[4] Noether was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics.

In 1924, Dutch mathematician B. L. van der Waerden joined her circle and soon became the leading expositor of Noether's ideas; her work was the foundation for the second volume of his influential 1931 textbook, Moderne Algebra.

In addition to her own publications, 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.

A family friend recounted a story years later about young Noether quickly solving a brain teaser at a children's party, showing logical acumen at an early age.

[24] One of just two women in a university of 986 students, Noether was allowed only to audit classes rather than participate fully, and she required the permission of individual professors whose lectures she wished to attend.

[22][25][26] During the 1903–1904 winter semester, she studied at the University of Göttingen, attending lectures given by astronomer Karl Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert.

[42][43] From 1913 to 1916, Noether published several papers extending and applying Hilbert's methods to mathematical objects such as fields of rational functions and the invariants of finite groups.

In a joint department meeting on the matter, one faculty member protested: "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?

"[40][50][52][53] According to Pavel Alexandrov's recollection, faculty members' opposition to Noether was based not just in sexism, but also in their objections to her social-democratic political beliefs and Jewish ancestry.

[45] The following year she published the paper Idealtheorie in Ringbereichen,[67] analyzing ascending chain conditions with regards to (mathematical) ideals, in which she proved the Lasker–Noether theorem in its full generality.

[70] After returning to Amsterdam, he wrote Moderne Algebra, a central two-volume text in the field; its second volume, published in 1931, borrowed heavily from Noether's work.

[40][71] Van der Waerden's visit was part of a convergence of mathematicians from all over the world to Göttingen, which had become a major hub of mathematical and physical research.

[b][76] She tried to arrange for him to obtain a position at Göttingen as a regular professor, but was able only to help him secure a scholarship to Princeton University for the 1927–1928 academic year from the Rockefeller Foundation.

[104] There is no information about the first two, but it is known that Wichmann supported a student initiative that unsuccessfully attempted to revoke Noether's dismissal[105] and died as a soldier on the Eastern Front during World War II.

[120][121] Several of her colleagues attended her lectures and she sometimes allowed others (including her students) to receive credit for her ideas, resulting in much of her work appearing in papers not under her name.

This attitude caused her problems in Germany, culminating in her eviction from a pension lodging building, after student leaders complained of living with "a Marxist-leaning Jewess".

[128][129] In September of the same year, Noether delivered a plenary address (großer Vortrag) on "Hyper-complex systems in their relations to commutative algebra and to number theory" at the International Congress of Mathematicians in Zürich.

"[91] One of the first actions of Hitler's administration was the Law for the Restoration of the Professional Civil Service which removed Jews and politically suspect government employees (including university professors) from their jobs unless they had "demonstrated their loyalty to Germany" by serving in World War I.

Hermann Weyl later wrote that "Emmy Noether – her courage, her frankness, her unconcern about her own fate, her conciliatory spirit – was in the midst of all the hatred and meanness, despair and sorrow surrounding us, a moral solace.

[132][133] As dozens of newly unemployed professors began searching for positions outside of Germany, their colleagues in the United States sought to provide assistance and job opportunities for them.

Albert Einstein and Hermann Weyl were appointed by the Institute for Advanced Study in Princeton, while others worked to find a sponsor required for legal immigration.

Another source of support at the college was the Bryn Mawr president, Marion Edwards Park, who enthusiastically invited mathematicians in the area to "see Dr. Noether in action!

[148] The latter, after having been forced out of his job at the Technische Hochschule Breslau, had accepted a position at the Research Institute for Mathematics and Mechanics in Tomsk, in the Siberian Federal District of Russia.

[151] A few days after Noether's death, her friends and associates at Bryn Mawr held a small memorial service at College President Park's house.

[153] In the months that followed, written tributes began to appear around the globe: Albert Einstein joined van der Waerden, Weyl, and Pavel Alexandrov in paying their respects.

[42] Her friend and colleague Hermann Weyl described her scholarly output in three epochs: (1) the period of relative dependence, 1907–1919 (2) the investigations grouped around the general theory of ideals 1920–1926

Beginning with Carl Friedrich Gauss's 1832 proof that prime numbers such as five can be factored in Gaussian integers,[159] Évariste Galois's introduction of permutation groups in 1832 (although, because of his death, his papers were published only in 1846, by Liouville), William Rowan Hamilton's description of quaternions in 1843, and Arthur Cayley's more modern definition of groups in 1854, research turned to determining the properties of ever-more-abstract systems defined by ever-more-universal rules.

[202] Together, these theorems not only solve the problem for general relativity, but also determine the conserved quantities for every system of physical laws that possesses some continuous symmetry.

As noted by Hermann Weyl in his obituary, Noether's contributions to topology illustrate her generosity with ideas and how her insights could transform entire fields of mathematics.

[259] In a letter to The New York Times, Albert Einstein wrote:[5] In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.