■ Block 01 / research
Research
Foundations other work depends on. Each entry explains what it is, why it is load-bearing, its open problems, and a reviewed timeline of progress.
Foundations other work depends on. Each entry explains what it is, why it is load-bearing, its open problems, and a reviewed timeline of progress.
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.
Dirichlet series, Euler products and contour integration turn questions about primes into questions about zeros of zeta and L-functions; the toolkit includes large sieve, zero-density bounds and sieves.