■ 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.
How large can a discrete structure be without containing a forbidden pattern? Ramsey theory, Turán problems and set systems, attacked mostly by random constructions, entropy and iterative algorithms.
How densely can equal balls be packed in ℝ^d? Solved in dimensions 1, 2, 3, 8 and 24; elsewhere open, with large gaps between bounds, and tied to error-correcting codes and lattice cryptography.