended the deadline, and she was finally awarded the prize on January 8, 1816. She did not attend the ceremony, though, for fear of the scandal that might result.
This work was foundational to the applied mathematics used in construction of skyscrapers today, and was important at the time to the new field of mathematical physics, especially to the study of acoustics and elasticity.
In her work on number theory, Sophie Germain made partial progress on a proof of Fermat's Last Theorem. For prime exponents less than 100, she showed there could be no solutions relatively prime to the exponent.
Accepted now into the community of scientists, Sophie Germain was allowed to attend sessions at the Institut de France, the first woman with this privilege. She continued her solo work and her correspondence until she died in 1831 of breast cancer.
Carl Friedrich Gauss had lobbied to have an honorary doctorate awarded to Sophie Germain by Göttingen University, but she died before it could be awarded.
A school in Paris -- L'École Sophie Germain -- and a street -- la rue Germain -- honor her memory in Paris today. Certain prime numbers are called "Sophie Germain primes."
Mary Somerville


(December 26, 1780 - November 29, 1872)
"Queen of Nineteenth Century Science"
mathematician, scientist, astronomer, geographer
• one of the first two women admitted to the Royal Astronomical Society
• Somerville College, Oxford University, is named for her
• dubbed "Queen of Nineteenth Century Science" by a newspaper on her death
Mary Fairfax, born in Jedburgh, Scotland, as the fifth of seven children of Vice-Admiral Sir William George Fairfax and Margaret Charters Fairfax, preferred the outdoors to reading. She did not have a good experience when sent to an elite boarding school, and was sent home in just a year.
At age 15 Mary noticed some algebraic formulas used as decoration in a fashion magazine, and on her own began to study algebra to make sense of them. She surreptitiously obtained a copy of Euclid's Elements of Geometry over her parents' opposition.
In 1804 Mary Fairfax married -- under pressure from family -- her cousin, Captain Samuel Greig. They had two sons. He too opposed Mary's studying mathematics and science, but after his death in 1807 -- followed by the death of one of their sons -- she returned to Scotland with her other son and began to study astronomy and mathematics seriously. She began solving math problems posed by a mathematics journal, and in 1811 won a medal for a solution she submitted.
She married Dr. William Somerville in 1812, another cousin. A surgeon, Dr. Somerville supported her study, writing and contact with scientists. They had three daughters and a son.
Four years after this marriage Mary Somerville and her family moved to London. They also traveled extensively in Europe. Mary Somerville began publishing papers on scientific subjects in 1826, using her own research, and after 1831, she began writing about the ideas and work of other scientists, too. One book prompted John Couch Adams to search for the planet Neptune, for which is he is credited as a co-discoverer.
Her translation and expansion of Pierre Laplace's Celestial Mechanics in 1831 won her acclaim and success. In 1833 she and Caroline Herschel were named honorary members of the Royal Astronomical Society, the first time women had won that recognition. Mary Somerville moved to Italy for her husband's health in 1838, and there she continued to work and to publish. Dr. Somerville died in 1860. In 1869, Mary Somerville published yet another major work, was awarded a gold medal from the Royal Geographical Society, and was elected to the American Philosophical Society.
Mary Somerville died in Naples in 1872, just before turning 92. She had been working on another mathematical article at the time. Her daughter published Personal Recollections of Mary Somerville the next year.
Significant writings:
• 1831 (first book) - The Mechanism of the Heavens - translating and explaining Pierre Laplace's celestial mechanics
• 1834 - On the Connection of the Physical Sciences - this book continued in new editions through 1877
• 1848 - Physical Geography - first book in England on Earth's physical surface
• 1869 - On Molecular and Microscopic Science - about physics and chemistry
Ada Lovelace

mathematician, computer pioneer
(December 10, 1815 - November 27, 1852)
Ada Augusta Byron was the only legitimate child of the Romantic poet, George Gordon, Lord Byron. Her mother was Anne Isabella Milbanke who took the baby at one month old away from her father's home. Ada Augusta Byron never saw her father again; he died when she was eight.
Ada Lovelace's mother, who had studied mathematics herself, decided that her daughter would be spared the father's eccentricities by studying more logical subjects like math and science, rather than literature or poetry. Young Ada Lovelace showed a genius for math from an early age. Her tutors included William Frend, William King and Mary Somerville. She also learned music, drawing and languages, and became fluent in French.
