$$
% Define your custom commands here
\newcommand{\bmat}[1]{\begin{bmatrix}#1\end{bmatrix}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\P}{\mathbb{P}}
\newcommand{\S}{\mathbb{S}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\S}{\mathbb{S}}
\newcommand{\norm}[2]{\|{#1}\|_{{}_{#2}}}
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\pdd}[2]{\frac{\partial^2 #1}{\partial #2^2}}
\newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|}
\newcommand{\abs}[1]{\left|{#1}\right|}
\newcommand{\mbf}[1]{\mathbf{#1}}
\newcommand{\mc}[1]{\mathcal{#1}}
\newcommand{\bm}[1]{\boldsymbol{#1}}
\newcommand{\nicefrac}[2]{{}^{#1}\!/_{\!#2}}
\newcommand{\argmin}{\operatorname*{arg\,min}}
\newcommand{\argmax}{\operatorname*{arg\,max}}
\newcommand{\dd}{\operatorname{d}\!}
$$
Mathematical puzzles, short proofs, and problems that caught my attention.