The Integral of x K_0(x)^5: Closed Forms and Limits

Why the tangent inside the sine drops out, two independent proofs of the closed form for every even power, and the cases where both proofs stop working.

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.