Trilemmas are everywhere. Defined as either a forced single choice among three unfavorable options or a two-out-of-three-only choice among favorable options, trilemmas involve trade-offs. The latter, ...

Determining which configurations of the cube are possible. The Fundamental Theorem of Cubology is a statement that characterizes which configurations are possible, and which configurations are ...

In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension ...

The Hairy Ball theorem, proved by Henri Poincaré in 1885, demonstrates that it's impossible to create a perfectly smooth hair ...