When talking about prominent figures of Mathematics, one would definitely be joking if they exclude Amalie Emmy Noether from the list. Despite being born during a period when patriarchial society was prevalent she has had great contributions to the field of Mathematics and Mathematical Physics. During the late 1800s and the early 1900s women were thought to be capable of only doing household chores and menial jobs. However, Emmy Noether took an unconventional path and decided on pursuing Mathematics at The University of Erlangen where her father, Max Noether lectured. After her graduation, she went on to complete her doctorate under the supervision of Paul Gordan. Her most notable works were on the fields of algebraic invariants, number fields, and algebraic topology. Among those dozens of research papers published her theorem also known as the Noether's theorem always stands out. When Einstein published his papers on the theory of general Relativity it summoned as many questions as it answered. One of the conundrums was energy wasn't conserved in some cases in general relativity (for example- the cosmological redshift).Einstein and other two physicists Hilbert and Klein were working to understand why the laws of conservation of energy were violated. That's when Emmy Noether kicked in the picture. Her expertise in symmetries led her to discover that the symmetries of a physical system are linked to physical quantities that are conserved, such as energy. This idea that linked symmetries of a system to the quantities that become conserved in the system later got known as Noether's theorem. Not only did Noether's theorem helped solve an anamoly in general relativity it also helped guiding the development of Modern Physics. Noether's theorem allowed particle physicists to realize that the conservation of net electric charge is related to the rotational symmetry of a plane around a point. Even though Noether's theorem had a significant effect on the development of Modern Physics, among mathematicians, she is best remembered for her contributions to abstract algebra. Nathan Jacobson wrote that "The development of abstract algebra, which is one of the most distinctive innovations of twentieth-century mathematics are largely due to her – in published papers, in lectures, and in personal influence on her contemporaries." Abstract algebra is the field of mathematics that deals with abstract algebraic structures such as rings, fields, etc.Her rather unusual but an elegant approach to look at the networks of relations among an entire set of objects enabled her to provide proofs to more general structures. Similarly, she gave a modern axiomatic definition of commutative rings and developed the foundations of commutative ring theory. In addition to this, her idea of algebraic structures also largely impacted the development of algebraic topology. It's amazing and frightening at the same time to see the amount of things Emmy Noether managed to accomplish throughout her career and considering the difficulties she had to go through throughout her career as a woman, it makes her work even more commendable and a slap to the stereotypical norms of the society back then that assumed women weren't capable enough for scholar work. She had to work without getting paid for several years were excluded from academic positions and wasn't considered worthy enough to teach because of her sexual orientation. However her love for Maths outweighed her limitations. She always found a way to Maths; be it by teaching Mathematics under Hilbert's name or by moving to other nations when she was dismissed from the university positions. Unfortunately, she passed away at the age of 53 but her works are still admired and studied. After her death Einstein wrote, "In the judgment of the most competent living mathematicians, Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered, methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians." Had she doubted her ability, had she considered herself inferior to men or tied herself with the stereotypical norms of the patriarchal society, she wouldn't stand where she stands today.
-Aryan Bista
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