Introduction to the proof of the Kakeya conjecture

TL;DR

This paper surveys the recent proof of the 3-dimensional Kakeya conjecture by Hong Wang and Joshua Zahl, explaining the problem, previous efforts, challenges, and new ideas involved.

Contribution

It provides a comprehensive overview of the proof of the Kakeya conjecture, highlighting the novel ideas introduced in the recent work.

Findings

The Kakeya conjecture has been proven in 3 dimensions.

The survey explains key new techniques used in the proof.

It discusses the historical context and difficulties of the problem.

Abstract

Recently, Hong Wang and Joshua Zahl announced a proof of the 3-dimensional Kakeya conjecture. This is a survey article on the proof of Kakeya. We introduce the problem, discuss previous work and some of the difficulties of the problem, and describe the new ideas in the recent work.