孔子曰︰「三人行，則必有我師。」 是故弟子不必不如師，師不必賢於弟子；聞道有先後，術業有專攻，如是而已。 韓愈《師說》
(translation) Confucius said "If three men are walking together, one of them is bound to be good enough to be my teacher. "A student is not necessarily inferior to his teacher, nor does a teacher necessarily be more virtuous and talented than his student. The real fact is that one might have learned the doctrine earlier than the other, or might be a master in his own special field． (On Teaching, Han Yu)
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I love teaching and sharing mathematics! As a math YouTuber @HaoXing and I have created numerous videos in different levels (from high school Olympiad to the topics related to my research) and different areas (algebra, analysis, number theory, probability and so on) of mathematics. In my YouTube channel, you can find math topics that are usually not covered in standard classes. For example, an elementary proof of prime number theorem, a detailed proof of existence and uniqueness of Haar measure on locally compact groups, the Gauss circle problem, spectral sequences among many others.
I have some old notes for the books/papers I read very carefully with proof gaps filled and incomplete solutions to exercises. Here are notes to A Course in Arithmetic by Jean-Pierre Serre, High-Dimensional Probability - An Introduction with Applications in Data Science by Roman Vershynin and THE RISING SEA - Foundations of Algebraic Geometry by Ravi Vakil