People have claimed that written science fiction is “dying” for decades now. Despite that, all these decades, more and more great science fiction books are being written. The classics, and even lots of modern stuff, have a huge influence on more “pop” mediums. Anime is no exception, with references to SF novels showing up everywhere.
Clannad, “The Dandelion Girl” by Robert F. Young: Kotomi reads it as a child in her arc, and it’s the source of the recurring line “Day before yesterday I saw a rabbit, and yesterday a deer, and today, you.” Japanese readers voted it the “6th best SF story of all time” in a magazine poll. In the US, it’s not well known enough to keep in print, although it was printed online by SciFiction. The story has also been adapted into a visual novel by fans.
Eureka Seven, Greg Egan/Greg Bear: The scientist character of that name is based upon the reclusive Australian author Greg Egan, who is especially popular in Japan. That Japanese poll? His “Reasons to be Cheerful” was voted the #1 best foreign SF story…and himself the #2 best foreign SF writer, behind only Philip K. Dick. The character’s nickname “Dr. Bear” also refers to the author Greg Bear.
Geneshaft, multiple books: All it’s episode title are references to classic SF stories/books. In some cases, they’re based on new names used for the Japanese publication, so they’re not obvious to English readers. For example, James P. Hogan’s “Thrice Upon a Time” was printed in Japanese as “未来からのホットライン“ (Hotline from the Future), and episode 6 is titled “過去からのホットライン”(“Hotline from the Past”).
Gurren Lagann: The subtitles for the two movies reference the science fiction novels “Childhood’s End” by Arthur C. Clarke and “The Lights in the Sky are Stars” by Frederic Brown. The first book is well-known, but the second hasn’t gotten much attention in the US since its publishing in 1953.
Melancholy of Haruhi Suzumiya, multiple books: The book-loving alien robot reads a number of SF books throughout the series. She seems especially fond of the Hyperion series; it includes the book she placidly calls “unique,” and the book she gives to Kyon with a hidden bookmark. The magazine which serializes the light novels also posted a list of “Nagato Yuki’s 100 Books,” with “Nagato’s Favorites” like “Permutation City” by Greg Egan and “Terminal Experiment” by Robert J. Sawyer…both books she could definitely relate to.
Nichijou/My Ordinary Life, episode 20, “The Sirens of Titan,” by Kurt Vonnegut, Jr.: The book is seen randomly and conspicuously in one of the intermissions. Of course, if it’s SF in Nichijou, it has to be something like Vonnegut.
Toward the Terra, “Slan” by A.E. van Vogt: The 1977 manga shares the basic premise of (oppressed psychic mutants who live among humans, and are hunted down for execution) and main character’s name (“Jommy”) of A.E. van Vogt’s 1940 novel. Although the two stories have the same premise, they take it in very different directions. Slan is pure pulp, but it’s still an enduring classic which hit a nerve with the nerdy SF fans of its time. They took up the slogan “fans are Slans!,” comparing themselves to the evolved, imaginative mutant race persecuted by mundane society.