The Daystrom Institute, mentioned prominently in Star Trek: The Next Generation (1987), Star Trek: Deep Space Nine (1993), Star Trek: Voyager (1995), and 'Star Trek: Picard' (2020) is named for Dr. Richard Daystrom, the guest character in this episode.
Robert Wesley was named for a pseudonym that Gene Roddenberry had used early in his career, and "Wesley" is Roddenberry's given middle name.
In his 1999 essay "Welcome Aboard the Enterprise", science fiction author Robert J. Sawyer writes, "...the ship's computers, as seen in 'The Ultimate Computer', were designed by a Nobel-prize-winning black cyberneticist, played with equal dignity by William Marshall. During the era of Martin Luther King and the Watts Riots, it was a powerful, important statement to have the white captain of the Enterprise deferring to black people; as Marshall observed thirty years later, the single most significant thing about his guest-starring role was that he, an African-American, was referred to as 'Sir' throughout the episode."
The script came from an unsolicited screenplay submitted by Laurence M. Wolfe, who was a mathematician. John Meredyth Lucas chose to adapt the story, feeling that it would be relatively inexpensive and quick to produce. D.C. Fontana rewrote much of the story, as much of the original screenplay was focused on Dr Daystrom and the M-5 Computer, with little emphasis on the show's regular characters.
Barry Russo, appearing here as Commodore Wesley, also appears in The Devil in the Dark (1967) as Lieutenant Commander Giotto.