Ada Lovelace met Charles Babbage in 1833, and became interested in a model he had constructed of a mechanical device to compute values of quadratic functions, the Difference Engine. She also studied his ideas on another machine, the Analytical Engine, which would use punched cards to "read" instructions and data for solving mathematical problems.
Babbage also became Lovelace's mentor, and helped Ada Lovelace begin mathematical studies with Augustus de Moyan in 1840 at the University of London.
Babbage himself never wrote about his own inventions, but in 1842, an Italian engineer Manabrea (later Italy's prime minister) described Babbage's Analytical Engine in an article published in French.
Augusta Lovelace was asked to translate this article into English for a British scientific journal. She added many notes of her own to the translation, since she was familiar with Babbage's work. Her additions showed how Babbage's Analytical Engine would work, and gave a set of instructions for using the Engine for calculating Bernoulli numbers. She published the translation and notes under the initials "A.A.L," concealing her identity as did many women who published before women were more accepted as intellectual equals.
Augusta Ada Byron married a William King (though not the same William King who had been her tutor) in 1835. In 1838 her husband became the first Earl of Lovelace, and Ada became countess of Lovelace. They had three children.
Ada Lovelace unknowingly developed an addiction to prescribed drugs including laudanum, opium and morphine, and displayed classic mood swings and withdrawal symptoms. She took up gambling and lost most of her fortune. She was suspected of an affair with a gambling comrade.
In 1852, Ada Lovelace died of uterine cancer. She was buried next to her famous father.
More than a hundred years after her death, in 1953, Ada Lovelace's notes on Babbage's Analytical Engine were republished after having been forgotten. The engine was now recognized as a model for a computer, and Ada Lovelace's notes as a description of a computer and software.
In 1980, the U.S. Department of Defense settled on the name "Ada" for a new standardized computer language, named in honor of Ada Lovelace.
Charlotte Angas Scott
(June 8, 1858 - November 10, 1931)
• first head of the mathematics department at Bryn Mawr College
• initiator of the College Entrance Examination Board
• one of the organizers of the American Mathematical Society
Charlotte Angas Scott was born in England. Her father, Caleb Scott, was president of Lancashire College, a Congregational minister and known as a social reformer; his father had been a reformer as well. Caleb Scott urged his daughter, Charlotte Angas Scott, to seek a university education, unusual for women in that time. She did so: she joined ten other young women at Hitchin College, soon renamed Girton College, part of Cambridge University.
As a pioneer in women's higher education, Charlotte Angas Scott and her classmates faced severe restrictions and on their participation and activities.
Not officially permitted to take the traditional oral exam at the end of Cambridge's program, Charlotte Scott took it unofficially -- and placed eighth in the ranking overall, including all male students. At the awards ceremony, the women's names were not included in the rankings read. But male students shouted "Scott of Girton!" over the name of the male student who was announced in the eighth place.
Charlotte Angas Scott went on, then, to graduate studies at the University of London while serving as a lecturer at Girton. In 1885, she moved to the United States to join the first faculty of the newly-founded Bryn Mawr College in Pennsylvania, the first women's college offering graduate degrees.
At Bryn Mawr, Charlotte Angas Scott promoted strict entrance policies and her efforts eventually led to the founding of the College Entrance Examination Board. Scott was the first chief examiner of the Board.
In 1909, Charlotte Scott was given the first endowed chair at Bryn Mawr, in recognition of her achievements.
Charlotte Angas Scott was a member of the council that transformed the New York Mathematical Society into the American Mathematical Society in 1895, and she served as the society's vice president in 1905. She was coeditor of the American Journal of Mathematics in 1899, and continued editing for that journal until her retirement. When arthritis forced a hiatus from publishing, Charlotte Scott took up gardening and bred a new chrysanthemum.
Charlotte Angas Scott never married, though she often visited with her relatives in England (where she was known as "Aunt Charlie"), and she also frequently visited her friend Frank Morley in Baltimore.
Charlotte Scott retired in 1925, though she remained at Bryn Mawr for a few more years until her last doctoral student had graduated. She died in England in 1931.
Works
• 1894: An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry. First edition, 1894. Second edition, 1924. Third edition published in 1961 as Projective Methods in Plane Geometry.
