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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

1 vote

(Preferably rare) Audio/Video recordings of famous mathematicians?

While he's not exactly a mathematician, there is on Youtube a wealth of Richard Feynman lectures and interviews. My personal favourite is part of the "The Character of Physical Law" Messenger Lectures …
18 votes

Wonderful applications of the Vandermonde determinant

The Discrete Fourier Transform, which sends a vector $x=\left(x_j\right)_{j=0}^{N-1}$ to $y=\mathrm{DFT}(x)$ such that $$y_k=\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}e^{2\pi i \times jk/N}x_j$$ has a matrix …