Screenwriter
Peter Benchley
Peter Benchley was not just one of the movie's screenwriters; he was the author of the original novel. After spending his childhood summers on Nantucket Island in New England, the idea for Jaws came to him when he read a small news article about a fisherman who caught a 4,500-pound shark off the coast of Long Island, New York. He wondered what might happen if a shark that big started preying on swimmers, and he pitched the idea to several book publishers. Finally, an editor at Doubleday took the bait (#sorrynotsorry) and paid Benchley to write the novel (source).
Jaws (the novel) was a huge hit, staying on the best-seller list for 44 weeks. By then, producers David Brown and Richard D. Zanuck had already acquired the film rights, and Jaws (the movie) was already in production.
Benchley wrote a first draft of the script—his first ever attempt at screenwriting—and then passed it along for others to finish. (Benchley makes a cameo in the film as the newscaster from the mainland.) Though it launched his successful writing career, Benchley ultimately grew to regret the way he portrayed sharks in Jaws and went on to become a passionate ocean conservationist (source).
Whodathunk?
Carl Gottlieb
Carl Gottlieb was the main screenwriter assigned to polishing and adapting Benchley's first script treatment. As much as the filmmakers loved the main idea of the book, they thought that the tone was too dark and the characters weren't likable enough. For instance, in the novel, Mayor Vaughn is in the pocket of the mafia and Hooper has an affair with Mrs. Brody and gets eaten by the shark (who's opposed to adultery, we assume).
So director Steven Spielberg brought in Gottlieb to add some humanity and humor to the story. (He makes a cameo in the movie as Ben Meadows, editor of the Amity newspaper and one of Mayor Vaughn's loyal stooges. Keep an eye out for the portly guy with the mustache.) Anyway, the fact that a film where five people get mauled and eaten by a shark is also really funny and heartwarming? That's Gottlieb's doing.