• 1899: "A Proof of Noether's Fundamental Theorem"
• 1907: Cartesian Plane Geometry, Part I: Analytical Conics
Sofia Kovalevskaya


(January 15, 1850 - February 10, 1891)
also: Sonya Kovalevskaya, Sofya Kovalevskaya, Sophia Kovalevskaia, Sonia Kovelevskaya, Sonya Korvin-Krukovsky, etc.
novelist, mathematician
• first woman to hold a university chair in modern Europe
• first woman on the editorial staff of a mathematical journal
Sofia Kovalevskaya's father was in the Russian Army and her mother was from a German family with many scholars; her maternal grandfather and great-grandfather were both mathematicians. She was born in Moscow, Russia, in 1850.
As a young child Sofia Kovalevskaya was fascinated with the unusual wallpaper on the wall of a room on the family estate: the lecture notes of Mikhail Ostrogradsky on differential and integral calculus.
Although her father provided her with private tutoring -- including calculus at age 15 -- he would not allow her to study abroad for further education, and Russian universities would not then admit women. But Sofia Kovalevskaya wanted to continue her studies in mathematics, so she found a solution: an amenable young student of paleontology, Vladimir Kovalensky, who entered into a marriage of convenience with her. In 1869, they left Russia with her sister, Anyuta. Sonja went to Heidelberg, Germany, Kovalensky went to Vienna, Austria, and Anyuta went to Paris, France.
In Heidelberg, Sofia Kovalevskaya obtained permission of the mathematics professors to allow her to study at the University of Heidelberg. After two years she went to Berlin to study with Karl Weierstrass. She had to study privately with him, as the university in Berlin would not allow any women to attend class sessions.
With Weierstrass' support Sofia Kovalevskaya pursued a degree in mathematics, and her work earned her a doctorate sum cumma laude from the University of Göttingen in 1874. Her doctoral dissertation on partial differential equations is today called the Cauch-Kovelevskaya Theorem. It so impressed the faculty that they awarded Kovalevskaya the doctorate without examination and without her having attended any classes at the university.
Sofia Kovalevskaya and her husband returned to Russia after she earned her doctorate. They were unable to find the academic positions they desired. They pursued commercial ventures and produced a daughter as well. Sofia Kovalevskaya began writing fiction, including a novella Vera Barantzova which won sufficient acclaim to be translated into several languages.
Kovalensky, immersed in a financial scandal for which he was about to be prosecuted, committed suicide in 1883, but Sofia Kovalevskaya had already returned to Berlin and mathematics, taking their daughter with her. She became a privatdozent at Stockholm University, paid by her students rather than the university.
In 1888 Sofia Kovalevskaya won the Prix Bordin from the French Academie Royale des Sciences for research now called the Kovelevskaya top. This research examined how Saturn's rings rotated.
She also won a prize from the Swedish Academy of Sciences in 1889, and that same year was appointed to a chair at the university - the first woman appointed to a chair at a modern European university. She was also elected to the Russian Academy of Sciences as a member that same year.
She only published ten papers before her death from influenza in 1891, after a trip to Paris to see Maxim Kovalensky, a relative of her late husband with whom she was having a love affair.
Alicia Stott


(June 8, 1860 - December 17, 1940)
mathematician
Alicia Boole Stott's father was the mathematician George Boole (for whom Boolean logic is named). He was teaching in Ireland when Alicia was born there, in 1860, and he died four years later. Alicia lived with her grandmother in England and her great-uncle in Cork for the next ten years before she rejoined her mother and sisters in London.
In her teens, Alicia Stott became interested in four-dimensional hypercubes, or tesseracts. She became secretary to John Falk, an associate of her brother-in-law, Howard Hinton, who had introduced her to tesseracts. Alicia Stott continued building models of wood to represent four-dimensional convex solids, which she named polytopes, and published an article on three-dimenstional sections of hypersolids in 1900.
She married Walter Stott, an actuary. They had two children, and Alicia Stott settled into the role of homemaker until her husband noted that her mathematical interests might also be of interest to the mathematician Pieter Hendrik Schoute at the University of Groningen. After the Stotts wrote to Schoute, and Schoute saw photographs of some models that Alicia Stott had built, Schoute moved to England to work with her.
Alicia Stott worked on deriving Archimedean solids from Platonic solids. With Schoute's encouragement, she published papers on her own and that the two of them developed together.
