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Gauss was a true genius in mathematics who can be compared with Archimedes and Newton. Because of his fundamental contributions to various fields of mathematics some of which are algebraic equation, differential equation, differential geometry and the theory of numbers, he has been called the founder of modern mathematics. He also achieved great contributions in electro-magnetism and astronomy. In this work which was prepared when he was eighteen, Gauss demonstrated the law of quadratic reciprocity, the theory of congruences and a new method for division of the circle. He reorganized the theory of numbers by introducing the concept of congruent numbers and thus initiated the modern theory of numbers.
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