Generalising ∫ sin²(tan x)/x² dx to Even Powers

Product formulas, Hankel-Parseval and Schwinger parameters solve the lower powers. Here is how far each one gets on the fifth.

Heisenberg and Schrödinger built two quantum theories that looked nothing alike but always agreed. Von Neumann's 1927 answer, the state vector in Hilbert space, explained why.

The rule that only large collections have entropy conflicts with a simple two-box thought experiment. The conflict disappears once you separate the two concepts that share the name.