Life of Bernhard Riemann - Coursework Example

Life of Bernhard Riemann Your Bernhard Riemann Historical and social context of Riemann’s short life are promptly recognized. Riemann was born to a pastor of Breselenz near Dannenberg in the kingdom of Hanover in 17 September 1826. He went to gymnasiums in Hanover (1840-1842) an in Luneburg (1842-1846) and studied at Gottingen (1846-1847, 1849-1851) and at Berlin (1847-1849). During 1851, Riemann got his doctorate and habilitated that refers to taking qualifying exam for becoming a lecturer in university, both at Gottingen under Gauss. At Gottingen, he became an associate professor in 1857 and a full professor in 1859(Laugwitz, 2008, p.1). This paper briefly explores Bernhard Riemann’s life, his contributions to mathematics, and the way his surroundings influenced his work. When it comes to learning about Riemann’s developing years, it is critical to consider that he lived among his family in an isolated Hanover Wendland which is a sparingly settled and undeveloped area on the Elbe River. His father Friedrich Bernhard Riemann relocated from Boiezenburg, on the Mecklenburg coast of Elbe. After Bernhard’s birth, his father assumed the parish in Quick-born near Breselenz. His wife and Riemann’s mother was daughter of a Hofrat in Hanover. Being isolated for a long period, Riemann found it problematic to associate with other people throughout his life. Through the two phases of his life as a student and as an educator, he remained fascinated by the security and solitude of Quickborn. However, he lost this anchorage after his father’s death in 1855. It appeared that he wasn’t interested in contacting with people rather he stubbornly discouraged the efforts at greater closeness by those who associated with him in spirit, such as, Eisenstein in Berlin. Dedekind was the only one who managed to take him out of loneliness sometimes; however, he has no clue about the real contents of his scientific contacts. It is quite clear that Riemann’s scientific thoughts are a reflection of his introvert nature (Laugwitz, 2008, p.1). He used to indulge in deep thinking and wanted to reach at the “explanation of existence and of historical development” by concentrating on the “inner perception” of the “laws of spiritual events” (W.511 as cited in Laugwitz, 2008, p.2). Rienmann wanted to explore the universe reflected in his soul as in a Leibniz monad. He found sanctuary in speculative meditation even when he wanted to work on mathematical papers, or to get into some vigorous activity for a physical experiment. Very often, he calls himself to work and under double compulsion to justify himself (Laugwitz, 2008, p.2).He referred “main thing in religion” to the “daily self-test before the face of God” which is followed though worldly call of work (cited in Laugwitz, 2008, p.2). It is this nature that led him to apologetically write to his father during one of his rare escapes with a group of some scientists, he explained to him as a justification that he spent all morning working diligently and moved ahead as much as if he was sitting on his desk with books(W.546 cited in Laugwitz, 2008, p.2). His perception and mode of life had physical parallels. The world considers him a hypochondriac that his widow later pleaded Dedekind to oppose in his biography (Dugac, 1976 as cited in Laugwitz, 2008, p.2). The fact is that Riemann’s physical health has always been poor as he suffered from chronic constipation for a long time (Neuenschwander 1981a, 238 as cited in Laugwitz, 2008, p.2). During 1862, he contracted pleurisy that led to his permanent lung damage. It was followed by his long stays in Italy. Though, it didn’t improve his health, but he gained some spiritual freedom (Laugwitz, 2008, p.2). Dedekind observed (W.555/556) that the days he spent in Italy were the shiniest ones in his life, that glorious land rich in art and nature made him the happiest. There, he felt that he was as free as any other human being, free from suppressing concerns he felt in Gottingen at every step. Due to this sense of freedom and awesome climate, Riemann health remained better and he very often he came across as the happiest(as cited in Laugwitz, 2008, p.2). As far as Riemann’s interests in physics and philosophy is concerned, there are hardly any clues (Laugwitz, 2008, p.2). Dedekind narrates rather impersonally that newlywed and recovering from illness, Riemann took “great interest” in the “art treasures and antiquities” of Italy during his 1863 visit from Sicily to Gottingen (as cited in (Laugwitz, 2008, p.3). During the visit to Italy, he got to meet