Mathematical Treasures

Mathematical Treasures

One of the major features in the MAA’s online magazine in the history of mathematics Loci: Convergence is the article entitled “Mathematical Treasures”. This article contains annotated copies of various book pages chosen from the George Arthur Plimpton and David Eugene Smith collections at Columbia University, one of the best collections of rare books and manuscripts in the country.

During the first half of the twentieth century, David Eugene Smith (1860-1944) was a moving force in the world of mathematics education. As the chairman of the mathematics education department at Columbia University’s Teachers College, Smith led the way in teaching reforms attuned to the Progressive Education Movement. He firmly believed that the teaching of mathematics should be closely associated with the history of the subject. As an historian of mathematics, he wrote and lectured widely on the subject and also collected historical mathematical materials: texts, documents and artifacts. Smith befriended the wealthy New York lawyer and publisher, George Arthur Plimpton (1855-1936), who was also a bibliophile and avid collector. Under Smith’s influence, Plimpton enriched his collection with mathematical manuscripts and many early Renaissance texts on arithmetic. When Plimpton died in 1936, he bequeathed his collection to Columbia University. Similarly, beginning in 1931, David Eugene Smith began donating his extensive collection of mathematical memorabilia: historical texts; correspondence; portraits of famous mathematicians; signatures and concrete artifacts to the Columbia University Library.

Although this entire collection is available to researchers through the Rare Books and Manuscript Collection at Columbia University, one must travel to that library to access it. Yet Smith believed that it was extremely important for teachers at all levels to be able to use the materials that he collected. Thus, it is fitting that the Mathematical Association of America is able to display selected pages from this huge collection of books and manuscripts to its membership with the hope that many will make use of these documents in their teaching. The Mathematical Treasures article has an index on its second page, with the authors of the documents listed alphabetically. Each page image is annotated and, if you click on the name of the page, you can download a high resolution version (150-200 dpi), which is sufficient for most teaching purposes.

The documents have been selected by the founding editors of Convergence, Victor Katz and Frank Swetz, who would like to particularly thank Dr. Michael Ryan, Director of Rare Books and Manuscripts and Jennifer Lee, Librarian for Public Service and Programs, for their assistance in making this display possible. The current editors of Convergence, Janet Beery and Kathleen Clark, hope to continue and expand this section.

We have included here a selection of three images from the Mathematical Treasures article. To see the rest, go to .

Victor J. Katz and Frank Swetz

1. This is an illustration from the geometry chapter (Allegory of Geometry) of the Margarita philosophica (Pearl of Wisdom) of Gregor Reisch (1467 – 1525). The first edition was published in 1503. This work was used as a university textbook in the early sixteenth century. Among its twelve chapters are seven dealing with the seven liberal arts commonly taught at the universities: the trivium of logic, rhetoric, grammar and the quadrivium of arithmetic, music, geometry, and astronomy.

2. This is the Tree of Proportions and Proportionality from the De Divina Proportione of Luca Pacioli (1445 – 1509), published in 1509. Some of the terms in Pacioli’s tree are familiar today; some are taken originally from the study of proportions by Nicomachus in his Arithmetic; but the meaning of some other terms are not generally known.

3. This is the title page of the Nova Scientia (1537) of Niccolo Tartaglia (1499-1557). In this work, Tartaglia discussed the mathematics of artillery and developed methods for determining the range of a cannon. The caption below the illustration reads, “The Mathematical sciences speak: Who wishes to know the various causes of things, learn about us. The way is open to all.” The illustration itself depicts a walled compound, the compound of knowledge. The high wall keeps out the man who attempts to scale it and enter improperly. Entrance into the compound is through a single door opened by Euclid. In the first courtyard, a crowd comprised of Tartaglia and the muses of the seven liberal arts watch a demonstration of Tartaglia’s new knowledge, a theory of trajectories. Beyond the first courtyard is a second smaller, more exclusive and highly elevated one. Its entrance is manned by Aristotle and Plato. Plato holds a banner proclaiming, “No one can enter who does not know geometry.” Enthroned at the rear of this compound, in the highest position of all, is philosophy.


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