Short answers, pulled from the story.
Emmy Noether was a German mathematician, born on the 23rd of March 1882, who made fundamental contributions to abstract algebra and developed theories of rings, fields, and algebras. She also proved Noether's theorem, which connects symmetry and conservation laws in physics. Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener described her as the most important woman in the history of mathematics.
Noether's theorem shows that a conservation law is associated with any continuous, differentiable symmetry of a physical system. For example, if physical laws behave the same regardless of orientation in space, the theorem shows angular momentum must be conserved. Felix Klein presented the paper, Invariante Variationsprobleme, on the 26th of July 1918, and physicists Leon M. Lederman and Christopher T. Hill have called the theorem possibly on a par with the Pythagorean theorem.
When David Hilbert and Felix Klein invited Noether to the University of Göttingen in 1915, the philosophical faculty objected to a woman becoming a privatdozent. She had no official position and lectured under Hilbert's name for four years until her habilitation was approved in 1919. The university began paying her only a small salary in 1923.
Noether developed the theory of ideals in commutative rings, and in her 1921 paper Idealtheorie in Ringbereichen she proved that every ideal in a ring satisfying the ascending chain condition is finitely generated. Objects satisfying the ascending chain condition are called Noetherian in her honor. Nathan Jacobson wrote that the development of abstract algebra is largely due to her.
In April 1933, Germany's Nazi government withdrew Noether's right to teach at Göttingen under the Law for the Restoration of the Professional Civil Service, which removed Jews from university positions. After negotiations with the Rockefeller Foundation, she took a position at Bryn Mawr College in Pennsylvania starting in late 1933, and also lectured at the Institute for Advanced Study in Princeton.
Emmy Noether died on the 14th of April 1935 at the age of 53. In April 1935 doctors discovered a tumor in her pelvis and an ovarian cyst during surgery. She appeared to recover for three days, then fell unconscious as her temperature soared to 109 degrees Fahrenheit. Her ashes were interred under the walkway around the cloisters of the Old Library at Bryn Mawr.