Joshua A. Lippincott was born in Burlington County, New Jersey on January 31, 1835 to Crispin and Elizabeth Garwood Lippincott. He prepared for college at the Pennington Seminary and enrolled at Dickinson College in Carlisle, Pennsylvania in 1855, along with his older half-brother, Benjamin Crispin Lippincott. While at the college, Joshua Lippincott was elected to the Belles Lettres Society. He graduated with his class and his brother in the early summer of 1858.
Lippincott immediately took up a post at his old school and remained at Pennington Seminary teaching mathematics and German until 1862. At that time, he became a high school principal and superintendent of schools in Scranton, Pennsylvania. Lippincott then moved on to Trenton, New Jersey in 1865 to become principal of the boy's section of the New Jersey State Model School there. He moved again in 1869 to teach school in Baltimore, Maryland for three years.
Lippincott also qualified as a Methodist pastor and served the Methodist Episcopal Church in Hackensack, New Jersey between 1872 and 1874. From there he returned to Dickinson as a professor of mathematics and astronomy. While at his alma mater, he became a chief advisor to Captain Richard Henry Pratt at the new Indian school in the town. Lippincott coined the often quoted phrase "to save the child we must kill the Indian in him" and believed that any Indian school must be located in a place like Pennsylvania, far removed from recent Native American areas. For this reason, he opposed the establishment of an Indian school in Lawrence, Kansas. Ironically, Lippincott ultimately accepted an appointment as the fourth chancellor of the fledgling University of Kansas when his predecessor there took over that new Indian school. He served as a capable leader for the university from 1883 to 1889 and then became pastor of the first Methodist Church of Topeka. Lippincott later returned east to Philadelphia, where he served as a trustee of Dickinson beginning in 1897 and as the corresponding secretary of the Methodist Hospital.
There are no records available to indicate that Lippincott married. Interestingly, however, Dickinson archival records reveal that a woman in a village near to Carlisle admitted in old age to an illegitimate child born of "the mathematics professor at the College" and stated that her immediate family had protected her and her child from the accompanying shame. It is not possible to prove whether or not this story is true, but this tale certainly does not seem immediately to fit the image of Lippincott as students and colleagues at Kansas described him -- as too "dour, pious, and grim." Joshua Allan Lippincott died in Los Angeles, California on December 30, 1906. He was seventy years old.