Primes, Diophantine equations and the arithmetic structures behind cryptography and much of modern mathematics.
Smooth cubic curves with a group law, central to modern number theory (modularity, Fermat's Last Theorem) and to deployed public-key cryptography.
The analytic function ζ(s) whose zeros encode the fluctuations in how primes are distributed; the object behind the Riemann Hypothesis and most of analytic number theory.