Emmy Noether

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Biography of Emmy Noether, notable German mathematician, who deserves to be called the creator of modern algebra. Her legacy is recognized by the entire scientific world.

Emmy Noether’s contribution had a wide and profound influence on the development of modern algebra and topology.

She studied the mathematical concepts of ring and ideal, unified the different previous approaches into a single theoretical body, and gave a new approach to algebraic geometry.

Thanks to the works of Emmy Noether, the brilliant Albert Einstein was able to carry out the mathematical formulation of some aspects of general relativity.

Emmy Noether’s early life and family

Emmy Noether was born on March 23, 1882 in the university city of Erlangen, in the federal state of Bavaria, in southern Germany.

Her parents were Ida Kaufmann and Max Noether.

Her father was already a renowned mathematician at the University of Heidelberg, before he moved to the University of Erlangen.

Her mother belonged to a very wealthy family.

In 1883, they had their son Alfred. Then in 1884 Emmy Noether’s little brother Fritz was born.

When she was seven, Emmy Noether attended the girls’ school in Erlangen. Until 1887, she studied German, English, French, and arithmetic. She also followed dance and piano classes.

Emmy Noether in her youth

After this basic training, her parents recommended that she study French and English to become a language teacher. However, she decided that she did not want to settle for teaching French or English to young ladies of wealthy classes.

For three years, until 1900, Emmy Noether prepared herself to enroll at Erlangen University. At that time women were not instructed for the entrance exam. Men back then were horrified by wise women.

Emmy was one of only two women, out of 986 students enrolled that year.

Despite successfully passing the entrance exam, she was only allowed to attend classes as a listener. In addition, to enter she had to ask for express permission from the professor who taught them.

In those years she attended the classes of distinguished mathematicians: Florence Blumenthal, David Hilbert, Félix Klein and Hermann Minkowski.

In 1907, she passed her thesis with the degree of doctor “cum laude”. The thesis became famous and focused on the invariants of algebra. However, because she was a woman, she was not eligible for a postdoctoral degree.

She continued her studies at the University of Göttingen, but returned to Erlangen where her father was a professor.

Erlangen University
Erlangen University is also the University of Nuremberg. Credit: Wikipedia. Author: Akriesch.

Early years in Emmy Noether’s working life

This is how Emmy Noether taught at the University of Erlangen for seven years, without receiving any salary. At that time she released her work on novel mathematical theories.

In 1908, Emmy was able to publish her doctoral thesis; With this, her prestige grew as did her numerous publications.

This thesis earned her the election of a member of the “Circolo Matematico di Palermo”, a mathematical society founded in Palermo, and highly recognized at the beginning of the 20th century.

The following year, in 1909, she was also elected a member of the “German Mathematical Society“.

These distinctions enabled her to start lecturing at some mathematicians’ meetings.

Emmy Noether received help from David Hilbert

In 1915, Emmy traveled to Göttingen at the invitation of two great German mathematicians: David Hilbert and Félix Klein. Both of them were determined to get a permanent job for her at the university.

David Hilbert
The great German mathematician, David Hilbert. Credit: Wikipedia

To obtain her teaching qualification, Emmy Noether presented an abstract algebra paper, along with twelve already published articles and two additional manuscripts.

The academic authorities could not stop authorizing her to practice as a teacher. But, this authorization to teach master classes, was conditional on the entire faculty agreeing on it. That was not the case.

Her friend and admirer David Hilbert solved this unfortunate situation by authorizing Emmy Noether to teach courses on her behalf.

Emmy Noether had to teach under the name of David Hilbert for four years and without receiving any payment. She was able to survive thanks to a small inheritance from her parents.

David Hilbert and Félix Klein hoped that Emmy Noether’s new mathematical theories could serve to validate Albert Einstein’s nascent general theory of relativity. This Einstein theory seemed to violate the law of conservation of energy.

