The moving sofa problem asks for the largest area of a planar shape that can move around a right-angled corner in an L-shaped hallway. Initially posed by Leo Moser in 1966, the problem became a well-known example of an elementary geometry question that is extremely difficult to answer, and was open until its solution in 2024 by Jineon Baek. In this talk I will explain the basics of moving sofa theory, survey the milestone developments in the subject including my own work and how it inspired Baek's groundbreaking proof, and show entertaining moving sofa animations. I will make a halfhearted (and probably unsuccessful) attempt to draw general philosophical conclusions around the use of computer-based experimentation in mathematical discovery.

The main goal of the talk will be to convince you that serious mathematical ideas are often hiding just around the corner. No prerequisite knowledge will be assumed, other than familiarity with the challenges of navigating furniture around obstacles.