mathematicians very often. It was similar to Riemann’s early visits to Berlin (1859) and Paris (1860) which were aimed at his scientific pursuits (Laugwitz, 2008, p.3). Besides his family, Riemann has close contacts with his immediate colleagues. With minimum outside contact, it is not surprising that he could only find a match in his circle of acquaintances (Laugwitz, 2008, p.3).According to Neuenschwander (Riemann, 1991, p. 48) Riemann wanted to marry a niece of the physicist Wilhelm Weber, but ended up marrying a friend of his sisters, however, the marriage appeared to be happy (as cited in Laugwitz, 2008, p.3). Political and Economic Situation Agriculture played crucial role in the North-German plain during the 19th century. During Riemann’s lifetime, there was development in communications and industrialization. Moreover, customs limitations slowly lost their importance. Riemann appeared to be less interested in political change, like Gauss. In 1837, Hanover’s union with England expired, but resulting suppression of liberal trends couldn’t influence rural parishes and gymnasiums in comparison to Gottingen University, because seven of reputed professors had to leave. At the time of 1848 revolution, Riemann was a student in Berlin (Laugwitz, 2008, p.3). Dedekind (W.544) stated that “The great political events of the year 1848 moved [Riemann] deeply; he witnessed the March revolution, and as a member of the corps formed by the students was on guard duty at the royal palace from 9 in the morning on March 24 until 1 in the afternoon of the next day” (as cited in Laugwitz, 2008, p.3). However, his thoughts about the whole change remained unknown as he died before the annexation of Hanover by Prussia on 3 October 1866(Laugwitz, 2008, p.4) During those days, those who were landless had other things to be concerned about than politics. The family has to provide for uneducated or unemployed members, such as, unmarried daughters and sisters. Old-age or surviving dependants pension was not provided. Teachers, pastors, and university professors have to stay in the job for a lifetime. However, an admirable exception was the provision of funds for the widows of Gottingen teachers, primarily because of Gauss. It is assumed that Riemann may have turned down the offer to work at Pisa because he didn’t want to lose support at Gottingen. Educators usually had to rely on their tutoring, taking students to board, or license to brew and serve beer for their secondary source of income. Higher education opportunities for son were costly, and it was expected that family would benefit before long. Riemann remained dependant on his father for quite long time. In that time, health care provisions were not sufficient enough. Since Riemann has always suffered from poor health, he was unable to take on the responsibility of second income, such as tutoring with his own scientific work. On the contrary, Dedekind revels that he relied on these income sources during his teaching period (as cited in Laugwitz, 2008, p.4). Riemann had one brother who was employed at a post office and four sisters. Official residence could accommodate a large family and expenses were low in a remote area, however, school and university education at a distant place was expensive and required sacrifices on part of family. At that time, even most talented students and teachers had to lead mediocre lives. During 1854, Riemann’s income from tuition fee was very low; moreover, he had to provide for his three surviving sisters when his brother died in 1857. He was excited when appointed as an associate professor with annual salary of 300 thaler(Laugwitz, 2008, p.4).It is interesting to note that in April 1858, Dedekind was offered 850 thaler for the job, and later when became a professor at Braunschweig in 1864, his annual salary was 1480 (Knus in Harborth, 1982 as cited in Laugwitz, 2008, p.5). Riemann’s Contributions to Mathematics Riemann’s father was his first teacher; therefore, he started his first arithmetic when he was only six. At ten, he used to have a teacher, but as it was a trend then, pupils soon became teachers. At the age of fourteen he lived with his grandmother, he sent gifts to the family. A very important gift was an original perpetual calendar. One of the best phases of his life was when he got admission in University of Gottingen at the age of nineteen (White). Riemann was esteemed and one of the brilliant German mathematicians of his time. He studied mathematics under the supervision of Gauses and explored physics in the presence of Wilhelm Weber. He made huge contribution to