Explore the intricacies of the Kakeya needle problem for rectifiable sets in this 54-minute lecture delivered by Marianna Csőrnyei from the University of Chicago at the 2022 Virtual Joint Mathematics Meetings. Delve into the AWM-AMS Noether Lecture as it covers key topics including the Besicovitch theorem, Kakeya theorem, simple and discrete sets, differential structure, dimensions, and culminates in a comprehensive proof. Gain insights into this complex mathematical concept through a structured presentation that builds from foundational principles to advanced theoretical applications.