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Gauss published works on number theory, the mathematical theory of map construction, and many other subjects. Instead, he drew important mathematical consequences from this work for what is today called potential theory , an important branch of mathematical physics arising in the study of electromagnetism and gravitation.

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Gauss also wrote on cartography , the theory of map projections. For his study of angle-preserving maps, he was awarded the prize of the Danish Academy of Sciences in Gauss also had other unpublished insights into the nature of complex functions and their integrals , some of which he divulged to friends. In fact, Gauss often withheld publication of his discoveries.

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For this to be the case, there must exist an alternative geometric description of space. Rather than publish such a description, Gauss confined himself to criticizing various a priori defenses of Euclidean geometry. It would seem that he was gradually convinced that there exists a logical alternative to Euclidean geometry. It is possible to draw these ideas together into an impressive whole, in which his concept of intrinsic curvature plays a central role, but Gauss never did this.

Some have attributed this failure to his innate conservatism , others to his incessant inventiveness that always drew him on to the next new idea, still others to his failure to find a central idea that would govern geometry once Euclidean geometry was no longer unique. All these explanations have some merit, though none has enough to be the whole explanation. Another topic on which Gauss largely concealed his ideas from his contemporaries was elliptic functions.

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  • He published an account in of an interesting infinite series , and he wrote but did not publish an account of the differential equation that the infinite series satisfies. He showed that the series, called the hypergeometric series, can be used to define many familiar and many new functions. But by then he knew how to use the differential equation to produce a very general theory of elliptic functions and to free the theory entirely from its origins in the theory of elliptic integrals.

    This was a major breakthrough, because, as Gauss had discovered in the s, the theory of elliptic functions naturally treats them as complex-valued functions of a complex variable, but the contemporary theory of complex integrals was utterly inadequate for the task. When some of this theory was published by the Norwegian Niels Abel and the German Carl Jacobi about , Gauss commented to a friend that Abel had come one-third of the way. Gauss delivered less than he might have in a variety of other ways also.

    He corresponded with many, but not all, of the people rash enough to write to him, but he did little to support them in public. A rare exception was when Lobachevsky was attacked by other Russians for his ideas on non-Euclidean geometry. In contrast, Gauss wrote a letter to Bolyai telling him that he had already discovered everything that Bolyai had just published. Carl Friedrich Gauss. Article Media.

    The law of quadratic recipocity, Gauss' "Golden Theorem"

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    See Article History. If you want to re-create his construction of a regular gon or see his proof of the Fundamental Theorem of Algebra, then this is not the book for you.

    On the other hand, if you would like to know more about the man who discovered those things and more, then you need to read this book. Gauss's father wanted Carl to be a laborer like himself, but his mother, teachers, his patron, the Duke, and others recognized his talent for mathematics and encouraged him to pursue his investigations with numbers.

    Gauss Contribution to Maths

    As a teacher in a public school, I would recommend this book about the life of Carl Friedrich Gauss to my students. After reading it, you may better feel encouraged to follow your own instincts and interests. Linda Y.

    The Prince of Mathematics: Carl Friedrich Gauss by M.B.W. Tent

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