Gould died of cancer at his home in New York City, according to his assistant, Stephanie Schur.
Gould, a Harvard University professor, joined the faculty in 1967 as a professor of geology. He advanced to associate professor in 1971 and to professor in 1973.
Gould was a best-selling author who was enamored of the mysteries of evolution. He was known for his engaging, often witty style evident in his collections of essays, which included "Ever Since Darwin", "The Panda's Thumb", and "The Mismeasure of Man," a study of intelligence testing and winner of the National Book Critics Award in 1982.
Much of Gould's work focused on the land snails of the West Indies, which he occasionally used to support a point in his articles for general readers.
One of America's best-known scientists, Gould wrote books that sought to make complex debates about geology, paleontology and evolutionary biology accessible to the public.
He analyzed evolutionary theory - criticizing elements of it at points - with comparisons to a range of disciplines, including popular culture and sports.
One of his most-championed causes was the idea of "punctuated equilibria" in which he emphasized that evolution consisted of relatively rapid spurts of species evolution rather than gradual, continuous transformations.
He also emphasized the importance of statistics in studying evolutionary variation, comparing the demise of the .400 hitter in baseball to the process by which evolutionary "outliers" disappeared.
Gould received his bachelor's degree from Antioch College in 1963 and enrolled in Columbia University. For his doctoral dissertation, Gould investigated fossil land snails of Bermuda. Gould also did work toward his doctorate at the American Museum of Natural History.
In one of his essays about evolution, "Darwin's Middle Road," which he wrote for his monthly column in Natural History magazine, Gould once said, "If genius has any common denominator, I would propose breadth of interest and the ability to construct fruitful analogies between fields."
Gould was also the recipient of several other awards including the National Magazine Award for Essays and Criticism for his column in Natural History in 1980 and the American Book Award in science for "Panda's Thumb" in 1981.
In 1975, Gould received the Schuchert Award, given each year by the Paleontological Society for excellence in research to a paleontologist under 40.