Felix Robertson was the first child born in Nashville and the first native-born citizen to become a physician. He graduated from the University of Pennsylvania Medical School in 1804. He organized 46 Nashvillians of Scottish descent to protest the murder of John Dickinson by Andrew Jackson in 1806, although he later became a friend of Andrew Jackson.

Robertson was one of the organizers of the Nashville Academy of Medicine and the Tennessee Medical Association. He advocated prison reform and was director of the state insane asylum system. Felix Robertson also introduced quinine into Tennessee, and in later years he devoted his practice to pediatrics and the care of children. He believed that mental illness was a disease and curable.

During his fifty-five year term as a trustee of the University of Nashville, Felix Robertson entertained the out-of-town students in his home on Sundays. His hobby was growing gourds, and his friends would send him gourd seeds from around the world.

Felix Robertson was a friend of all of Tennessee's three presidents. He did not favor secession and spent his life during the Civil War as a recluse in his home on Cherry Street.