Carl Friedrich Gauss – The One True Mathematician
Looking at the historical period that spans roughly the last two decades of the eighteenth and first half of the nineteenth century, one of all major political events is in the focus: The French Revolution, Napoleon’s rise and fall. And yet other things happened at that time, which, if we value them with their lasting value, can not underestimate anything compared to the bloody wars in which Europe was trying to create its future life form. Who would have even thought that even in these lively times a peaceful scientific phenomenon in the untiring work found its own fulfillment: Karl Friedrich Gauss, the greatest mathematic genius of all time, created its uninterrupted works. Almost there is no other example of such a superiority of a scientist who would be unlimited and generally recognized as Gauss’s case. When once King Hannover gave him a memorial to cast a medal with the inscription “Georgius V. Rex Hannoverae Mathematicorum Principle”, he gave him an honorary title, which no one has ever disputed since then. As a “Principle Mathematicorum”, it is known and worshiped not only by German mathematicians but by mathematicians all over the world.
Before 165 years, April 30, 1777, Karl Friedrich Gauss was born in Braunschweig. His father, Gerhard Diederich Gauss, was a mason and possessedand his mother was a born beggar. Seven years later, Gauss started the CatherineFolk School (a public school named after St. Catherine). There, according to the school archive, after the two-year school attendance came to the so-called computing class, his unusual mathematical abilities were revealed.
A well-known story is how a teacher gave the pupils a job to sum all numbers from 1 to 40. For a few moments, Gauss had solved the task in his head. He recalled that the required sum can be divided into partial sums of 1 + 40, 2 + 39, 3 + 38, i.e., each giving 41. Since 20 such partial sums can be made, the result is 20 × 41 = 820. Every pupil knows this method today. It is contained in the well-known formula for the sum of the arithmetic order. The fact that a nine-year-old boy came to such an idea in the moment was the first manifestation of his exceptional mathematical intelligence. This unusual talent was soon observed, and Duke Karl Wilhelm Ferdinand from Braunschweig allowed young Gauss the attendance of higher schools. So Gauss arrived in Catharineum in 1788, and successfully completed it in 1793 and at Carolinum, the right preparatory school for the university. He went to Göttingen University to study in 1795 – 98, after which he returned to Braunschweig and remained there without having a permanent job, privately taught, until 1807. That year he was invited to Göttingen as a professor of astronomy and director of the observatory, and he held that place until his death.
That the moment of appearing such a powerful mathematical talent as Gauss falls in the last decade of the 18th century has to be described as a happy fate of destiny. After Newton’s and Leibnitz’s discovery of the infinitesimal account in the 17th century, he began to stir up mathematics. At a time when Gauss began his scientific work, the tide of the discovery had somewhat calmed down. There was a moment of need for a powerful mind that would critically clarify the various issues that were not dealt with with due strenuousness, but which would give a new deciding impetus for further development and deepening of the achieved knowledge.
The first scientific work of the 19-year-old Gauss is his seventh-century structure. The problem was resolved on March 30, 1976, and he gave his beloved friend, the Hungarian mathematician Wolfgang Bolyaii, a small tile on which he made this account. Over the previous two thousand years it was believed that all of the correct polygons with odd number of pages, with a divider and ruler, can only be constructed of a triangle, a five-octet and a fifteenth century. Gauss not only gave the structure of the seventh octave, but also demonstrated that it would have been possible to construct each polygon, whose number of pages is such an prime number, that when decreasing for one, the potency of the number two is exponent again its potency number two. The respective prim numbers are now called gauss’s prim numbers, and so far they are known for five: 3, 5, 17, 257, 65537. One solution for the 257-thesis was later published by Richelot, and Hermes managed to reach the 65537-terco during a ten-year study. Gauss’s theory of division of the circle, on which these facts are based, forms one chapter of 1801 published by Gauss’s masterpiece “Disquisitiones arithmeticae”, which forms the basis of modern numerical theory.
In 1899, Gauss gained an academic degree in Helmstedt on the basis of his first outstanding evidence of the so-called Fundamental Theory of Algebra, which speaks of the existence of the root of algebraic equations.
