Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.

Expectation is a statistical fiction, like having 2.5 children.

The best paradoxes raise questions about what kinds of contradictions can occur-what species of impossibilities are possible.

Paradox is thus a much deeper and universal concept than the ancients would have dreamed. Rather than an oddity, it is a mainstay of the philosophy of science.

The assumption that anything true is knowable is the grandfather of paradoxes.

The more improbable the message, the less "compressible" it is, and the more bandwidth it requires. This is Shannon's point: the essence is its improbability.

At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox.