today’s scientist is emmy noether, a mathematician from the early 20th century. noether did a crazy amount of mathematics research in abstract algebra, so much so that her work is divided into three epochs. i’ll do my best to give the highlights of each epoch, but i’m slightly crunched for time today and definitely won’t do her justice, so i’d highly recommend reading about noether on your own time!
epoch 1: from 1908-1919, noether’s work was focused on studying invariants (things that remain constant under transformations). this epoch spawned what is arguably noether’s most famous discovery, her namesake theorem. noether’s theorem equates symmetry of a physical system to conservation. consider a physical system where everything behaves the same, regardless of how it’s oriented. then it’s physical laws must have rotational symmetry, so noether’s theorem tells us that angular momentum is conserved. this theorem leads to the coolest results ever, because i can say something like “this physical system’s laws remain the same no matter what time it is”, and somehow noether’s theorem gives me conservation of energy from that.
epoch 2: from 1920 to 1926, noether was concerned with ascending chain conditions. a sequence of sets is called ascending if every set is contained in the set after it (and descending works in reverse). a collection of sets is said to satisfy the ascending chain condition if any ascending sequence becomes constant after a finite number of steps (that is, after a finite number of steps, consecutive sets in the sequence become equal). noether’s work was concerned with proving statements about objects that satisfy chain conditions. she made so many crucial discoveries about objects that satisfy ascending chain conditions that they are now described as noetherian in her honor.
epoch 3: from 1927 to 1935, noether worked in different types of noncommutative algebras. with artin, brauer, and hesse, she founded the theory of central simple algebras, and she also proved several key theorems in division algebras.
phew! that was a whole lot of science words. tldr: noether did a LOT of stuff, and we owe her for many crucial developments in mathematics and physics.
bonus fun fact: noether was originally denied from teaching at the university of göttingen. her reaction to this was to completely ignore them and begin teaching under hilbert’s (yeah, the hotel guy) name instead. they would advertise lectures under hilbert’s name, and noether would just show up and teach them. absolute icon!
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"I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bath house."
-Hilbert
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(written 3/11/21)
