mathematical community as well as many others. He is considered by many to be one of the

Transcription

1 Kramer 1 Johann Friedrich Carl Gauss is a name that is instantly recognized by members of the mathematical community as well as many others. He is considered by many to be one of the greatest mathematicians of all time. Gauss was born into a poor family in Brunswick, Germany where neither of his parents had much schooling. However this did not stop him from doing things like teaching himself to read and write. Once he became old enough to attend school, he immediately drew attention from his teachers. His teachers from elementary school helped him a lot by guiding his education and then helping him get into the Collegium Carolinum, a top secondary school for science at the time. Gauss was always a good student and the idea of being able to gain knowledge meant a lot to him so he always put school first and took advantage of his opportunities. After the Collegium Carolinium, Gauss attended the University of Gottingen which took him away from home. However, he was free to study on his own and study whatever he wanted. This is where he developed a lot of his major ideas, many of them went on to make great contributions to mathematics. Gauss earned his doctoral degree from the University of Helmstedt for what we know as the fundamental theorem of algebra. Gauss has made a lot of contributions to math that we are still using today. One of the areas he contributed to is number theory, which has a lot of application to many things we use today. Now let s see how Gauss got started. Johann Friedrich Carl Gauss was born in Brunswick on April 30, 1777 (Buhler 5). He was the only child of Gebhard Dietrich Gauss and Dorothea Benze, however, he did have a halfbrotherfrom his father s previous marriage (Buhler 5). Even from an early age it was easy to see that he was very intelligent. By the age of three, Gauss knew how to count and perform basic calculations (Buhler 7). He started to attract attention once he started elementary school,

2 Kramer 2 which was in 1784 when he was seven or eight years old. However, before entering school, Gauss had taught himself how to read and write and he did so without the help of his parents (Buhler 7). His teacher, Buttner, was very impressed by Gauss and he took a special interest which meant helping and encouraging him. In fact, Buttner even got a special math book for Gauss from Hamburg (Buhler 7). Now, at this point in his childhood it was clear that Gauss was gifted and many people considered him a prodigy. The assistant to Buttner, Martin Bartels, was one of the people who recognized Gauss s ability and he devoted a lot of time and attention to him (Buhler 7). However, his parents didn t really appreciate the advantage of doing good in school but, this is somewhat understandable since they lived in a time where they were in need and neither of his parents had much of an education themselves (Buhler 7). Eventually, in 1788, Gauss left his parents after Buttner had helped him get into a secondary school. Now that Gauss was in a secondary school, things were different. For the first time, Gauss had regularly scheduled classes and he was also in larger classes with students around the same age as him. However, his classes required him to know Latin. This forced Gauss to spend a lot of time learning and gaining a good understanding of the language. Also, he spent time learning High German. As he got older, Gauss s reputation grew. Since Gauss was seen as a prodigy, he was introduced to the Duke of Brunswick-Wolfenbuttel in 1791, who ended up being very impressed (Finkel). Therefore, he granted Gauss a yearly salary, which at the time was basically a scholarship (Finkel). Gauss was a very good student and he had an excellent academic record. As a result, Gauss was selected to attend the Collegium Carolinum where he studied from 1792 to 1795 (Finkel). This was a really good thing to happen to Gauss because the Collegium Carolinum was a new school that was concentrating on science, and it was one of

3 Kramer 3 the best schools of its kind. Gauss was incredibly happy with the fact that he could increase his knowledge here and he realized how great the opportunity was, so he centered his life around school and his work and put all nonacademic interests behind him (Buhler 16). However, he did make several good friends during his time there. The library at the Collegium Carolinum was very good and it had all of the classic math books and Gauss studied a lot of them (Buhler 16). When Gauss left the Collegium Carolinum, he had developed a very strong interest in math and he wanted to learn more. Gauss left his hometown of Brunswick and the Collegium Carolinum to continue his studies in mathematics at the University of Gottingen in 1795, at the age of eighteen(buhler 17). At the time, there was a local university, the University of Helmstedt, that the Duke wanted Gauss to attend. However, Helmstedt was an old school and it was not really centered around science and it did not have the resources that Gottingen had (Buhler 16). In fact, Gauss claimed that he chose Gottingen because of its library (Buhler 16). So, Gauss spent the next three years at Gottingen, however, while staying there he studied completely on his own and studied only what he wanted to(buhler 17). Gauss was on his own to do as he pleased. After three years at Gottingen, Gauss decided to leave for unknown reasons and he did so without any degree(buhler 17). By the time he left Gottingen, Gauss had already studied and learned what he needed to in order to continue with all of his ideas and mathematical papers (Buhler 17). Shortly after leaving Gottingen, Gauss submitted his dissertation to the University of Helmstedt. He was granted a doctoral degree and he didn t even have to give an oral presentation of his work (Finkel). His dissertation was what we know call the fundamental theorem of algebra.

4 Kramer 4 Until the point of his dissertation, the only published work that Gauss had was that a 17- gon could be constructed(buhler 39). However, he still had a lot of ideas as well as unfinished essays. At this point in his life, Gauss had moved back to Brunswick, however, he had no secure income but, the Duke had agreed to keep paying him a salary (Buhler 39). The Duke was very active in Gauss s work. He called for Gauss to submit his dissertation and he also paid for the publication of it (Buhler 39). His dissertation was about the fundamental theorem of algebra, which was reoccurring in Gauss s work. In his dissertation, he gave several proofs of the fundamental theorem of algebra. The fundamental theorem of algebra is one example of how great Gauss really was. He figured out something that we rely on today and that we apply to a lot of different things. Gauss has also made contributions to the area of math known as number theory. Number theory is a big area of math that we still use a lot today for things such as computer security. Some of his work in number theory includes divisibility rules for three, nine, and eleven and congruences for rational numbers modulo a natural number (Buhler 21). Gauss also proved the uniqueness of factorization of integers into primes and defined the concept of greatest common divisors (Buhler 21). Also, he worked with what Fermat and Euler had already done and tried to improve on their ideas. In conclusion, Gauss started as a gifted boy in Brunswick, Germany. He quickly became noticed for his intelligence by many. He continued to work hard and to be a good student and earned his doctoral degree by giving us the fundamental theorem of algebra. He went on to make more contributions in areas of math such as number theory. Gauss s ability and insight

5 Kramer 5 were incredible and his work is still highly valued today. These are reasons why he is considered to be one of the greatest mathematicians of all time.

6 Kramer 6 Buhler, W.K. Gauss: A Biographical Study. New York: Springer-Verlag, Finkel, B.F. Biography: Karl Frederich Gauss. 27 September 2015.