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A: Mitte, Leipzig, Sachsen, Germany

Karl Friedrich Gauss, the Prince of Mathematicians, Issues Disquisitiones arithmeticae

Painting of Carl Friedrich Gauss by Christian Albrecht Jensen (1840).
Painting of Carl Friedrich Gauss by Christian Albrecht Jensen (1840).

In 1801, at the age of 24, Carl Friedrich Gauss published Disquisitiones arithmeticae in Leipzig, revolutionizing number theory.

"In this book [Gauss] standardized the notation; he systematized the existing theory and extended it; and he classified the problems to be studied and the known methods of attack and introduced new methods. . . . [The Disquisitiones] not only began the modern theory of numbers but determined the directions of work in the subject up to the present time" (Kline, Mathematical Thought from Ancient to Modern Times [1972] 813).

The typesetters of this work had difficulty understanding Gauss's new and difficult mathematics, creating numerous elaborate mistakes which Gauss was unable to correct in proof. After the book was printed Gauss insisted that, in addition to an unusually lengthy four-page errata, the worst mistakes be corrected by cancel leaves to be inserted in the copies before sale. Copies vary in the number of cancel leaves—a topic about which I have never seen a comprehensive bibliographical analysis.

The difficulty of understanding Gauss's highly technical work was hardly alleviated by the sloppy typesetting.  The few mathematicians who were able to read the Disquisitiones immediately hailed Gauss as their prince, but the full understanding required for further development did not occur until publication in 1863 of Johan Peter Gustav Lejeune Dirichlet's less austere exposition in his Vorlesungen über Zahlentheorie.

Hook & Norman, The Haskell F. Norman Library of Science and Medicine (1991) no. 878. Carter & Muir, Printing and the Mind of Man (1967) no. 257.

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