Gauss publishes Disquisitiones Arithmeticae (1795–1801)

Carl Friedrich Gauss published Disquisitiones Arithmeticae in Leipzig in 1801, consolidating number theory as a discipline. Written in 1798, the work covered elementary and algebraic number theory. The publication followed his 1799 doctoral thesis and reflected ideas developed during his studies at the Collegium Carolinum and University of Göttingen.

Episodes

Background and detail

Background. Gauss began his work on number theory in 1795, as stated in the preface to the Disquisitiones. He attended the Collegium Carolinum from 1792 to 1795, supported by the Duke of Brunswick, and later studied at the University of Göttingen until 1798. His mathematical diary from 1796 to 1814 reveals that many ideas for the Disquisitiones originated during this period.

Contents. The Disquisitiones Arithmeticae consolidated number theory as a discipline, covering both elementary and algebraic number theory. It included analytic results on class numbers, suggesting Gauss knew the class number formula by 1801. An unfinished chapter consisting of work done during 1797–1799 was found among his papers after his death.

Publication. Written in 1798 when Gauss was 21, the book was published in 1801 when he was 24. The publication occurred in Leipzig. The work was later translated into French in 1807 and German in 1889, ensuring its continued influence on mathematical scholarship.

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