These questions are based on the feature article “Emmy Noether’s vision.”
1. When and where was Emmy Noether born, and who were her parents?
Possible student response: Amalie Emmy Noether was born in 1882 in Erlangen, Germany. Her parents were Max Noether, a well-known mathematician and professor, and Ida Amalia Noether.
2. Describe Emmy Noether’s education.
Possible student response: As a child, she solved puzzles that stumped other children, but her mathematical genius was not obvious. Women could audit university courses at the University of Erlangen with the permission of the professor, but could not be official university students until 1904. As soon as the rules changed, Emmy Noether enrolled in the University of Erlangen, where her father was a professor. She earned her Ph.D. in mathematics in 1907.
3. Where did Emmy Noether work?
Possible student response: Noether worked without pay at the University of Erlangen until 1915. She then moved to the University of Göttingen after being recruited by mathematicians David Hilbert and Felix Klein. After the Nazi-led government removed her from the university in 1933, she moved to Bryn Mawr College in Pennsylvania. While Noether was in the United States, she also lectured at the Institute for Advanced Study in Princeton, N.J.
4. What obstacles did Emmy Noether face during her pursuit of an academic career? Find a quote from a scientist mentioned in the article that exemplifies the challenge that she faced as a woman pursuing a career in academia.
Possible student response: Women were not allowed to take university courses for credit until 1904 at the University of Erlangen, so she was only able to audit classes until this rule changed. She worked without pay at the University of Erlangen from 1907 to 1915. Based on her accomplishments, she was invited to the University of Göttingen in 1915, but even there, she could not teach under her own name until 1919 and did not receive a salary until 1923. In 1933, the Nazi-led government removed Noether from her university position because she was Jewish and was suspected of having political beliefs that did not align with the Nazi party. When Noether died in 1935, Albert Einstein wrote in the New York Times: “Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.” But Einstein’s compliment emphasized the fact that Noether was a woman, rather than saying she was a genius and leaving it at that. Other mathematicians that eulogized Noether commented on her appearance and romantic life, showing that even those who admired her judged her by different standards than they judged men.
5. What are conservation laws? Give an example of a law of conservation.
Possible student response: Conservation laws state that a particular quantity must stay constant over time. The law of conservation of energy explains that the energy of an isolated system will remain constant over time.
6. What is the difference between discrete and continuous symmetry? Give an example of continuous symmetry.
Possible student response: The symmetries that we see and admire around us, such as human faces or snowflake patterns, are discrete — the symmetries hold only for certain values. However, continuous symmetries hold no matter how far an object moves in space or time. An example of continuous symmetry is translational symmetry, in which the laws of physics remain the same as we move about the cosmos.
7. What is Noether’s theorem? How does it relate to the conservation laws of energy, momentum and angular momentum?
Possible student response: Noether’s theorem defines a link between conservation laws and continuous symmetries. For every continuous symmetry, there is a corresponding quantity that remains constant (or is conserved).
According to Noether’s theorem, energy conservation comes from translational symmetry in time. For example, a rocket launch converts chemical energy in fuel into kinetic energy and potential energy, but the total energy remains constant over time.
Likewise, momentum conservation is due to translational symmetry in space. For example, when one ball in Newton’s cradle hits the row, a ball on the other end flies outward, conserving momentum.
The conservation of angular momentum emerges from rotational symmetry, the idea that physics stays the same as we spin around in space. For example, a skater’s twirl speeds up when the skater’s arms are pulled in. That’s because total angular momentum must stay the same.
8. Why is Noether’s theorem important for a variety of real-world applications?
Possible student response: Conservation laws govern the equations of motion for a wide variety of systems, from balls rolling down a hill to nuclear fusion and from waves on the ocean to air flowing over an airplane wing. With certainty in the laws, scientists can solve problems related to these motions.
9. In what other ways is Noether’s theorem important for modern physics?
Possible student response: Noether’s theorem provided connections that revealed a rhyme and reason behind properties of the universe that once seemed arbitrary. Her theorem became a foundation of the standard model of particle physics, which describes nature on tiny scales and predicted the existence of the Higgs boson — a subatomic particle, discovered in 2012, that helps scientists understand how particles get their mass. Today, physicists are still searching for new particles predicted by Noether’s theorem. And researchers are relying on her theorem to fully understand potential theories that might unite gravity and quantum physics.
10. Describe another one of Noether’s theorems mentioned in the article. What else did she accomplish?
Possible student response: Noether’s second theorem shows that generally covariant theories (Einstein’s general relativity is an example) adhere to a strange type of conservation law. In such theories, the equations apply whether an observer is accelerating or standing still. In addition to her theorems, Noether also started the discipline of abstract algebra.
11. What questions do you still have after reading the article?
Possible student response: What are the mathematical details of how Noether’s first theorem works? What exactly is a generally covariant theory? What is the meaning of Noether’s second theorem? What were her specific contributions to abstract algebra? What new physics theories have been developed with the aid of Noether’s theorem? What other women contributed to the history of science but are not as well-known as they should be? What other women tried to contribute to the history of science but were prevented by various obstacles? What systemic or social obstacles remain today, depending on a person’s gender, race and economic status?
12. If you were asked to describe Emmy Noether to a friend, what would you say? Find a quote from the article that highlights her accomplishments.
Emmy Noether was an influential German, Jewish mathematician who proved a theorem that revolutionized the way that physicists study the universe. Despite the challenges she faced as a woman pioneer in STEM, she gained respect for her academic talents. Emily Conover describes Noether’s ideas in math as “so prominent that her name has become an adjective.”
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