The Professor's backstory identifies him as Roy Hinkley (though his actual name is rarely mentioned during the series), a high-school science teacher who was born in Cleveland, Ohio.
In several episodes, brief remarks are made on his past: in the pilot he is described as a research scientist and "well-known scoutmaster"; in another when a big game hunter comes to the island and asks the Professor what sports he took, the answer is "chess"; after kissing Ginger for a prolonged period (during filming of a silent movie), he claims that he was able to hold his breath during the kissing because he used to be a "scuba diver"; in another, when the castaways try to recreate who killed "Randolph Blake", the Professor threatens to "...cancel his subscription to the Science Quarterly".
In several episodes, electric power for phonographs or washing machines is generated by employing someone (usually Gilligan) to manually pedal, or turn, a pulley, which the Professor has engineered.
A running joke about the Professor was his ability to build nearly anything from coconuts and bamboo, yet he was somehow unable to repair the damaged Minnow, construct a seaworthy raft or find other means to leave the island.
The show's producer, Sherwood Schwartz, answered this paradox in an interview, when he said that the Professor's behavior was logical and quite typical; people often ignore the obvious solution because of their own biases and preferences.
Furthermore, in an early episode, "Goodbye Island", he attempts to do so with a native tree syrup, which proves a disastrous failure that results in the Minnow being completely destroyed.
(Also, earlier in the series, Gilligan and Skipper built a raft to sail for help; however, the island was revealed to be near a shark-filled area that made such a journey too dangerous for anything other than an actual boat.)
In the parody movie Back to the Beach, a character played by Bob Denver and obviously based on Gilligan mentions knowing "a guy who could build a nuclear reactor out of coconuts but couldn't fix a two-foot hole in a boat."