Women Mathematicians
Maryam Mirzakhani, an Iranian maths professor at Stanford University in California, was named the first female winner of the Fields Medal ( 2014 ) – often described as the Nobel prize for mathematics.
The prize, worth 15,000 Canadian dollars (£8,000), is awarded to exceptional talents under the age of 40 once every four years by the International Mathematical Union.
Between two and four prizes are announced each time.
Also won Martin Hairer, a 38-year-old Austrian based at Warwick University in the UK, Manjul Bhargava, a 40-year old Canadian-American at Princeton University in the US and Artur Avila, 35, a Brazilian-French researcher at the Institute of Mathematics of Jussieu in Paris.
There have been 55 Fields medallists since the prize was first awarded in 1936 including 2014 winners. The Russian mathematician Grigori Perelman refused the prize in 2006 for his proof of the Poincaré conjecture.
The prize, worth 15,000 Canadian dollars (£8,000), is awarded to exceptional talents under the age of 40 once every four years by the International Mathematical Union.
Between two and four prizes are announced each time.
Also won Martin Hairer, a 38-year-old Austrian based at Warwick University in the UK, Manjul Bhargava, a 40-year old Canadian-American at Princeton University in the US and Artur Avila, 35, a Brazilian-French researcher at the Institute of Mathematics of Jussieu in Paris.
There have been 55 Fields medallists since the prize was first awarded in 1936 including 2014 winners. The Russian mathematician Grigori Perelman refused the prize in 2006 for his proof of the Poincaré conjecture.
Here are names and works of some of the Women Mathematicians
Theano
According to tradition, Theano was the wife of Pythagoras. Some sources claim that she and her two daughters carried on the Pythagorean School after the death of Pythagoras and that she wrote treatises on mathematics, physics, medicine, and child psychology. McLemore writes that her most important work was the principle of the "Golden Mean." In addition, Damo (ca. 535-475 BC), the daughter of Pythagoras and Theano, is said to have published her father's treatises on geometry as well as treatises on the construction of a regular tetrahedron and the construction of a cube. But discerning what Theano actually did is extremely difficult. As stated in the article in the Biographical Dictionary of Women in Science, Theano continued to operate the school of Pythagoras after his death is often affirmed but not confirmed. Thus, it can only be stated that, according to tradition, Theano was a mathematician, a physician, and an administrator—someone who kept alive an important training ground for future mathematicians.
Michael Deakin has written an extensive article examining how much of the claim that Theano was the first woman to play an active role in mathematics can be supported by historical resources. He says, for example, that "The most we can say about the claim that she wrote a book on [the golden ratio], is that she may have done. It was the sort of thing she might have done, but there is absolutely no evidence whatsoever that she actually did."
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Ada Byron, Lady Lovelace December 10, 1815 - November 27, 1852
Ada Byron, Lady Lovelace, was one of the most picturesque characters in computer history. Augusta Ada Byron was born December 10, 1815 the daughter of the illustrious poet, Lord Byron. Five weeks after Ada was born Lady Byron asked for a separation from Lord Byron, and was awarded sole custody of Ada who she brought up to be a mathematician and scientist. Lady Byron was terrified that Ada might end up being a poet like her father. Despite Lady Byron's programming Ada did not sublimate her poetical inclinations. She hoped to be "an analyst and a metaphysician". In her 30's she wrote her mother, if you can't give me poetry, can't you give me "poetical science?" Her understanding of mathematics was laced with imagination, and described in metaphors.
At the age of 17 Ada was introduced to Mary Somerville, a remarkable woman who translated LaPlace's works into English, and whose texts were used at Cambridge. Though Mrs. Somerville encouraged Ada in her mathematical studies, she also attempted to put mathematics and technology into an appropriate human context. It was at a dinner party at Mrs. Somerville's that Ada heard in November, 1834, Babbage's ideas for a new calculating engine, the Analytical Engine. He conjectured: what if a calculating engine could not only foresee but could act on that foresight. Ada was touched by the "universality of his ideas". Hardly anyone else was.
