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 time, he was shattered by the death of his benefactor, The Duke of Brunswick, who was killed fighting for the Prussian army. In 1807 Gauss left Brunswick to take up the position of director of the Gottingen observatory. This was a time of many changes for Carl Gauss. Gauss had made his way to Gottingen by late 1807.
The following year his father died, and a year following that tragedy, his wife Johanna died giving birth to their second son, who was to die shortly after her. Understandably Gauss’s life was shattered, he turned to his friends and colleagues for support. The next year, Gauss was married a second time. His new wife was named Minna, she was the best friend of Johanna. Although the couple had three children, this second marriage seemed to be somewhat of a expedience for Gauss. Gauss’s work was not visibly affected by these life altering events.
In 1809, he went on to publish his second book Theoria motus corporum coelestium in sectionibus conicis Solem ambientium. This publishing was a profound two volume thesis on the motion of celestial bodies. Gauss’s contributions in the field of theoretical astronomy continued until the year 1817. Gauss himself continued making observations until the age of seventy. In 1818, Gauss was asked to carry out a geodesic (a study in which predictions are made of exact points or area sizes of the earth’s surface) survey of the state of Hanover, to link with the existing Danish grid.
Gauss eagerly accepted the job, and took personal charge of the survey. He made his measurements by day, and reduced them by night, using his incredible mental ability for calculations. To aid him in his survey, Gauss invented the heliotrope, which worked by reflecting the Sun’s rays using a design of mirrors and a small telescope. But inaccurate base lines used for the survey and an unsatisfactory network of triangles. Gauss often doubted his work in the profession, but over the course of ten years, from 1820 to 1830, published over seventy papers.
From the early 1800’s Gauss had had an interest in the question of the possible existence of a non-Euclidean geometry. In a book review of 1816 Gauss discussed proofs which suggested and supported his belief in non-Euclidean geometry (which was later proved to exist), though he was quite vague. Gauss later confined in one of his fellow theoreticians that he believed his reputation would suffer if he admitted to the public the existence of such a geometry. The period of time from 1817 to 1832 was a particularly hard time for Gauss.
He took in his sick mother, who stayed with him until her death twenty-two years later. At the same time he was in a dispute with his wife and her family about whether they should move to Berlin, where Gauss had been offered a job. Minna, his wife, and hr family were enthusiastic about the move, but Gauss, who did not like change, decided to stay in Gottingen. Minna died in 1831 after a long illness. In 1832, Gauss and a colleague of his, Wilhelm Weber, began studying the theory of terrestrial magnetism.
Gauss was quite enthusiastic about this prospect and by 1840, had written three important papers on the subject. These papers all dealt the current theories on terrestrial magnetism, absolute measure for magnetic force, and an empirical definition of terrestrial magnetism. Gauss and Weber achieved much in their six years together. The two discovered Kirchoff’s laws, as well as building a primitive telegraph device. However, this was just an enjoyable hobby of Gauss’s. He was more interested in the task of setting up a world wide net of magnetic observation points.
This vocation produced a great deal of concrete results. The Magnetischer Verein and its journal were conceived, and the atlas of geomagnetism was published. From 1850 onwards Gauss’s work was that of nearly all practical nature. He disputed over a modified Foucalt pendulum in 1854, and was also able to attend the opening of the new railway link between Hanover and Gottingen, but this outing proved to be his last. The health of Carl Gauss deteriorated slowly and he died in his sleep early in the morning of February 23, 1855. Carl Gauss’s influence in the worlds of science and mathematics has been immeasurable.
His abstract findings have changed the way in which we study our world. In Gauss’s lifetime he did work on a number of concepts for which he never published, because he felt them to be incomplete. Every one of these ideas (including complex variable, non-Euclidean geometry, and the mathematical foundations of physics) was later discovered by other mathematicians. Although he was not awarded the credit for these particular discoveries, he found his reward with the pursuit of such research, and finding the truth for its own sake. He is a great man and his achievements will not be forgotten.