Gibson first adapted the story of Helen Keller and her teacher, Annie Sullivan, into a TV teleplay called The Miracle Worker in 1957 for the Playhouse 90 series.
In 1958, Gibson made his Broadway debut, writing the play Two for the Seesaw, a New York City love story about a married lawyer Henry Fonda and a kooky dancer Anne Bancroft. He received his first Tony nomination for Best Play for the show, which was a hit for 750 performances at the Booth Theatre.
Gibson's next Broadway outing may have ran less performances hardly--a healthy 719, but is considered his masterpiece. The stage version of The Miracle Worker opened at the Playhouse Theatre on October 19, 1959 with Bancroft as Sullivan and Patty Duke as Keller. He won the Tony Award for Best Play in 1960.
In 1962, he saw both plays make it to Hollywood, writing the screenplay for The Miracle Worker himself and receiving an Academy Award nomination for his work.
Gibson's next big Broadway project was adapting the Clifford Odets' play about a boxer, Golden Boy, into a musical for Sammy Davis, Jr. He received a third Tony nomination for the show. His other contribution to musical theater was the book to the famous flop Raggedy Ann, which played for five performances at the Nederlander Theatre in 1986. Two for the Seesaw also was adapted into the musical Seesaw, but its director/choreographer Michael Bennett wrote the book himself.
Gibson's other Broadway plays are A Cry of Players, a short-lived Miracle Worker spin-off called Monday After the Miracle and Golda. Goldman tinkered with the latter multi-character show, which ran for three months in the late 1970s, for years, spinning it into a one-woman hit for Tovah Feldshuh in 2003 with the new title Golda's Balcony.