The Wikipedia entry on the .ai TLD notes that it has an MX record, so you can send e-mails to name@ai: https://de.wikipedia.org/wiki/.ai

The story of Vince Cate (http://offshore.ai/vince/), a CMU graduate who emigrated to the Anguilles in the 90s and (as far as I know) runs the AI registry there is also quite interesting, there's e.g. an old WIRED article from 97 about some of his business endeavors there: https://www.wired.com/1997/07/crypto-2/. The Anguilla News website has a more recent article on him: https://news.ai/vince-cate-in-search-of-bees/