Dario Amodei is, in his telling, the accidental CEO of an accidental business—one that just happens to be among the fastest-growing on the planet. “When we first started Anthropic, we didn’t have any idea about how we would make money, or when, or under what conditions,” he says. Anthropic is the San Francisco–based AI company that Amodei cofounded and leads. And it hasn’t taken long for it to start pulling in lots of money, under lots of conditions. The startup has emerged as one of the leading...