A Massachusetts native, Alexis Caswell graduated first in Brown's Class of 1822. He became a tutor at Columbian College (George Washington University) and in 1827 was ordained a Baptist minister. Soon after, he was called from a position in Nova Scotia to assist the ailing pastor of Providence's First Baptist Church. After serving for a time as minister, he took a professorship in mathematics and natural history upon the resignation of Professor Alva Woods. He served in this capacity from 1828 to 1850, when he became professor of mathematics and astronomy, a position which he occupied until 1855, when he was named professor of natural philosophy and astronomy.
During the 1840-41 school year, he was president pro tempore while President Wayland traveled in Europe. He was named regent of the University and assisted Wayland from 1852 to 1855. When Wayland announced his retirement, some expected that Caswell, the senior member of the faculty, would become president. However, he would wait another 15 years before that honor was bestowed upon him.
Caswell accepted the presidency in 1868, at the age of 69. His was not expected to be a dynamic presidency, though while he was in office he managed to revitalize the alumni group, and oversee increases in the endowment, tuition, faculty salaries and enrollment. Caswell resigned in 1872 at the age of 73. Three years later he accepted another presidency -- that of Rhode Island Hospital.