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#from-scratch 2 posts
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Connections in Math: the two kinds of random
Two files of a million digits, statistically identical, and yet one compresses to three lines and the other never will. Chasing that gap splits the idea of 'compressible' into two very different things — and leads to a strange wall: you can always prove a thing can be compressed, but never that it can't.
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Connections in Math: deriving the SVD from scratch
Most books state the Singular Value Decomposition as a finished theorem. Here we arrive at it naturally, without even aiming for it — letting the structure of any linear map hand us the factorization for free.