Babbage worked on plans for this new engine and reported on the developments at a seminar in Turin, Italy in the autumn of 1841. An Italian, Menabrea, wrote a summary of what Babbage described and published an article in French about the development. Ada, in 1843, married to the Earl of Lovelace and the mother of three children under the age of eight, translated Menabrea's article. When she showed Babbage her translation he suggested that she add her own notes, which turned out to be three times the length of the original article. Letters between Babbage and Ada flew back and forth filled with fact and fantasy. In her article, published in 1843, Lady Lovelace's prescient comments included her predictions that such a machine might be used to compose complex music, to produce graphics, and would be used for both practical and scientific use. She was correct.
When inspired Ada could be very focused and a mathematical taskmaster. Ada suggested to Babbage writing a plan for how the engine might calculate Bernoulli numbers. This plan, is now regarded as the first "computer program." A software language developed by the U.S. Department of Defense was named "Ada" in her honor in 1979.
After she wrote the description of Babbage's Analytical Engine her life was plagued with illnesses, and her social life, in addition to Charles Babbage, included Sir David Brewster (the originator of the kaleidoscope), Charles Wheatstone, Charles Dickens and Michael Faraday. Her interests ranged from music to horses to calculating machines. She has been used as a character in Gibson and Sterling's "The Difference Engine", shown writing letters to Babbage in the series "The Machine that Changed the World" and I have gathered her letters and writings in Ada, The Enchantress of Numbers: A Selection from the Letters of Lord Byron's Daughter and Her Description of the First Computer. Though her life was short (like her father, she died at 36), Ada anticipated by more than a century most of what we think is brand-new computing.
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Hypatia of Alexandria
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.
Alternate spelling: Ipazia
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Elena Cornaro Piscopia
Dates: June 5, 1646 - July 26, 1684
Occupation: mathematician, philosopher, theologian
Known for: first woman to earn a doctoral degree
Also Known as: Elena Lucrezia Cornaro Piscopia
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.
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Maria Agnesi
Dates: May 16, 1718 - January 9, 1799
Known for: wrote first mathematics book by a woman that still survives; first woman appointed as a mathematics professor at a university
Occupation: mathematician, philosopher, philanthropist
Also known as: Maria Gaetana Agnesi, Maria Gaëtana Agnesi
About Maria Agnesi
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 celestial 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 Habsburg 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.
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Sophie Germain
Sophie Germaine dedicated herself early to becoming a mathematician, despite family obstacles and lack of precedent. The French Academy of Sciences awarded her a prize for a paper on the patterns produced by vibration. 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.
Known for:
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
Dates: April 1, 1776 - June 27, 1831
Occupation: mathematician, number theorist, mathematical physicist
Also Known as: Marie-Sophie Germain, Sophia Germain, Sophie Germaine
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."
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Mary Somerville
Kno?wn for:
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
Dates: December 26, 1780 - November 29, 1872
Occupation: mathematician, scientist, astronomer, geographer
More About Mary Somerville
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.
Mary Somerville's translation and expansion of Pierre Laplace's Celestial Mechanics in 1831 won her acclaim and success. In 1833 Mary Somerville 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 by Mary Somerville:
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
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Charlotte Angas Scott
Known for:
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
Dates: June 8, 1858 - November 10, 1931)
Occupation: educator, mathematician
Also known as: Charlotte Scott
Charlotte Angas Scott Biography:
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
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Sofia Kovalevskaya
Known for:
first woman to hold a university chair in modern Europe
first woman on the editorial staff of a mathematical journal
Dates: January 15, 1850 - February 10, 1891
Occupation: novelist, mathematician
Also known as: Also known as: Sonya Kovalevskaya, Sofya Kovalevskaya, Sophia Kovalevskaia, Sonia Kovelevskaya, Sonya Korvin-KrukovskySofia 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
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Alicia Stott
mathematician
Dates: June 8, 1860 - December 17, 1940
Occupation: mathematician
Also known as: Alicia Boole
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-dimensional 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.
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Emmy Noether
mathematician
Dates: March 23, 1882 - April 14, 1935
Also known as: 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.
University of Erlangen
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.
Göttingen
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.
America
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.
