OpenAI’s ChatGPT made its first big splash in November 2022 when it was unveiled as a free research tool for public use. Several other large language models were introduced soon after. Here we explore some of the implications of these new technologies for the college mathematics classroom, though we believe our work here may be relevant to other educational contexts. We start with a brief overview of how ChatGPT and its friends work. We provide a handful of diverse examples that display the unique capabilities and present limitations of the technology. We also briefly review the many concerns and hopes people have about ChatGPT. Then, we zero in on the specifics of how human students learn and what ChatGPT can do to help facilitate that process. Finally, we summarize our current stance, that ChatGPT offers us a new opportunity to understand ourselves better and that it offers us a new opportunity to reevaluate what we want from education in general and math education in particular.