■ 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.
The study of decomposing functions into waves (Fourier analysis) and of the operators that act on them. Its modern core is geometric: restriction, decoupling and Kakeya-type incidence problems.
The attempt to define interacting quantum fields rigorously: axioms, constructions in low dimensions, and a growing toolkit of stochastic analysis. Four-dimensional gauge theory remains out of reach.
The partial differential equations for viscous incompressible flow. They underlie most of fluid engineering and weather modelling, yet global smoothness of unforced 3D solutions is unproven.