What is mathematical beauty, and why are we as mathematicians drawn to it? In art we praise proportion, harmony, simplicity and economy, and we ascribe these virtues to mathematical objects and proofs as well.

In this talk I want to highlight a different family of aesthetic virtues:

the riotous, the infinitely detailed, the kaleidoscopic, and that which can draw our minds into a state of enchantment ("glamour"). I will tell my own personal story of mathematical enchantment, starting with a question about the geometry of modular curves, and ascending towards perfectoid spaces, diamonds, and the Langlands program.