# The Main Contributions of John Carl Friedrich Gauss – Famous German Mathematician and Physicist

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Many may have heard this story; it is about a very intelligent student. One time in school his teacher asks every student in class to add from 1 to 100. Every student starts working on this task which would usually take a long time. However this student completed the task so quickly that the teacher thought he was randomly making up numbers. At last it turns out that the student is correct, the teacher asks the student how has he do it and it turns out the student has discovered a short cut way. This student is the famous German mathematician and physicist John Carl Friedrich Gauss.

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Gauss was born in Brunswick, Germany during the year 1777 on the 30th of April. Throughout his life, he has made many great discoveries that cover numerous of areas of study.

One of Gauss’s most important accomplishments was in 1797. He had discovered the proof for the fundamental theorem of algebra. This theory states that every polynomial that is not constant also having a complex coefficient will have at least one root. Even though the first proof given by him was not fully correct, he had provided 3 other proves later on that had successfully proven the theory.

Gauss also has great contribution to the development of number theory. He had shown in his book Disquisitiones Arithmeticae which was published during 1801, many important content including the introduction to the symbol of congruence and the use of this symbol with modular arithmetic. It also contains theories for binary and ternary quadratic forms, proofs for the law of quadratic reciprocity, and also showing that a 17-sided polygon can be constructed by only using a ruler and compass.

Another topic that Gauss has made significant discovery in was elliptic functions. However he kept his idea and did not publish it for a reason that no one knows. He has discovered an infinite series called the hyper geometric series and the equation that satisfied the series. Also, he knows how to use this differential equation to create a general theory of elliptic functions. This is very important because by the time Gauss had made his discovery. People still treat these series as complex-valued functions and complex variables, but the contemporary theory of complex integrals, which was used to solve these problems was not a very good tool for the task. However as stated before Gauss did not publish his discovery and afterwards part of his theory was discovered and published by someone else.

Another great discovery made by Gauss was the Theorema Egregium or the Remarkable theory. This theory is a major discovery of differential geometry, the mathematics that involves curves and surfaces. This discovery was led to by an earlier discovery also made by Gauss, the Gaussian curvature. The Theorema Egregium established an important property of the notion of curvature, which states that the curvature of a surface can be find by measuring angles and distance on the surface.

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