Submission statement: this is a remarkably accessible presentation (with hand-drawn diagrams!) on the concept of geometric invariants and their use in the proof of an early 20th century problem about equivalence between polyhedra.
The MIT Admissions website lets student bloggers write about essentially whatever they want - Lydia has written a number of excellent posts that are entirely unrelated to MIT admissions as well. In particular, this writeup is related to one of the MIT classes she's taking (a seminar in mathematics).
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