Manjul Bhargava - Magic Squares, Cubes, and Hypercubes: From Ancient Origins to Recent Advances

The 2026 Einstein Lectures will focus on the topic of number theory. From 19 to 20 October, 2026, Fields Medalist Manjul Bhargava will give three lectures on this topic. "Magic Squares, Cubes, and Hypercubes: From Ancient Origins to Recent Advances" is the second of three Einstein Lectures. Inscribed on a wall near the entrance of the majestic Parshvanath Jain Temple in Khajuraho (built around 960 CE) is a 4 × 4 magic square with remarkable arithmetic properties. We will explain why this magic square is the unique one of its kind, up to certain transformations. This answers a question posed by the legendary geometer HSM Coxeter in 1938. We will also explain why there is a unique such magic object in every dimension.