Emi Neter - lays the foundation for modern algebra

Neter, thought of becoming a language teacher, in the end followed in the footsteps of her father, a professor of mathematics at a time when women were forbidden to study at universities. Worked at the University of Göttingen - a stronghold of the mathematicians - most of them Jewish, and was fired with the rise of the Nazis

Today, March 23, in 1882, Emmy Amalie Noether was born, a mathematician who changed both the face of mathematics and the face of physics and even received praise from Einstein. Emily Nether's father, Max Nether was an important mathematician, and a professor in Erlangen but he came from a family of merchants. Her mother, Ida Kapomann, came from a wealthy Jewish family in Cologne.

My mother was the oldest of four children, she was not unusual in her childhood. Her teachers and classmates knew my mother as wise, sociable and well-liked. However, she was one of the few Jews in her class.

After finishing elementary school, she attended the state high school for girls in Erlangen. In high school she studied German, English, French and mathematics and also took piano lessons. At this point she intended to become a language teacher and after improving her studies in English and French she passed the Bavarian state matriculation exams in 1900 with a very good grade, with the lowest grade being in teaching skill.

However Neter did not become a language teacher. Instead, she decided to take a difficult route for women at the time and study mathematics at university. Women were only allowed to study at German universities unofficially and every professor had to give them permission to participate in his course. Neter obtained permission to attend courses in Erlangen in 1900-1902. She was one of only two girls to do so. In addition to math courses, she continued to be interested in languages ​​and also studied with a professor of Roman studies and with the historian.

At the same time, she began preparing for the general exams that allowed those who passed them to be admitted to any of the universities - what we now call matriculation exams, which she eventually passed in Nuremberg in July 1903, after which she moved to the University of Göttingen where she studied with Karl Schwarzschild, Otto Blumenthal, David Hilbert Felix Klein and Hermann Minkowski. Again she was not allowed to study as a full-time student, and could only listen to lectures and not take exams. After one semester in Göttingen she returned to Erlingen.

In the meantime the law was changed and women could study on an equal basis with men and indeed in 1904 she began to study only mathematics in Erlingen. In 1907 she received her PHD degree after completing a doctoral thesis under the guidance of Paul Gordon in which she merged Gordon's practical approach with David Hilbert's theoretical approach thirty years earlier.

After completing the doctorate, the accepted advancement in the academy was supposed to be recognition, however this track was not open to women and therefore Neter stayed in Erlengen and helped her father, mainly due to his disabilities. Neter also worked on independent research. In particular, she was influenced by Ernst Fischer, who succeeded Gordon in the chair of mathematics when he retired in 1911. Nether wrote about Fischer's influence: "Above all I want to thank Mr. Fischer from whom I received a great impetus to study abstract algebra from the arithmetical point of view and this was the area that dominated all my later works More".

Fischer's influence moved Nether towards Hilbert's abstract approach and away from Gordon's practical approach. Gordon also recognized her achievements, and realized that despite the impressive achievement, his theory had limitations.

Nether's prestige grew rapidly as her works were published. In 1908 she was elected to the Palermo Mathematical Circle, and in 1909 she was invited to join the German Mathematical Society and in the same year she was invited to lecture at the society's annual meeting in Salzburg, where she lectured on the fields she researched. In 1913 she lectured in Vienna, also at a meeting of the German Mathematical Society. In Vienna she visited Franz Martens and the two discussed mathematical matters.

Natar trial
During the years she worked in Erlangen, she advised two doctoral theses for students who were officially supervised by her father. In 1915 Hilbert and Klein invited her to return to Göttingen. The reason was that Hilbert began researching in the field of physics, in particular on ideas about the theory of relativity close to those of Einstein and thus theoretical physics won the principle of equivalence between symmetries and conservation laws, called Nether's theorem.

These fundamental findings were praised by Einstein in a letter to Hilbert, in which he referred to the penetration of Nether's mathematical thinking into physics. Neter came to Göttingen during the First World War, and during this difficult period she lived in poverty and became an extreme socialist, but these were fruitful years in everything related to mathematics.

After a long struggle by Hilbert and Klein with the university authorities, she was recognized and in 1919 she received the status of a lecturer from abroad. Hilbert allowed Nether to teach when he published her courses under his name "with the assistance of Dr. Emi Nether".

In 1919 Neter moved on to develop the theory of ideals which became a central topic in mathematics. Her work from 1921 in which she laid the foundations for this theory is an important milestone in the development of modern algebra.

In 1924 van der Wierden arrived in Göttingen and spent a sabbatical year doing research with Nether. After his return to Amsterdam he wrote his book "Modern Algebra". Most of the second volume of the book was devoted to Neter's work. From 1927 onwards Nether collaborated with Helmut Hesse and Richard Brauer on non-commutative algebra. The three together proved the Albert-Brower-Hesse-Nather theorem (Adrian Albert reached the same results at the same time, in the United States).

Her main research in the field was published in 1932. In addition to studying and researching, Neter helped edit the mathematical yearbook. Most of her works appeared in studies written by colleagues and students and not under her name. In this year she also won the prize for the promotion of mathematical knowledge named after Alfred Ackerman Townbar.

In April 1933, the Nazis came to power and Nether's contribution to mathematics was not considered. She was fired from the University of Göttingen just because she was Jewish. She did not receive a pension or any other form of compensation but despite this she considers herself more fortunate than others. On May 10, 1933, she writes to Helmut Hesse. "I have a small inheritance, and I never built on the pension."

She received an invitation to be a visiting professor at Bryn Mawr College in Pennsylvania, USA and in October 1933 she sailed to the USA. She wanted to wait for a job application at the University of Oxford in Britain, but accepted the American invitation after it became clear that she had to leave quickly. Together with the Head of the Faculty of Mathematics, Anna Wheeler for the translation of Jordan's book "Modern Algebra". In early 1934 she lectured at the Institute for Advanced Studies in Princeton.

Neter returned to visit Germany in the summer of 1934 and there she met for what turned out to be the last time with her brother and visited Artin in Hamburg. She returned to the US where her position at Brin was extended and she continued her weekly lecture at Princeton, which was attended by her colleague Richard Bauer.

Nether's death was quick and unexpected. In April 1935, the doctors discovered that she had a tumor. Two days later they operated on her and discovered additional tumors that were considered benign and therefore were not removed. The operation was considered a success and for three days her condition improved, but on the fourth day she collapsed and developed a high fever. She died that day.

Although she received little recognition in her lifetime considering her contribution to the advancement of mathematics, she was honored posthumously in many ways. A crater on the moon is named after her, a street in her hometown is named after her and the school she attended is now named after my mother Neter. Many organizations called for scholarships and lectures in her name. The Institute for Mathematical Studies at Bar Ilan University is also named after her.

For the full review, the Institute of Mathematics at the University of St. Andreas in Scotland

Here it is finally here - the divine particle - a review following Peter Higgs and François Englert winning the Nobel Prize, in which Nether's contribution is also mentioned. Dr. Moshe Nachmani
Emi Neter (or: about women and mathematics and conservation laws that are less good and better) - on Gadi Alexandrovich's blog "not accurate"