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Teaching and Research with Original Sources from the Euler Archive

Dominic Klyve (Central Washington University), Lee Stemkoski (Adelphi University), and Erik Tou (Carthage College)

Introduction: Teaching, Research, and Primary Sources

If the number of books, papers, and conference sessions in recent years is any indication, the history of mathematics is growing ever more popular. Mathematicians have long been fascinated by stories of the masters who helped to build our discipline, but in recent years an increasing number of people have been using original sources when teaching and studying the history of mathematics. Original sources here refers to the papers and books in which mathematicians stated conjectures, proved theorems, and generally went about their work. Studying original sources is fun and exciting; seeing the raw first versions of major ideas in mathematics often gives us more insight into the creation of mathematics than does studying re-written, streamlined textbooks.

In general, original sources in the history of mathematics play two important roles. The first of these is fairly classical: collections of original sources are used by scholars in the field to study and understand the work of the original writers. The second role is newer: there has been an increasing effort in recent years to include original sources in the mathematics classroom. In part due to the work of David Pengelley, Janet Barnett, and Reinhard Laubenbacher (see [5], [7], [8]), a growing number of mathematics students are learning their field by reading original sources written by some of the greatest mathematicians of all time. For a particularly exciting example of this work, and for a chance to get involved, see the 16 projects in the Convergence article "Primary Historical Sources in the Classroom: Discrete Mathematics and Computer Science" or, for even more projects, Teaching Discrete Mathematics via Primary Historical Sources. Both are collaborative efforts by scholars at New Mexico State University, Old Dominion University, and Colorado State University at Pueblo.

Where does one find original sources? Traditionally these have been available only in dusty library stacks, and in source books—single volumes of original sources deemed to be of general interest. More recently, projects such as Google Books are making more of these original sources available online. Google Books, however, is far from being finished with its goal of scanning the world’s books into its database. Additionally, the very size of the database makes it difficult to browse, and the lack of meta-data sometimes makes the works hard to interpret.

If one decides to study original sources in mathematics, one can hardly do better than to read the words of Leonhard Euler, one of the greatest didactic writers in the history of mathematics. More than perhaps any other mathematician, Euler wrote to be understood. His works brim with examples, computations, and even dead-ends in his thinking process—the kind of digression academics are usually taught to avoid in their publications. Unfortunately, most of Euler’s works have never been collected in source books, and only a few are available on sites such as Google Books. It was precisely to correct this large gap in the availability of sources in the history of mathematics that the Euler Archive was created.

This article will introduce the reader to the Euler Archive, give some specific examples of how it has been used in mathematics teaching and research, and suggest some ways that researchers and teachers can take advantage of the site.

Dominic Klyve (Central Washington University), Lee Stemkoski (Adelphi University), and Erik Tou (Carthage College), "Teaching and Research with Original Sources from the Euler Archive," Convergence (August 2013), DOI:10.4169/loci003672