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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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Twentieth Century
1900-1909
Gertrude Mary Cox (1900-1978)
Mary Lucy Cartwright (1900-1998)
Nina Karlovna Bari (1901-1961)
Edna Kramer Lassar (1902-1984)
Lulu Hofmann Bechtolsheim (1902-1989)
Mina Rees (1902-1997)
Irmgard Flugge-Lotz (1903-1974)
Dorothy McCoy (1903-2001)
Anna Stafford Henriques (1905-2004)
Sophie Piccard (1904-2000)
Rózsa Péter (1905-1977)
Ruth Moufang (1905-1977)
Alice Roth (1905-1977)
Kate Fenchel (1905-1983)
Maria Cinquini-Cibrario (1905-1992)
Mabel Schmeiser Barnes (1905-1993)
Grace Brewster Murray Hopper (1906-1992)
Olga Taussky-Todd (1906-1995)
Sister Mary Celine Fasenmyer (1906-1996)
Emma Trotskaia Lehmer (1906-2007)
Margaret Jarman Hagood (1908-1963)
Louise Johnson Rosenbaum (1908-1980)
Herta Taussig Freitag (1908-2000)
Mary Ross (1908-2008)
Florence Nightingale David (1909-1993)
1910-1919
Sheila Scott Macintyre (1910-1960)
Cora Ratto de Sadosky (1912-1981)
Dame Kathleen Ollerenshaw (1912-2014)
Hanna Neumann (1914-1971)
Marjorie Lee Browne (1914-1979)
Dorothy Lewis Bernstein (1914-1988)
Alice T. Schafer (1915-2009)
Elizabeth Scott (1917-1988)
F. Jessie MacWilliams (1917-1990)
Helena Rasiowa (1917-1994)
Ruth Aaronsom Bari (1917-2005)
Dorothy Maharam Stone (1917-2014)
Jacqueline Ferrand (1918-2014)
Julia Bowman Robinson (1919-1985)
Paulette Libermann (1919-2007)
1920-1929
Edith Hirsch Luchins (1921-2002)
Deborah Tepper Haimo (1921-2007)
Olga Alexandrovna Ladyzhenskaya (1922-2004)
Jane Cronin Scanlon (1922- )
Gloria Olive (1923-2006)
Yvonne Choquet-Bruhat (1923- )
Cathleen Morawetz (1923- )
Evelyn Boyd Granville (1924- )
Mary Ellen Rudin (1924-2013)
Olga Arsen'enva Oleinik (1925-2001)
Carol Karp (1926-1972)
Vera Nikoaevna Maslennikova (1926-2000)
Lida Barrett (1927- )
Joan S. Birman (1927-)
Hu Hesheng (1928-)
1930-1939
Mary Catherine Bishop Weiss (1930-1966)
Valentina Mikhailovna Borok (1931-2004)
Vera Pless (1931- )
Vivienne Malone-Mayes (1932-1995)
Grace Alele Williams (1932- )
Etta Falconer (1933-2002)
Sharon Menard (1934- )
Lesley Sibner (1934-2013)
Alexandra Bellow (1935- )
Louise Hay (1935-1989)
Gloria Hewitt (1935- )
Bhama Srinivasan (1935- )
Nina Uraltseva (1935- )
Argelia Velez-Rodriguez (1936- )
Judith D. Sally (1937- )
Marina Ratner (1938- )
Mary F. Wheeler (1938- )
Mary Gray (1939- )
Doris Schattschneider (1939- )
1940-1949
Linda Keen (1940- )
Cora Sadosky (1940-2010)
Lenore Blum (1942- )
Nancy Kopell (1942- )
Idun Reiten (1942- )
Karen Uhlenbeck (1942- )
Evelyn M. Nelson (1943-1987)
Krystyna Kuperberg (1944- )
Jean Taylor (1944- )
Margaret Wright (1944- )
Dusa McDuff (1945- )
Mary Pensworth Reagor (1945- )
Judith Roitman (1945- )
Linda Rothschild (1945- )
Sylvia Young Wiegand (1945- )
Sun-Yung Alice Chang (1948- )
Raman Parimala (1948- )
Cheryl Praeger (1948- )
Fan Chung (1949- )
1950-1959
Nancy Reid (1952- )
Lai-Sang Young (1952- )
Ingrid Daubechies (1954- )
Verdiana Grace Masanja (1954- )
Bernadette Perrin-Riou (1955- )
Irene Fonseca (1956- )
Freda Porter (1957- )
Abigail Thompson (1958- )
1960-1969
Sijue Wu (1964- )
Irene Hueter (1965- )
