Much like how Martin Gardner was a big influence in my adolescence, Raymond Smullyan was a strong presence in my teen years. I got his book The Lady or the Tiger? in 1982, at age 12, and devoured it. Aside from the logic puzzles about ladies and tigers behind doors whose labels might be true or false, or vampires who always lie but some of whom are also insane and believe only false things, the book includes a "mathematical novel" that gently but thoroughly teaches the concepts behind Gödel's First Incompleteness Theorem. Although I didn't fully grasp either its profoundness or its essential simplicity until revisiting the topic in computer science courses in college, it resonated pretty deeply with me at the time.
Over the next decade I picked up every Smullyan book I ran across in bookstores, and shortly after college I bought two of his textbooks, I think via the Library of Science book club: Gödel's Incompleteness Theorems and Recursion Theory for Metamathematics. These were much drier and academic, and I was stymied on page 5 by the use of the word "denumerable" without defining it; I couldn't find it in any of my college textbooks, and in the days before WWW search engines, that was that. (I see now that it's simply another word for "countably infinite"; perhaps it's time to take another crack at reading these books...)
The event of his death turned up a video of his appearance on the Tonight Show in 1982, which I never knew about and would have loved to have seen at the time. It's great to see Johnny Carson take seriously the task of solving the logic puzzles that Smullyan posed; today I can't imagine a late-night interviewer doing anything but laughing them off with jokes.
Frank Lantz wrote a nice tribute to Smullyan five years ago: "Smullyan’s puzzles are songs that play your brain like a piano, twisted 4-dimensional shapes made out of statements and beliefs, they combine the delicate impossibility of a Zen koan with the mechanical precision of a door knob."
I had completely forgotten that The Lady or the Tiger? was based on a short story by the same name, which, having been written in 1882, is in the public domain and is readable for free online. It's interesting that the story poses the choice between two doors as not a logic puzzle but an ethical dilemma: if you were a princess and your father the king sentenced your lover to either be eaten by a tiger or happily married to another woman but out of your life forever, which would you choose?
Random footnote: the story's author, Frank Stockton, also wrote the story "The Griffin and the Minor Canon", which I only knew of due to Chandler Groover's recent interactive adaptation in Twine.