  Underlying the Riemann Hypothesis there is a question whose full answer still
eludes us: what do the zeros of the Riemann zeta function really mean? As a
step toward answering this, Andr\'e Weil proposed a series of conjectures that
include a simplified version of the Riemann Hypothesis in which the meaning of
the zeros becomes somewhat easier to understand. Grothendieck and others worked
for decades to prove Weil's conjectures, inventing a large chunk of modern
algebraic geometry in the process. This quest, still in part unfulfilled, led
Grothendieck to dream of "motives": mysterious building blocks that could
explain the zeros (and poles) of Weil's analogue of the Riemann zeta function.
This exposition by a complete amateur tries to sketch some of these ideas in
ways that other amateurs can enjoy.
