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The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth. Everybody who looks at the spectacle of modern algebra will be struck by this complementarity of freedom and necessity.
Teaching and Research with Original Sources from the Euler Archive
Getting Started: Navigating the Archive
The main limiting factor in digitizing Euler's works is the sheer volume of material. Eneström's index lists 866 distinct works, a number which includes 31 books and over 30,000 pages of material. What's more, this count does not include the more than one thousand letters written by Euler or the nearly two thousand received! Naturally, any attempt at archiving and organizing this material will require the user to make use of many different search features.
There are several different facets of any work of Euler's: the form in which it appeared (book, article, pamphlet, or private letter), the places it was published (Berlin or St. Petersburg, academic or private journal), the date it was produced or published (often very different dates), or the subject matter it contains (anything ranging from mathematics to music theory to philosophy). Taken together, these data comprise what might rightly be called a "fingerprint" for any of Euler's works. To clear through this thicket, the Euler Archive begins with a discrete list of categories that any user may employ in their search. These are:
Subject: Are you most interested in Euler as a mathematician? His mathematical papers and books are subdivided by discipline, including topics such as number theory, differential equations, and infinite series. Are you interested in Euler's works in physics and astronomy? These works are also subdivided, into topics ranging from planetary motion to optics to mechanics. A sample of this list is shown below:
Date of publication: When did the work appear in print? What other works of Euler appeared near the same time? Where was Euler working and living at the time?
Date of presentation: If you're looking for a paper: when did Euler present it to the Academy for peer review? Often, the publication date is many years after the date of presentation (in some cases as many as 50 years!), so this is an important datum to have.
Index Number: Eneström's index of Euler's works assigns a number to 866 of Euler's books and articles. For those who are well-versed in Euler scholarship, this can provide a shortcut to the work in question.
Translation: Which of Euler's works have been translated into English? Are there commentaries for these works? The Euler Archive maintains a list of known and pending translations of Euler’s works. Those interested in attempting their own translation can “sign up” on the Archive, to minimize unnecessary duplications. Those interested in analyzing a work that doesn’t require a translation may explore this listing of over 150 papers and books.
Clearly, the wide range of available searches offers any user the ability to quickly find a particular work, and also identify that work's fingerprint. However, the Archive can be used for casual browsing as well. Any user interested in finding Euler's original work can simply choose the subject material that she finds appealing, or the type of publication that is most amenable to her needs (letters, books, or articles).
For those who want more context for Euler’s works, the Euler Archive also provides a series of short, historical vignettes on topics ranging from Euler’s life to his contemporaries to histories of the Berlin and St. Petersburg Academies. Each of these articles provides a list of sources for further reading.
Klyve, Dominic, Lee Stemkoski and Erik Tou, "Teaching and Research with Original Sources from the Euler Archive," Loci (April 2011), DOI: 10.4169/loci003672