Gibbs is a remarkably brilliant individual whose intelligence has largely gone unrecognized by the public. He lived a largely secluded life, spending most of it within a small geographic area around Yale University in New Haven, Connecticut. His modest nature contributed to his near-invisibility, as he made little effort to promote himself or seek recognition.

During his early tenure at Yale, Gibbs's dedication to his work was so profound that he chose not to receive a salary for the first decade. This profound commitment to his field and his complete focus on academia illustrate the depth of his character, as highlighted in Bill Bryson's book, "A Short History of Nearly Everything."