In 1914, Schoute's colleagues at Groningen invited Alicia Stott to a celebration, planning to award to her an honorary degree. But when Schoute died before the ceremony could be held, Alicia Stott returned to the her middle class life at home.
In 1930, Alicia Stott began collaborating with H. S. M. Coxeter on the geometry of kaleidoscopes. She also constructed cardboard models of the "snub 24-cell."
She died in 1940.
Emmy Noether


(March 23, 1882 - April 14, 1935)
mathematician
Amalie Noether, Emily Noether, Amelie Noether
Born in Germany and named Amalie Emmy Noether, she was known as Emmy. Her father was a mathematics professor at the University of Erlangen and her mother was from a wealthy family.
Emmy Noether studied arithmetic and languages but was not permitted -- as a girl -- to enroll in the college preparatory school, the gymnasium. Her graduation qualified her to teach French and English in girls' schools, apparently her career intention -- but then she changed her mind and decided she wanted to study mathematics at the university level.
To enroll in a university, she had to get permission of the professors to take an entrance exam -- she did and she passed, after sitting in on mathematics lectures at the University of Erlangen. She was then allowed to audit courses -- first at the University of Erlangen and then the University of Göttingen, neither of which would permit a woman to attend classes for credit. Finally, in 1904, the University of Erlangen decided to permit women to enroll as regular students, and Emmy Noether returned there. Her dissertation in algebraic math earned her a doctorate summa cum laude in 1908.
For seven years, Noether worked at the University of Erlangen without any salary, sometimes acting as a substitute lecturer for her father when he was ill. In 1908 she was invited to join the Circolo Matematico di Palermo and in 1909 to join the German Mathematical Society -- but she still could not obtain a paying position at a University in Germany.
In 1915, Emmy Noether's mentors, Felix Klein and David Hilbert, invited her to join them at the Mathematical Institute in Göttingen, again without compensation. There, she pursued important mathematical work that confirmed key parts of the general theory of relativity.
Hilbert continued to work to get Noether accepted as a faculty member at Göttingen, but he was unsuccessful against the cultural and official biases against women scholars. He was able to allow her to lecture -- in his own courses, and without salary. In 1919 she won the right to be a privatdozent -- she could teach students, and they would pay her directly, but the university did not pay her anything. In 1922, the University gave her a position as an adjunct professor with a small salary and no tenure or benefits.
Emmy Noether was a popular teacher with the students. She was seen as warm and enthusiastic. Her lectures were participatory, demanding that students help work out the mathematics being studied.
Emmy Noether's work in the 1920s on ring theory and ideals was foundational in abstract algebra. Her work earned her enough recognition that she was invited as a visiting professor in 1928-1929 at the University of Moscow and in 1930 at the University of Frankfurt.
Though she was never able to gain a regular faculty position at Göttingen, she was one of many Jewish faculty members who were purged by the Nazis in 1933. In America, the Emergency Committee to Aid Displaced German Scholars obtained for Emmy Noether an offer of a professorship at Bryn Mawr College in America, and they paid, with the Rockefeller Foundation, her first year's salary. The grant was renewed for two more years in 1934. This was the first time that Emmy Noether was paid a full professor's salary and accepted as a full faculty member.
But her success was not to last long. In 1935, she developed complications from an operation to remove a uterine tumor, and she died shortly after, on April 14.
After World War II ended, the University of Erlangen honored her memory, and in that city a coed gymnasium specializing in math was named for her. Her ashes are buried near Bryn Mawr's Library.
A quote by Emmy Noether:
If one proves the equality of two numbers a and b by showing first that "a is less than or equal to b" and then "a is greater than or equal to b", it is unfair, one should instead show that they are really equal by disclosing the inner ground for their equality.
About Emmy Noether, by Lee Smolin:
The connection between symmetries and conservation laws is one of the great discoveries of twentieth century physics . But I think very few non-experts will have heard either of it or its maker — Emily Noether, a great German mathematician. But it is as essential to twentieth century physics as famous ideas like the impossibility of exceeding the speed of light.
It is not difficult to teach Noether's theorem, as it is called; there is a beautiful and intuitive idea behind it. I've explained it every time I've taught introductory physics. But no textbook at this level mentions it. And without it one does not really understand why the world is such that riding a bicycle is safe.

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