Carl Gauss

Carl GaussCarl Gauss was a man who is known for makinga great deal breakthroughs in the wide variety of his work in both mathematicsand physics. He is responsible for immeasurable contributions to the fieldsof number theory, analysis, differential geometry, geodesy, magnetism,astronomy, and optics, as well as many more. The concepts that he himselfcreated have had an immense influence in many areas of the mathematic andscientific world.Carl Gauss was born Johann Carl FriedrichGauss, on the thirtieth of April, 1777, in Brunswick, Duchy of Brunswick(now Germany). Gauss was born into an impoverished family, raised as theonly son of a bricklayer.

Despite the hard living conditions, Gauss’s brillianceshone through at a young age. At the age of only two years, the young Carlgradually learned from his parents how to pronounce the letters of thealphabet. Carl then set to teaching himself how to read by sounding outthe combinations of the letters. Around the time that Carl was teachinghimself to read aloud, he also taught himself the meanings of number symbolsand learned to do arithmetical calculations.When Carl Gauss reached the age of seven,he began elementary school.

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His potential for brilliance was recognizedimmediately. Gauss’s teacher Herr Buttner, had assigned the class a difficultproblem of addition in which the students were to find the sum of the integersfrom one to one hundred. While his classmates toiled over the addition,Carl sat and pondered the question. He invented the shortcut formula onthe spot, and wrote down the correct answer. Carl came to the conclusionthat the sum of the integers was 50 pairs of numbers each pair summingto one hundred and one, thus simple multiplication followed and the answercould be found.This act of sheer genius was so astoundingto Herr Buttner that the teacher took the young Gauss under his wing andtaught him fervently on the subject of arithmetic. He paid for the besttextbooks obtainable out of his own pocket and presented them to Gauss,who reportedly flashed through them.

In 1788 Gauss began his education at theGymnasium, with the assistance of his past teacher Buttner, where he learnedHigh German and Latin. After receiving a scholarship from the Duke of Brunswick,Gauss entered Brunswick Collegium Carolinum in 1792. During his time spentat the academy Gauss independently discovered Bode’s law, the binomialtheorem, and the arithmetic-geometric mean, as well as the law of quadraticreciprocity and the prime number theorem. In 1795, an ambitious Gauss leftBrunswick to study at Gottingen University. His teacher there was Kaestner,whom Gauss was known to often ridicule.

During his entire time spent atGottingen Gauss was known to acquire only one friend among his peers, FarkasBolyai, whom he met in 1799 and stayed in touch with for many years.In 1798 Gauss left Gottingen without adiploma. This did not mean that his efforts spent in the university werewasted. 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 ofGreek mathematics.In the summer of 1801 Gauss published hisfirst book, Disquisitiones Arithmeticae, under a gratuity from the Dukeof Brunswick. The book had seven sections, each of these sections but thelast, which documented his construction of the 17-gon, were devoted tonumber theory.In June of 1801, Zach an astronomer whomGauss had come to know two or three years before, published the orbitalpositions of, Ceres, a new “small planet”, otherwise know as an asteroid.

Part of Zach’s publication included Gauss’s prediction for the orbit ofthis celestial body, which greatly differed from those predictions madeby others. When Ceres was rediscovered it was almost exactly where Gausshad predicted it to be.Although Gauss did not disclose his methodsat the time, it was found that he had used his least squares approximationmethod. This successful prediction started off Gauss’s long involvementwith the field of astronomy.On October ninth, 1805 Gauss was married toJohana Ostoff. Although Gauss lived a happy personal life for the firsttime, 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 upthe position of director of the Gottingen observatory. This was a timeof many changes for Carl Gauss.

Gauss had made his way to Gottingen bylate 1807. The following year his father died, and a year following thattragedy, his wife Johanna died giving birth to their second son, who wasto die shortly after her. Understandably Gauss’s life was shattered, heturned to his friends and colleagues for support. The next year, Gausswas married a second time. His new wife was named Minna, she was the bestfriend of Johanna. Although the couple had three children, this secondmarriage seemed to be somewhat of a expedience for Gauss.Gauss’s work was not visibly affected bythese life altering events.

In 1809, he went on to publish his second bookTheoria motus corporum coelestium in sectionibus conicis Solem ambientium.This publishing was a profound two volume thesis on the motion of celestialbodies. Gauss’s contributions in the field of theoretical astronomy continueduntil the year 1817. Gauss himself continued making observations untilthe age of seventy.In 1818, Gauss was asked to carry out ageodesic (a study in which predictions are made of exact points or areasizes of the earth’s surface) survey of the state of Hanover, to link withthe existing Danish grid. Gauss eagerly accepted the job, and took personalcharge of the survey. He made his measurements by day, and reduced themby night, using his incredible mental ability for calculations. To aidhim in his survey, Gauss invented the heliotrope, which worked by reflectingthe Sun’s rays using a design of mirrors and a small telescope.

But inaccuratebase 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 seventypapers. From the early 1800’s Gauss had had an interest in the questionof the possible existence of a non-Euclidean geometry.

In a book reviewof 1816 Gauss discussed proofs which suggested and supported his beliefin non-Euclidean geometry (which was later proved to exist), though hewas quite vague. Gauss later confined in one of his fellow theoreticiansthat he believed his reputation would suffer if he admitted to the publicthe existence of such a geometry.The period of time from 1817 to 1832 wasa particularly hard time for Gauss. He took in his sick mother, who stayedwith him until her death twenty-two years later. At the same time he wasin a dispute with his wife and her family about whether they should moveto Berlin, where Gauss had been offered a job.

Minna, his wife, and hrfamily 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. Gausswas quite enthusiastic about this prospect and by 1840, had written threeimportant papers on the subject.

These papers all dealt the current theorieson terrestrial magnetism, absolute measure for magnetic force, and an empiricaldefinition of terrestrial magnetism.Gauss and Weber achieved much in theirsix years together. The two discovered Kirchoff’s laws, as well as buildinga primitive telegraph device.

However, this was just an enjoyable hobbyof Gauss’s. He was more interested in the task of setting up a world widenet of magnetic observation points. This vocation produced a great dealof concrete results. The Magnetischer Verein and its journal were conceived,and the atlas of geomagnetism was published.From 1850 onwards Gauss’s work was thatof nearly all practical nature. He disputed over a modified Foucalt pendulumin 1854, and was also able to attend the opening of the new railway linkbetween Hanover and Gottingen, but this outing proved to be his last. Thehealth of Carl Gauss deteriorated slowly and he died in his sleep earlyin the morning of February 23, 1855.

Carl Gauss’s influence in the worlds ofscience and mathematics has been immeasurable. His abstract findings havechanged the way in which we study our world. In Gauss’s lifetime he didwork on a number of concepts for which he never published, because he feltthem to be incomplete. Every one of these ideas (including complex variable,non-Euclidean geometry, and the mathematical foundations of physics) waslater discovered by other mathematicians.

Although he was not awarded thecredit for these particular discoveries, he found his reward with the pursuitof such research, and finding the truth for its own sake. He is a greatman and his achievements will not be forgotten.