They were her boys.
And she revolutionized the way to they thought about things.
And she proved it.
No, not a physical proof, for there is no such thing. But a Mathematical proof. Ironclad, never changing — Well almost.
To imitate, but not too much, if our discipline is not to become a marsh, a large one to be sure, but stagnant, with neither life nor movement. First imitate to learn, and then renew ourselves. … I love, at least when I am able, to regard science from a personal point of view, and always, again when possible, go beyond current opinions and look at the problem from a new perspective. I have the impression that some ways must be left behind, some mental habits must be abandoned, if we are not to clip the wings of progress. Even to science we must sometimes repeat Charon’s cry: By another way, by other ports, not here, you will find passage across the shore. In my role as teacher I hope to be able to show you other ways, if not other ports. — Giuseppe Vitali
Emmy was a teacher too. And she fabricated some mathematics that binds them all, as they sought their own passages and ports of call. The Rings that Bind.
For she had had obstacles and a vast ocean to cross in her own passage in life — she was able to reach another shore and dwell for only a short while. But her perspective and rings will live on forever.
Amalie Emmy Noether, Architect Rational, ( 23 March 1882 – 14 April 1935), sometimes referred to as Emily or Emmy, was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, Norbert Wiener and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and algebras. In physics, Noether’s theorem explains the fundamental connection between symmetry and conservation laws. [Wikipedia, revised]
She had to overcome the obstacle that she was a woman in a man dominated endeavour and an age when women were limited by laws and tradition.
She was born to a Jewish family in the Bavarian town of Erlangen; her father was mathematician Max Noether. Emmy originally planned to teach French and English after passing the required examinations, but instead studied mathematics at the University of Erlangen, where her father lectured. After completing her dissertation in 1907 under the supervision of Paul Gordan, she worked at the Mathematical Institute of Erlangen without pay for seven years (at the time women were largely excluded from academic positions)
In 1915, she was invited by David Hilbert and Felix Klein to join the mathematics department at the University of Göttingen, a world-renowned center of mathematical research. The philosophical faculty objected, however, and she spent four years lecturing under Hilbert’s name. Her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent.
Noether remained a leading member of the Göttingen mathematics department until 1933; her students were sometimes called the “Noether boys“. [Wikipedia, revised]
The remarkable thing is understanding never stays put.
It is important always to get a new understanding … … … understanding can be improved
“Before Noether’s Theorem the principle of conservation of energy was shrouded in mystery, leading to the obscure physical systems of Mach and Ostwald. Noether’s simple and profound mathematical formulation did much to demystify physics.” — Ransom Stephens
Her ideas spread throughout the physics and mathematics communities, for Göttingen was the center of the universe for math and physics at the time, but she wasn’t concerned too much about gaining fame from it.
For Architects, the world exists primarily to be analyzed, understood, explained – and re-designed. External reality in itself is unimportant, little more than raw material to be organized into structural models. What is important for Architects is that they grasp fundamental principles and natural laws, and that their designs are elegant, that is, efficient and coherent. [Please Understand Me II]
Another problem was she was Jewish, and when Hitler came to power, she had to emigrate to the US.
When Adolf Hitler became the German Reichskanzler in January 1933, Nazi activity around the country increased dramatically. At the University of Göttingen the German Student Association led the attack on the “un-German spirit” attributed to Jews and was aided by a privatdozent named Werner Weber, a former student of Emmy Noether. Antisemitic attitudes created a climate hostile to Jewish professors. One young protester reportedly demanded: “Aryan students want Aryan mathematics and not Jewish mathematics.”
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. In April 1933 Noether received a notice from the Prussian Ministry for Sciences, Art, and Public Education which read: “On the basis of paragraph 3 of the Civil Service Code of 7 April 1933, I hereby withdraw from you the right to teach at the University of Göttingen.” Several of Noether’s colleagues, including Max Born and Richard Courant, also had their positions revoked. Noether accepted the decision calmly, providing support for others during this difficult time. 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.” Typically, Noether remained focused on mathematics, gathering students in her apartment to discuss class field theory. When one of her students appeared in the uniform of the Nazi paramilitary organization Sturmabteilung (SA), she showed no sign of agitation and, reportedly, even laughed about it later. [Wikipedia, revised]
Emmy was about ideas.
Ruthless pragmatists about ideas, and insatiably curious, Architects are driven to find the most efficient means to their ends, and they will learn in any manner and degree they can. They will listen to amateurs if their ideas are useful, and will ignore the experts if theirs are not. Authority derived from office, credential, or celebrity does not impress them. Architects are interested only in what make sense, and thus only statements that are consistent and coherent carry any weight with them. [Please Understand Me II]
Einstein was to say about her:
The efforts of most human-beings are consumed in the struggle for their daily bread, but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. Beneath the effort directed toward the accumulation of worldly goods lies all too frequently the illusion that this is the most substantial and desirable end to be achieved; but there is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual’s own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.
In Göttingen, Noether supervised more than a dozen doctoral students. Her first student was a woman, Grete Hermann, who helped Werner Heisenberg on quantum theory plus Hermann’s critique of John Von Neumann’s no-hidden variable theory is still very relevant and important today. Noether also supervised others like Max Deuring, Hans Fitting, Chiungtze Tsen, Ernst Witt, and Wolfgang Krull which further developed their own ideas because Emmy was to be able to show them other ways.
Some consider Noether’s theorem, as it is now called, as important as Einstein’s theory of relativity; it undergirds much of today’s vanguard research in physics, including the hunt for the almighty Higgs boson.
In 1933, she had to flee her own country, Germany, to the shores of America. She obtained a teaching position at Bryn Mawr College, in Pennsylvania, with the help from Einstein. After only two years in America, a hasty operation to remove ovarian cancer, she died — probably from an infection. Her body was cremated and the ashes interred under the walkway around the cloisters at Bryn Mawr, but her ideas live on, still relevant today and tomorrow.