The Kakeya conjecture

Abstract

The geometry of lines is a fundamental part of mathematics and the way we interact with the physical world. Core concepts such as distance and angle, and the accompanying theory of trigonometry, have been studied since antiquity and taught to countless generations of students. However, there are simple questions about lines which have stumped some of the greatest minds in mathematics over the last fifty years. One notable example is the Kakeya conjecture, which asks how lines which point in different directions can be packed together in a small space.