The mother of modern algebra
Emmy Noether
(Erlangen, Germania, 23/03/1882 - Bryn Mawr, Pennsylvania, 04/04/1935)
Historical context
In the late nineteenth century, the University of Göttingen was a benchmark for mathematics thanks to the contributions of Gauss, Dirichlet, and Riemann. In the 1920s, it became the world center of the discipline, with professors such as Hilbert, Noether, Landau, Weyl, Carathéodorye, and Minkowski, who died young. It attracted students from around the world, including the Italians Fermi, Levi, Civita, and Volterra. It became the model for the world’s leading physics and mathematics research centers, such as the Institute for Advanced Study in Princeton. In 1933, the rise of Nazism led to the flight of scientists, especially Jews, often to the United States, which thus became a world leader in research after World War II. Hilbert’s response to the Nazi minister who asked him “how was mathematics doing in Göttingen now that it had been freed from Jewish influence” is emblematic: “Mathematics in Göttingen? It no longer exists.”
Biography
Emmy Noether is recognized as one of the most important figures in 20th-century mathematics and is commonly referred to as the “mother of modern algebra” for her fundamental role in the development of abstract algebra and ring theory.
Emmy Noether was born in Erlangen, Bavaria, on March 23, 1882. Her father, Max Noether, was a prominent mathematician and a professor at the University of Erlangen. After graduating from a women’s college, Emmy expressed a desire to continue her studies in mathematics. However, German school regulations at the time prohibited regular university admission for women, allowing them at most to attend as auditors, without the right to sit exams. Between 1900 and 1903, Noether therefore attended lectures in mathematics, Romance, and history as an auditor. After taking her high school diploma privately, she moved for the 1903-04 semester to Göttingen, which, thanks to the efforts of Felix Klein, was emerging as a center of German mathematics. In addition to Klein, her professors included Minkowski, Hilbert, Otto Blumenthal (1876-1944), and Carl Runge (1856-1927). Following a change in the law, Noether was able to enroll at the University of Erlangen – Faculty of Philosophy – where she took courses exclusively in mathematics, being the only woman in a group of forty-six men.
After graduating, he began working at the Mathematical Institute in Erlangen without a formal contract or salary. His academic reputation grew rapidly, as did the number of his scientific publications.
In the spring of 1915, David Hilbert wanted to hire her in his department at the University of Göttingen, recognizing her—along with Einstein—as one of the most brilliant mathematical minds of the time. However, some professors at the university showed little interest in her extraordinary scientific abilities, focusing instead exclusively on the fact that she was a woman.
“What will our soldiers think when they return to university and find themselves forced to study at the mercy of a woman?” asked their faculty colleagues.
Hilbert then hired her as his assistant, even managing to get her to give lectures, which were officially announced under the name of Professor David Hilbert, and which, obviously, were unpaid.
In 1919, after having solved, the previous year, one of the most difficult problems to arise with Einstein’s theory of relativity, she was the first woman in Germany to receive permission to obtain a teaching qualification, with the comment that “only in exceptional cases is a woman’s mind capable of being creative in mathematics.”
Her research focused on abstract algebra, ring theory, and mathematical physics, with her most famous work being Noether’s Theorem of 1915, which links symmetries to conservation laws in physics.
Through his works, she organized and systematized abstract algebra, laying the conceptual foundation for much of modern algebra. Her method allowed for the unification of diverse mathematical concepts, highlighting the logical coherence of mathematical theories.
She spent the next few years receiving respect and esteem for her innovative work, and for her merits, she was granted permission to give a speech at the International Congress of Mathematicians in Zurich in 1932. The following year, the Nazi government expelled her, along with many other Jewish colleagues, from the University of Göttingen, and Emmy found asylum in the United States, where she obtained a position at Bryn Mawr College in Pennsylvania. There, in 1935, she underwent surgery that suddenly became complicated and led to her death after only four days. She was only 53 years old and “at the height of her creative power,” as Weil wrote in her obituary. Among the many eulogy speeches were that of Albert Einstein, published in the New York Times, and that of Van der Waerden, the only one in German, published in the journal “Mathematische Annalen,” which Emmy had long worked to organize. The latter was published in 1935 during the Nazi regime, despite the fact that it was about a Jew.
https://matematica.unibocconi.eu/matematici/emmy-noether
https://www.mondadorieducation.it/fisica-scientifica-ss2/madre-algebra-moderna/