geometry, complex analysis, and mathematical physics (Weisstein, 2007). It is true that the amount of work he produced was low due to his small life and poor health, but originality and power of his work on function and geometry was incredible. In 1850, he produced his first paper on the theory of functions of a complex variable. This theory introduced a method of treating the theory of functions. During 1854, Riemann created his acclaimed memoire on hypotheses that laid the foundations of geometry (Ball, 1960, p. 382). He revealed in this hypothesis that there are different kinds of lines and surfaces; therefore, there are different kinds of space of three dimensions (White). According to Ball (1960) as White (n.d.) states that “The axioms of place geometry are true within the limits of experiment on the surface of a sheet of paper, and yet we know that the sheet is really covered with a number of small ridges and furrows upon which the axioms are not true, As well they may not be true for a very small portion of space.” It is evident that more complex mathematical ideas usually come from the examination of questions that seem simple. Similarly, studying the behavior of Riemann’s zeta function is a complex object. However, investigation of function’s theory originated from an examination of prime numbers’ distribution. It may seem adequate to find the next known prime number, but this is not the case. Mathematicians today are not satisfied with finding a large number of primes and observing their distribution since there is infinite number of primes, rather they try to find a general rule that decides the distribution of primes of any magnitude. This quest led mathematicians like Riemann to use theory of complex function in order to illustrate the distribution of primes (Patterson, 1988 as cited in Erickson, 2005, p.22). In 1859, Riemann came up with his remarkable challenges to mathematicians, his hypotheses on prime numbers. It was to determine that how many prime numbers are less than any given number n (White). The equation for Riemann’s hypotheses (as cited in White) is: Riemann Zeta Function ζ(S) is a vital complex function and its behavior influences the distribution of prime numbers among the natural numbers (Erickson, 2005, p.22). Later, he presented memoirs on elliptic functions and on the distribution of primes (Ball, 1960, p. 382). He examined the conformal representation of areas, a problem which was later investigated by H.A. Schwarz and F.H. Schottky (Ball, 1960, p. 383). In addition, in multiple periodic functions, it is justified to that his memoir in Borchardt’s Journal in 1857, he worked for Abelian functions what Abel had done for elliptic functions (Ball, 1960, p. 383). His work laid the foundations of general relativity. He examined the Riemann zeta function that led to Riemann’s hypothesis. Moreover, he came up with the definition of integral and invented Riemann’s surfaces. In addition, he came up with the function that was continuous at an infinite number of points in an interval, but its integral was still present (Segal, 1978 as cited in Weisstein, 2007). In Uber eine Frage der Warmeleitung, he came up with the theory of quadratic forms. He also stressed that the broadcast of electricity is not instantaneous, rather occurred through the luminiferous ether at the speed of light (Weisstein, 2007). As Laugwitz (2008, p.1) narrates, in June of 1862, he married to a friend to his sisters named, Elise Koch. His health condition has always been compromising. Most of his life was spent in Italy where his only daughter, Ida, was born. During the early days of war with Prussia, Riemann went to south again. He died on 20 July 1866 at a tragically young age at 39 in Selasca on Lago Maggiore. Regardless of his poor health, Riemann’s contributions to the world in general, and mathematics in particular are robust and will be remembered forever. References Ball, W.W. Rouse. (1960).A Short Account of the History of Mathematics. New York: Dover Publications, Inc. Erickson,C. (2005). A Geometric Perspective on the Riemann Zeta Function’s Partial Sums. Retrieved from http://web.stanford.edu/group/journal/cgi-bin/wordpress/wp-content/uploads/2012/09/Erickson_NatSci_2005.pdf Laugwitz,D. (2008). Bernhard Riemann 1826-1866: Turning Points in the Conception of Mathematics. (A. Schenitzer,Trans).Boston: Birkhauser. Weisstein,W.E.(2007). Riemann, Bernhard (1826-1866).Retrieved from http://scienceworld.wolfram.com/biography/Riemann.html White,B.(n.d.). Bernhard Riemann: 1826-1865. Retrieved from http://www.math.wichita.edu/history/Men/riemann.html Read More