Albert Einstein
Albert Einstein, the genius of the 20th century, admired Emmy Noether. Credit: Wikipedia

Emmy Noether’s beautiful and powerful theorem

Emmy Noether developed a theorem that is key to understanding the most sophisticated physics. It is an extremely elegant theorem that incorporates the beauty of the concepts of symmetry into the principles of physics.

She proved her theorem in 1915, but did not publish it until 1918.

Many mathematicians claim that Emmy Noether developed the most beautiful theorem in the world, endowed with mathematical potential of great consequence. It is one of the theorems where physics and mathematics connect in a very elegant way.

What Emmy Noether did was relate the symmetry of a system to the physical quantities that remain. Such is the case of energy, which is neither created nor destroyed, but is transformed. That is called a conserved amount.

And that affects all physical systems, from a single crystal to a planetary system.

Emmy Noether created a fundamental tool for theoretical physics. She solved the problem not only for general relativity, but she determined the quantities conserved for any system of physical laws that possesses some kind of continuous symmetry.

When Einstein received the work from Emmy Noether, he wrote to David Hilbert, expressing his admiration for this brilliant mathematician.

Emmy Noether as an accredited teacher

In 1922, Emmy Noether was named “extraordinary and unofficial professor” (sic). She was not entitled to a salary, but was able to obtain small remunerations, due to her degree in algebra.

In 1923 Emmy Noether received a small salary at the University of Gottingen. However, she was never awarded the rank of full professor.

But still, she surrounded herself with a group of students and researchers in Göttingen, who had already become distinguished professors and researchers.

Göttingen University
The University of Göttingen has the title of University of Excellence. Credit: Wikipedia

During these years, Emmy Noether carried out her fundamental studies on abstract algebra, group theory, ring theory, and number theory.

Emmy Noether developed principles that unified algebra, geometry, linear algebra, topology and logic.

During the 1928-29 academic year, Emmy Noether spent a semester as a visiting professor at the “Moscow University” and was invited to the “International Mathematical Congress” in Bologna.

In September 1932 she was invited to the “International Congress of Mathematics” in Zurich. She was the first woman to deliver a conference in the plenary of these congresses. That same year. Emmy Noether received the “Alfred Ackermann-Teubner Memorial Prize“, established for the Advancement of Mathematical Knowledge.

Emmy Noether was forced to leave Germany

Being an intellectual, a pacifist and a Jew paid tribute to Emma Noether. In April 1933 her right to practice as a teacher was withdrawn.

With the rise of Nazism, Emmy Noether was fired from the University of Göttingen. Soon after, she was forced to leave Germany.

At the end of that year 1933, she left for the United States as a visiting professor for a year at a women’s university in the city of Bryn Mawr (Pennsylvania): “Bryn Mawr College”, thanks to a grant from the Rockefeller Foundation.

In February 1934 she began working in Princeton (New Jersey), at the “Institute for Advanced Studies”, where Albert Einstein was also located.

In the summer of 1934, she returned for the last time to Germany to see her brother Fritz, visit old friends, and close her home.

Emmy Noether’s death and recognitions

In 1935, they detected a tumor in the pelvis and an ovarian cyst. She underwent surgery, but a series of complications led to her death four days later, on April 14, 1935.

In a letter that Albert Einstein addressed to “The New York Times” on May 1, 1935, he said: “Her visionary friends of science in the USA were fortunate to be able to make the necessary arrangements with the Bryn Mawr College and the University until the day of her death, Princeton was to find in the United States not only colleagues who appreciated her friendship, but also grateful wards, whose enthusiasm made her last years the happiest and perhaps the most fruitful of her entire career. “

They are named after Emmy Noether:

  • A street in Erlangen, her birth city.
  • A path in Gotingen.
  • A roundabout near Munich, the “Emmy-Noether-Ring“.
  • Her old Institute in Erlangen.
  • A crater on the Moon.
  • Asteroid 7001 Noether, 6,122 meters in diameter, in the asteroid belt.
  • Various university buildings.
  • Many concepts in algebra: noetherian rings, noetherian groups, noetherian modules, noetherian topological spaces.

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