Suppose we are given a collection of diverse mathematical objects. How might we compare their complexity in a productive way? The development of the ultraproduct construction in the 50s and 60s, a kind of infinite average, led to an approach to this question via Keisler’s order (1967). This order was long thought to have four or five classes, linearly ordered. The talk will explain Keisler’s order and the recent theorem of Malliaris and Shelah stated in the title.