# Gauss, Carl Friedrich

Gauss was extremely careful and rigorous in all his work, insisting on a complete proof of any result before he would publish it. As a consequence, he made many discoveries that were not credited to him and had to be remade by others later; for example, he anticipated Bolyai and Lobachevsky in non-Euclidean geometry, Jacobi in the double periodicity of elliptic functions, Cauchy in the theory of functions of a complex variable, and Hamilton in quaternions. However, his published works were enough to establish his reputation as one of the greatest mathematicians of all time. Gauss early discovered the law of quadratic reciprocity and, independently of Legendre, the method of least squares. He showed that a regular polygon of ^{p}(2^{q}+1)(2^{r}+1) … , where 2^{q} + 1, 2^{r} + 1, … are prime numbers.

In 1801, following the discovery of the asteroid Ceres by Piazzi, Gauss calculated its orbit on the basis of very few accurate observations, and it was rediscovered the following year in the precise location he had predicted for it. He tested his method again successfully on the orbits of other asteroids discovered over the next few years and finally presented in his

Gauss was also interested in electric and magnetic phenomena and after about 1830 was involved in research in collaboration with Wilhelm Weber. In 1833 he invented the electric telegraph. He also made studies of terrestrial magnetism and electromagnetic theory. During the last years of his life Gauss was concerned with topics now falling under the general heading of topology, which had not yet been developed at that time, and he correctly predicted that this subject would become of great importance in mathematics.

See biography by T. Hall (tr. 1970).

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2023, Columbia University Press. All rights reserved.

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