Frederick A. P. Barnard
Frederick A. P. Barnard was Columbia's 10th President (1864-1889), and probably the most important figure in Columbia history that you know nothing about. "Admirable Frederick" had the double misfortune of being far ahead of his time, and giving his namesake to the women's college that bears his name, resulting in a much stronger association with a school that was founded after his tenure, than the one he transformed.
Barnard was responsible for almost single-handedly dragging Columbia, kicking and screaming, into the future of higher education. Whereas Columbia had been a sleepy commuter college for New York's anglican community when Barnard took his post, he left it a rapidly rising university, a trajectory that it would maintain for the next 40 years. Barnard had seen the future of higher education in Germany, where Universities served as centers of research and training grounds for professional academics, as opposed to finishing schools for teenagers of the priveleged.