Marquand was the son of Henry Gurdon Marquand, a prominent philanthropist and art collector. After graduating from Princeton in 1874, Allan obtained his Ph.D. in Philosophy in 1880, at the Johns Hopkins University. His thesis, supervised by Charles Sanders Peirce, was on the logic of Philodemus. In June 1896, he married Eleanor Cross Marquand daughter of Richard J. Cross and Matilda Redmond Cross. He returned to Princeton in 1881 to teach Latin and logic.
During the 1881–82 academic year, Marquand built a mechanical logical machine that is still extant; he was inspired by related efforts of William S. Jevons in the UK. In 1887, following a suggestion of Peirce's, he outlined a machine to do logic using electric circuits. This necessitated his development of Marquand diagrams.
According to Lavin (1983: 8), the President of Princeton, McCosh, deemed "unorthodox and unCalvinistic" Marquand's relatively mathematical approach to the teaching logic, an approach he had learned at Peirce's feet. Hence in 1883, Marquand was offered a position teaching art history, a position he held until his death and at which he excelled. He was elected chairman of the Department of Art and Archaeology in 1905. He also served as the first director of the Princeton University Art Museum, a position he held until his 1922 retirement.
- Ketner, Kenneth Lane, (assisted by A. F. Stewart) 1984, "The Early History of Computer Design: C. S. Peirce and Marquand's Logical Machines," Princeton University Library Chronicle : 187–211.
- Lavin, Marilyn Aronberg, 1983. The Eye of the Tiger: The Founding and Development of the Department of Art and Archaeology, 1883–1923. Princeton: The Dept. of Art and Archaeology and the Art Museum.
- Marquand, Allan
- 1883, in C.S. Peirce, ed., Studies in Logic by members of the Johns Hopkins University, Little, Brown, and Company, Boston, MA, 1883. Reprinted 1983. John Benjamins.
- 1886, "A New Logical Machine," Proceedings of the American Academy of Arts and Sciences 21: 303–07, Little, Brown, and Company, Boston, MA, 1886. Google Books Eprint.
- Peirce, C.S., 1993, "Letter, Peirce to A. Marquand" dated 30 December 1886, in Kloesel, C. et al., eds., Writings of Charles S. Peirce: A Chronological Edition: Volume 5: 1884–1886. Indiana University Press: 421-22, with an image of the letter page with the circuits on p. 423.