A strong incentive for some problem of applied mathematics was given to young Gauss on January 1, 1801 when Piazzi discovered Ceres, the first of so-called small planets or asteroids. Gauss set the task of calculating Kepler’s movement of a new star whose observation was limited to a very small interval. This problem leads to the 8th level equation, and extensive approaches to the approximate account were needed to solve it, which Gauss first had to overcome. Based on his results, Ceres was re-discovered and this success brought Gaussian’s first moments of glory. Based on these works, which he further elaborated, he created his great work published in 1809, “Theoria motus corporum coelestium in sectionibus conicis Solem ambientium”, which became the law of computational astronomy.
As the director of the Göttingen observatory, Gauss worked on calculating the disturbance of Pallas, the other small planet, which was 28th III. 1802 discovered by Olbers. This task, which required enormous computational work, ran a long way but did not manage to end. Nonetheless, dealing with this task has become extraordinarily fruitful, as evidenced by the three major discussions that came out in 1812, 1814 and 1818. They concern mathematical analysis of very important hypergeometric order, mechanical quadrature problem and secular disorders.
In 1816 Gauss was entrusted with the task of carrying out the land survey of Hanover. Gauss underwent this for the then times a very difficult task with only his own energy. He worked on these measurements from 1821 to 1825, but his entire work was completed by his assistants only in 1841. The scientific result of this work is made up of several important geodetic articles, of which the “least squares method” was published in 1821 and 1823. years. This method of equalizing too many observations has so far remained an inexhaustible handy tool for computing in the geodesist. Gauss hypothetical expectations, which add to his geodetic works, went a long way further. In 1827, the “Disquisitiones circa superficies curvas” debated with geometry of curved surfaces. After Riemann has expanded to more dimensions, this classical debate has grown, and lately, especially in the hands of Italian mathematicians – to mention Riccion’s poem – in the imposing construction of multidimensional differential geometry, a branch of geometry that would play a decisive role in the development of modern physics.
At the Assembly of Natural Science in Berlin in 1828, Gauss met Alexander von Humboldt. Later this acquaintance developed into a friendship that lasted for a lifetime. Gauss, along with 27 years younger Wilhelm Weber, began to experiment with Humboldt’s quest to deal with Earth Earth magnetism. From this physically oriented activity, in 1832, there was a significant debate about the absolute magnitude of the magnetic measurements, as well as further discussion that came from the period 1838 to 1840 on Earth’s magnetism and potential theory. The result of technical significance arising from joint collaboration Gauss and Weber is a generalized electromagnetic telegraph construction.
In addition to these prominent contributions, which were still known to Gauss’s life, he found in his legacy a multitude of results that he did not publish and which were independently discovered by other mathematicians later on. So he still had a far-reaching knowledge of the elliptical functions as a young man. Most of these results were later found by Jacobi, and especially the ingenious yet unhappy Norse Niels Henrik Abel (1802-1829). Gauss also addressed the ancient problem of parallel axioms. He came to the full knowledge of the possibility of the existence of non-euclidean geometry, which later became a general mathematician through the articles of Hungarian Bolyai, the son of the already mentioned Wolfgang Bolyai, and Russi of Lobachevsky. The fact that Gauss did not reveal these things should be attributed to his unusual conscientiousness, which required him to release the magazine only in full length, form and content until the finishing touches of the finishing touches.
Despite great scientific successes and externally looking at a lively way of life, Gauss lacked happiness and satisfaction. Whether his diary, the only document openly revealing his closed and withdrawn nature, can, in addition to the dubious formulas, also come to this sentence, written with fine pencil moves: “Death suits me from this life.” These words, clothed with their arrogant tragedy, cast a fiery spark of light on the mental state of a great man whose promete spirit had not given him peace or allowed rest, but had always driven him further to new challenges. His job not only sought the highest concentration, but often the enormous calculation, which he was able to carry out with tough perseverance and almost inhuman diligence. There must have been periods of exhaustion and discouragement that could grow to life-saturation. Additionally, Gauss was at that time – in 1807 – he had material problems, and he also suffered because of lack of understanding of his closest environment, which could not understand his work energy devoted to such impractical things.
Gauss died on February 23, 1855.
When today we looked back at the life and work of Karl Friedrich Gauss, this most prominent mathematician at all, then this should be a symbol for the undisguised expansion that has been in the field of mathematics in natural sciences and technology since the Gauss era and deepened the understanding we have has given the current development of this science, starting with the most difficult problems of mathematical analysis, to the very basic issues that arise in the field of pure logic.
Mathematics is not only the most intense weapon in our successful struggle to overcome natural forces. It is above all one of the most intimate professions of the human spirit. If under the music we understand the art of tones, then under mathematics we understand art of life.