Carl Gauss Essays - Differential Geometers, Number Theorists

Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world. Carl Gauss was born Johann Carl Friedrich Gauss, on the thirtieth of April, 1777, in Brunswick, Duchy of Brunswick (now Germany). Gauss was born into an impoverished family, raised as the only son of a bricklayer. Despite the hard living conditions, Gauss's brilliance shone through at a young age. At the age of only two years, the young Carl gradually learned from his parents how to pronounce the letters of the alphabet. Carl then set to teaching himself how to read by sounding out the combinations of the letters. Around the time that Carl was teaching himself to read aloud, he also taught himself the meanings of number symbols and learned to do arithmetical calculations. When Carl Gauss reached the age of seven, he began elementary school. His potential for brilliance was recognized immediately. Gauss's teacher Herr Buttner, had assigned the class a difficult problem of addition in which the students were to find the sum of the integers from one to one hundred. While his classmates toiled over the addition, Carl sat and pondered the question. He invented the shortcut formula on the spot, and wrote down the correct answer. Carl came to the conclusion that the sum of the integers was 50 pairs of numbers each pair summing to one hundred and one, thus simple multiplication followed and the answer could be found. This act of sheer genius was so astounding to Herr Buttner that the teacher took the young Gauss under his wing and taught him fervently on the subject of arithmetic. He paid for the best textbooks obtainable out of his own pocket and presented them to Gauss, who reportedly flashed through them. In 1788 Gauss began his education at the Gymnasium, with the assistance of his past teacher Buttner, where he learned High German and Latin. After receiving a scholarship from the Duke of Brunswick, Gauss entered Brunswick Collegium Carolinum in 1792. During his time spent at the academy Gauss independently discovered Bode's law, the binomial theorem, and the arithmetic-geometric mean, as well as the law of quadratic reciprocity and the prime number theorem. In 1795, an ambitious Gauss left Brunswick to study at Gottingen University. His teacher there was Kaestner, whom Gauss was known to often ridicule. During his entire time spent at Gottingen Gauss was known to acquire only one friend among his peers, Farkas Bolyai, whom he met in 1799 and stayed in touch with for many years. In 1798 Gauss left Gottingen without a diploma. This did not mean that his efforts spent in the university were wasted. By this time he had made on of his most important discoveries, this was the construction of a regular seventeen-gon by ruler and compasses. This was the most important advancement in this field since the time of Greek mathematics. In the summer of 1801 Gauss published his first book, Disquisitiones Arithmeticae, under a gratuity from the Duke of Brunswick. The book had seven sections, each of these sections but the last, which documented his construction of the 17-gon, were devoted to number theory. In June of 1801, Zach an astronomer whom Gauss had come to know two or three years before, published the orbital positions of, Ceres, a new "small planet", otherwise know as an asteroid. Part of Zach's publication included Gauss's prediction for the orbit of this celestial body, which greatly differed from those predictions made by others. When Ceres was rediscovered it was almost exactly where Gauss had predicted it to be. Although Gauss did not disclose his methods at the time, it was found that he had used his least squares approximation method. This successful prediction started off Gauss's long involvement with the field of astronomy.On October ninth, 1805 Gauss was married to Johana Ostoff. Although Gauss lived a happy personal life for the first