Emmy Noether Google Doodle

Emmy Noether: 133rd Birthday of the Most Important Woman of Mathematics

Emmy Noether (German: official name Amalie Emmy Noether; 23 March 1882 – 14 April 1935), was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, Norbert Wiener and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and algebras. In physics, Emmy Noether‘s theorem explains the fundamental connection between symmetry and conservation laws.

Emmy Noether Google Doodle

Emmy Noether: Google Doodle

Emmy Noether was born to a Jewish family in the Bavarian town of Erlangen; her father was mathematician Max Noether. Emmy Noether originally planned to teach French and English after passing the required examinations, but instead studied mathematics at the University of Erlangen, where her father lectured. After completing her dissertation in 1907 under the supervision of Paul Gordan, she worked at the Mathematical Institute of Erlangen without pay for seven years (at the time women were largely excluded from academic positions). In 1915, she was invited by David Hilbert and Felix Klein to join the mathematics department at the University of Göttingen, a world-renowned center of mathematical research. The philosophical faculty objected, however, and she spent four years lecturing under Hilbert’s name. Her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent.

Emmy Noether remained a leading member of the Göttingen mathematics department until 1933; her students were sometimes called the “Noether boys”. In 1924, Dutch mathematician B. L. van der Waerden joined her circle and soon became the leading expositor of Emmy Noether’s ideas: her work was the foundation for the second volume of his influential 1931 textbook, Moderne Algebra. By the time of her plenary address at the 1932 International Congress of Mathematicians in Zürich, her algebraic acumen was recognized around the world. The following year, Germany’s Nazi government dismissed Jews from university positions, and Emmy Noether moved to the United States to take up a position at Bryn Mawr College in Pennsylvania. In 1935 she underwent surgery for an ovarian cyst and, despite signs of a recovery, died four days later at the age of 53.

Emmy Noether

Emmy Noether

Emmy Noether’s mathematical work has been divided into three “epochs”.

Emmy Noether: The first epoch

In the first (1908–19), she made significant contributions to the theories of algebraic invariants and number fields. Her work on differential invariants in the calculus of variations, Emmy Noether’s theorem, has been called “one of the most important mathematical theorems ever proved in guiding the development of modern physics”.

Emmy Noether: The second epoch

In the second epoch (1920–26), she began work that “changed the face of abstract algebra”. In her classic paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains, 1921) Emmy Noether developed the theory of ideals in commutative rings into a powerful tool with wide-ranging applications. She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor.

Emmy Noether: The third epoch

In the third epoch (1927–35), she published major works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. In addition to her own publications, Emmy Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.

Biography of Emmy Noether

Emmy’s father, Max Noether, was descended from a family of wholesale traders in Germany. He had been paralyzed by polio at the age of fourteen. He regained mobility, but one leg remained affected. Largely self-taught, he was awarded a doctorate from the University of Heidelberg in 1868. After teaching there for seven years, he took a position in the Bavarian city of Erlangen, where he met and married Ida Amalia Kaufmann, the daughter of a prosperous merchant. Max Noether’s mathematical contributions were to algebraic geometry mainly, following in the footsteps of Alfred Clebsch. His best known results are the Brill–Noether theorem and the residue, or AF+BG theorem; several other theorems are associated with him, including Max Noether’s theorem.

Emmy Noether was born on 23 March 1882, the first of four children. Her first name was “Amalie”, after her mother and paternal grandmother, but she began using her middle name at a young age. As a girl, she was well liked. She did not stand out academically although she was known for being clever and friendly. Emmy was near-sighted and talked with a minor lisp during childhood. A family friend recounted a story years later about young Emmy quickly solving a brain teaser at a children’s party, showing logical acumen at that early age.Emmy was taught to cook and clean, as were most girls of the time, and she took piano lessons. She pursued none of these activities with passion, although she loved to dance.

She had three younger brothers. The eldest, Alfred, was born in 1883, was awarded a doctorate in chemistry from Erlangen in 1909, but died nine years later. Fritz Noether, born in 1884, is remembered for his academic accomplishments: after studying in Munich he made a reputation for himself in applied mathematics. The youngest, Gustav Robert, was born in 1889. Very little is known about his life; he suffered from chronic illness and died in 1928.

Seminal work in abstract algebra

Although Emmy Noether’s theorem had a profound effect upon physics, among mathematicians she is best remembered for her seminal contributions to abstract algebra. As Nathan Jacobson says in his Introduction to Noether’s Collected Papers,

The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her – in published papers, in lectures, and in personal influence on her contemporaries.

in a ring. The following year she published a landmark paper called Idealtheorie in Ringbereichen, analyzing ascending chain conditions with regard to (mathematical) ideals. Noted algebraist Irving Kaplansky called this work “revolutionary”; the publication gave rise to the term “Noetherian ring” and the naming of several other mathematical objects as Noetherian.

In 1924 a young Dutch mathematician, B. L. van der Waerden, arrived at the University of Göttingen. He immediately began working with Noether, who provided invaluable methods of abstract conceptualization. Van der Waerden later said that her originality was “absolute beyond comparison”. In 1931 he published Moderne Algebra, a central text in the field; its second volume borrowed heavily from Noether’s work. Although Emmy Noether did not seek recognition, he included as a note in the seventh edition “based in part on lectures by E. Artin and E. Noether”. She sometimes allowed her colleagues and students to receive credit for her ideas, helping them develop their careers at the expense of her own.

Van der Waerden’s visit was part of a convergence of mathematicians from all over the world to Göttingen, which became a major hub of mathematical and physical research. From 1926 to 1930 Russian topologist Pavel Alexandrov lectured at the university, and he and Noether quickly became good friends. He began referring to her as der Noether, using the masculine German article as a term of endearment to show his respect. She tried to arrange for him to obtain a position at Göttingen as a regular professor, but was only able to help him secure a scholarship from the Rockefeller Foundation. They met regularly and enjoyed discussions about the intersections of algebra and topology. In his 1935 memorial address, Alexandrov named Emmy Noether “the greatest woman mathematician of all time”.

Country list of the Emmy Noether Google Doodle

Australia, Austria, Bahrain, Bulgaria, Canada, Chile, Colombia, Croatia, Egypt, Finland, Germany, Ghana, Greece, Hong Kong, Iceland, Iraq, Israel, Japan, Jordan, Kenya, Kuwait, Latvia, Lebanon, Libya, Mexico, Morocco, New Zealand, Nigeria, Oman, Palestine,  Peru, Poland, Portugal, Qatar, Saudi Arabia, Serbia, Singapore, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Tunisia, Turkey, Ukraine, United Arab Emirates and the United States