Rickart was born in Osage City, Kansas, and earned his B.A.
In 1941, he received his PhD from the University of Michigan under Theophil Henry Hildebrandt with the thesis Integration in a Convex Linear Topological Space.
[2] Rickart was for two years the Benjamin Pierce Instructor at Harvard University.
In the late 1950s and early 1960s, he was one of the pioneers in introducing the "new math" into American schools.
[2] He died in North Branford, Connecticut where he lived, survived by his wife, Annabel Erickson Rickart, three sons, and four grandchildren.