Rotating needles in space: the road to the Kakeya conjecture, and why it matters

A recent tradition of the ICM is to have a non-technical popular article written for each of its medallists. (This is separate from the older tradition of having a laudatio for the winner, which is similar but aimed at a more advanced audience.) I was approached to write such an article for Hong Wang on the occasion of her Fields Medal. I have uploaded my initial version of this article, “Rotating needles in space: the road to the Kakeya conjecture, and why it matters“, to the arXiv. Chris Sogge gave the corresponding laudatio; both should eventually appear in the Proceedings of the ICM.