His perception and mode of life had physical parallels. The world considers him a hypochondriac that his widow later pleaded Dedekind to oppose in his biography (Dugac, 1976 as cited in Laugwitz, 2008, p.2). The fact is that Riemann’s physical health has always been poor as he suffered from chronic constipation for a long time (Neuenschwander 1981a, 238 as cited in Laugwitz, 2008, p.2). During 1862, he contracted pleurisy that led to his permanent lung damage. It was followed by his long stays in Italy.

Though, it didn’t improve his health, but he gained some spiritual freedom (Laugwitz, 2008, p.2). Dedekind observed (W.555/556) that the days he spent in Italy were the shiniest ones in his life, that glorious land rich in art and nature made him the happiest. There, he felt that he was as free as any other human being, free from suppressing concerns he felt in Gottingen at every step. Due to this sense of freedom and awesome climate, Riemann health remained better and he very often he came across as the happiest(as cited in Laugwitz, 2008, p.2). As far as Riemann’s interests in physics and philosophy is concerned, there are hardly any clues (Laugwitz, 2008, p.2). Dedekind narrates rather impersonally that newlywed and recovering from illness, Riemann took “great interest” in the “art treasures and antiquities” of Italy during his 1863 visit from Sicily to Gottingen (as cited in (Laugwitz, 2008, p.3). During the visit to Italy, he got to meet mathematicians very often.

It was similar to Riemann’s early visits to Berlin (1859) and Paris (1860) which were aimed at his scientific pursuits (Laugwitz, 2008, p.3). Besides his family, Riemann has close contacts with his immediate colleagues. With minimum outside contact, it is not surprising that he could only find a match in his circle of acquaintances (Laugwitz, 2008, p.3).According to Neuenschwander (Riemann, 1991, p. 48) Riemann wanted to marry a niece of the physicist Wilhelm Weber, but ended up marrying a friend of his sisters, however, the marriage appeared to be happy (as cited in Laugwitz, 2008, p.3). Political and Economic Situation Agriculture played crucial role in the North-German plain during the 19th century.

During Riemann’s lifetime, there was development in communications and industrialization. Moreover, customs limitations slowly lost their importance. Riemann appeared to be less interested in political change, like Gauss. In 1837, Hanover’s union with England expired, but resulting suppression of liberal trends couldn’t influence rural parishes and gymnasiums in comparison to Gottingen University, because seven of reputed professors had to leave. At the time of 1848 revolution, Riemann was a student in Berlin (Laugwitz, 2008, p.3). Dedekind (W.544) stated that “The great political events of the year 1848 moved [Riemann] deeply; he witnessed the March revolution, and as a member of the corps formed by the students was on guard duty at the royal palace from 9 in the morning on March 24 until 1 in the afternoon of the next day” (as cited in Laugwitz, 2008, p.3). However, his thoughts about the whole change remained unknown as he died before the annexation of Hanover by Prussia on 3 October 1866(Laugwitz, 2008, p.4) During those days, those who were landless had other things to be concerned about than politics.

The family has to provide for uneducated or unemployed members, such as, unmarried daughters and sisters. Old-age or surviving dependants pension was not provided. Teachers, pastors, and university professors have to stay in the job for a lifetime. However, an admirable exception was the provision of funds for the widows of Gottingen teachers, primarily because of Gauss. It is assumed that Riemann may have turned down the offer to work at Pisa because he didn’t want to lose support at Gottingen.

Educators usually had to rely on their tutoring, taking students to board, or license to brew and serve beer for their secondary source of income.

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