Jefferson's youthful enthusiasm matured into a considered view of the important role of mathematics in the great scheme of things, which we can see from the catalogue of his library in the library classification he designed. (This is the library he sold to the government, after the British troops had burned the congressional library in Washington in 1814, to ensure that the nation's legislators could continue to be guided by the best sources of information and ideas.) Mathematics forms chapter 25 to 29 of the structure of the library, being the part of philosophy—that is, the work governed by the faculty of reason—which isn't ethical or legal. And the mathematics books he owned ranged from editions of the great classical mathematicians (Euclid, Archimedes, Diophantus) to some of the best 17th- and 18th-century texts (Newton, Keill, MacLaurin, Emerson and so forth).

There's one non-mathematical book owned by Jefferson which is also relevant to the story: he had bought at auction in Amsterdam in 1789 a copy of Theodor de Bry's great 1619 edition of travels to the Americas, the first volume of which contained Thomas Harriot's Briefe and true report of the new found land of Virginia, a report on Ralegh's 1585 expedition to these shores by the first European mathematician to visit America, Thomas Harriot. In his great Enlightenment treatise Notes on the State of Virginia, of 1785, Jefferson was in a sense following in the footsteps of Harriot, his mathematical predecessor of two centuries before: both students of native American languages, promoting scientific knowledge of the territories on the eastern seaboard and westward, both using the format of a simple report as vehicle for a wider ideological tract.