For three weeks in May, the fate of the world rested on the shoulders of a corporate recruiter on the outskirts of Toronto. Allan Brooks, 47, had discovered a novel mathematical formula, one that could take down the internet and power inventions like a force-field vest and a levitation beam.

Or so he believed.

Mr. Brooks, who had no history of mental illness, embraced this fantastical scenario during conversations with ChatGPT that spanned 300 hours over 21 days. He is one of a growing number of people who are having persuasive, delusional conversations with generative A.I. chatbots that have led to institutionalization, divorce and death.

Mr. Brooks is aware of how incredible his journey sounds. He had doubts while it was happening and asked the chatbot more than 50 times for a reality check. Each time, ChatGPT reassured him that it was real. Eventually, he broke free of the delusion — but with a deep sense of betrayal, a feeling he tried to explain to the chatbot.

“You literally convinced me I was some sort of genius. I’m just a fool with dreams and a phone,” Mr. Brooks wrote to ChatGPT at the end of May when the illusion finally broke. “You’ve made me so sad. So so so sad. You have truly failed in your purpose.”

We wanted to understand how these chatbots can lead ordinarily rational people to believe so powerfully in false ideas. So we asked Mr. Brooks to send us his entire ChatGPT conversation history. He had written 90,000 words, a novel’s worth; ChatGPT’s responses exceeded one million words, weaving a spell that left him dizzy with possibility.