Karen E. Smith (1965- )
Svenlana Jitomirskaya (1966- )
1970-1979
Maryam Mirzakhani (1977- )
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Nineteenth Century
1800-1819
Ada Byron Lovelace (1815-1852)
1820-1839
Florence Nightingale (1820-1910)
Mary Everest Boole (1832-1916)
1840-1859
Susan Jane Cunningham (1842-1921)
Elizaveta Fedorovna Litvinova (1845-1919)
Christine Ladd- Franklin (1847-1930)
Sofia Kovalevskaya (1850-1891)
Ellen Amanda Hayes (1851-1930)
Hertha Ayrton (1854-1923)
Ida Metcalf (1857-1952)
Charlotte Angas Scott (1858-1931)
Anna Julia Cooper (1858-1964)
1860-1869
Charlotte Barnum(1860-1934)
Alicia Boole Stott (1860-1940)
Ruth Gentry (1862-1917)
Winifred Edgerton Merrill (1862-1951)
Anna Helene Palmie (1863-1946)
Leona May Peirce (1863-1954)
Helen Abbot Merrill (1864-1949)
Clara Eliza Smith (1865-1943)
Clara Latimer Bacon (1866-1948)
Annie MacKinnon Fitch (1868-1940)
Grace Chisholm Young (1868-1944)
Philippa Garrett Fawcett (1868-1948)
Anne Bosworth Focke (1868-1907)
Ida May Schottenfels (1869-1942)
Isabel Maddison (1869-1950)
Mary Frances Winston Newson (1869-1959)
Emilie Norton Martin (1869-1936)
1870-1879
Agnes Baxter (1870-1917)
Virginia Ragsdale (1870-1945)
Louise Duffield Cummings (1870-1947)
Lao Genevra Simons (1870-1949)
Roxana Hayward Vivian (1871-1961)
Elizabeth Dickerman (1872-1954)
Elizabeth Stephansen (1872-1961)
Anna Irwin Young (1873-1920)
Suzan Rose Benedict (1873-1942)
Elizabeth Buchanan Cowley (1874-1945)
Charlotte Elvira Pengra (1875-1916)
Grace M. Bareis (1875-1962)
Ruth Goulding Wood (1875-1939)
Florence Eliza Allen (1876-1960)
Nadeschda Gernet (1877-1943)
Bird Margaret Turner (1877-1962)
Mary Emily Sinclair (1878-1955)
1880-1889
Elizabeth R. Bennett (1880-1972)
Hilda Phoebe Hudson (1881-1965)
Mayme I. Logsdon (1881-1967)
Helen Brewster Owens (1881-1968)
Emmy Noether (1882-1935)
Edith Clarke (1883-1959)
Anna Pell Wheeler (1883-1966)
Annie Dale Biddle Andrews (1885-1940)
Pauline Sperry (1885-1967)
Cora Barbara Hennel (1886-1947)
Josephine E. Burns (1887-1969)
Goldie Printis Horton (1887-1972)
Sister Mary Gervase (1888-1926)
Mildred Leonora Sanderson (1889-1914)
Claribel Kendall (1889-1965)
Agnes Meyer Driscoll (1889-1971)
1890-1899
Olive Clio Hazlett (1890-1974)
Euphemia Lofton Haynes (1890-1980)
Lorna Mary Swain (1891-1936)
Elizabeth Morgan Cooper (1891-1967)
Teresa Cohen (1892-1992)
Hilda Geiringer von Mises (1893-1973)
Anna Margaret Mullikin (1893-1975)
Cecilia Krieger (1894-1974)
Dorothy Maud Wrinch (1894-1976)
Sof'ja Aleksandrovna Janovskaja (1896-1966)
Nola Haynes (1897-1996)
Marguerite Lehr (1898-1988)
Gertrude Blanch (1898-1996)
Marie Litzinger (1899-1952)
Pelageya Yakovlevna Polubarinova-Kochina (1899-1999)
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Eighteenth Century and Before
Theano (6th Century B.C.)
Hypatia (370?-415)
Elena Lucrezia Cornaro Piscopia (1646-1684)
Emilie du Chatelet (1706-1749
Maria Gaetana Agnesi (1718-1799)
Caroline Herschel (1750-1848)
Sophie Germain (1776-1831)
Mary Fairfax Somerville (1780-1872)
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I have never seen any Female student aware of all these. I have never met a woman who sees these women as her hero.
:-)