Mathematics

The Mathematics concentration at Harvard is focused on the pure, theoretical study of numbers—Applied Mathematics is a separate concentration, focused on interdisciplinary pursuits and discussed above. Houghton has materials serving students in both fields, and the library is especially rich in historical and theoretical material about pure mathematics, which can also be studied in relation to other concentrations involving logical analysis, such as Philosophy.

The library has many items that should be of interest to students focused on the history of mathematics. A handwritten set of astronomy texts from the thirteenth century (MS Lat 361, 009439684), for example, also contains a tract titled De Algebra et Almuchabela, possibly written by Al-Khwarizmi, an Arab mathematician so important that the word “algorithm” stems from his name. Houghton also owns a fourteenth-century manuscript of Euclid’s Elementorum (MS Lat 359, 009439639), still one of the most important works about geometry in history, as well as an exquisite 1847 copy of the same work in color (Typ 805.47.3730, 005304664). Needless to say, both of these works can be studied in conjunction with the Classics.

The language of numbers is universal, but it has been studied in multiple tongues. Houghton’s archive contains many materials about mathematics that, like the manuscripts above, can make use of the university’s language departments. The library, for instance, owns the family papers of Carl Friedrich Gauss (MS Ger 232, 009504696), one of the most important mathematicians in history. The papers provide insight into Gauss’ private life, humanizing a titan in the field and providing precious material for mathematical historians. It also holds William James’ copy of De l’Infini Mathématique (WJ 614.89.1, 012193150) with its previous owner’s annotations. The work, published in 1896, can be compared to modern theories about infinity, highlighting the progress in the field in the last century.

Modern pure mathematics is also an important part of the Houghton archive, and a particular collection contains many items about the matter. The papers of W. V. Quine (MS Am 2587, 008937558), a Harvard professor and one of the twentieth century’s most brilliant philosophers, includes not only material about philosophy, but also about linguistics, psychology, mathematics, and computer science, an interdisciplinary mélange that emphasizes the subjects’ overreaching nature. The papers contain Quine’s correspondence with some of the twentieth century’s most important mathematicians, such as Kurt Gödel (415) and Hilary Putnam (885), also a Harvard professor, but they also hold letters between the philosopher and current professor Warren D. Goldfarb (419), the Walter Beverly Pearson Professor of Modern Mathematics and Mathematical Logic in the Department of Philosophy.

Part of Quine’s archive is dedicated to other authors’ essays and papers, and among those students can find plenty of items concerning pure mathematics and its relation to other fields. C. H. Denbow’s “On Detached Languages” (1625) and B. H. Partee’s “Semantics: Mathematics of Psychology?” (2064), for instance, can be studied in conjunction with Linguistics, whereas A. K. Dewdney’s “Computer Recreations” (1645) can be assessed in relation to Computer Science. Meanwhile, J. J. Dilworth’s “Change for Sets versus Non-Sets” (1647) and “Not All Sets Are Abstract” (1650) tackle pure mathematics questions and can be taken into account in concentrators’ research projects in the department.