A personal reflection on the poor state of mathematical pedagogy at the graduate level. Even in well-regarded textbooks, proofs are often high-level outlines rather than complete arguments, requiring students to fill in enormous gaps on their own. The author shares a personal experience collaborating with professional mathematicians to untangle an obscure proof in a Galois Theory textbook, noting that even experts found the intermediate steps unclear. The post argues that better accompanying notes with rigorous, detailed exposition would greatly benefit students, and the author expresses intent to write such accompaniments for topics like s-arc transitivity of graphs and field extensions.
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