Georg Friedrich Bernhard Riemann was a revolutionary mathematician. He was born on September 17, 1826 in Breselenz, a village in Germany. His father, Friedrich Bernhard Riemann, who was a Lutheran minister, taught Riemann until he was ten. Then, Georg Friedrich Bernhard Riemann was taught by a teacher from a local school. Riemann had always displayed an interest in mathematics, especially when he studied at Lüneburg at the age of fourteen. His teacher gave him a textbook on a number theory by Legendre and six days later, Riemann had completed the 859 page book claiming to have mastered it. Once Riemann was nineteen, he attended the University of Göttingen in Germany. It was there that he began formulating ideas and theories that would drastically change the world of math forever.
In 1851, Riemann completed his doctoral thesis on the theory of complex functions at Göttingen for geometry. He combined the theory of complex functions, the theory of harmonic functions along with the potential theory and discovered that the existence of a wide class of complex functions satisfied only modest requirements. This proved that “complex functions could be expected to occur widely in math and that the theories of complex and harmonic functions were henceforth inseparable. Riemann also introduced the Laurent series expansion for functions having poles and branch points.” His mapping theorem stated that “any simply connected domain of the the complex plane having at least two boundary points can be conformally mapped onto the unit disk.” This lead to the idea of conformal mapping and simple connectivity. Riemann then decided to take Gauss’ geometric studies even further after Gauss asserted that one should ignore Euclidean space and treat eac...
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...on in a geodesic coordinate system such a metric is flat Euclidean, in the same way that a curved surface up to higher-order terms looks like its tangent plane. Beings living on the surface may discover the curvature of their world and compute it at any point as a consequence of observed deviations from Pythagoras’ theorem.”
Aside from developing is own hypotheses and studies, Georg Friedrich Bernhard Riemann was an inspiration to countless mathematicians as well. Riemann’s work with loci and algebraic functions was further studied by Charles- Emile Picard and Poincare. Both men were able to prove that a locus given by an equation f (x, y) = O can intersect itself at isolated points but along curves as well. Riemann also inspired the infamous Albert Eistein. Evidently, Eistein’s theory of general relativity was based off of Riemann’s ideas of Riemannian geometry.
From the concrete structure of the Baroque period to the free-form structure of the Modern period each composer brings forth a new understanding and value to their time period. Within these pieces that they creatively compose it brings new light and displays the culture of the time period. The composers each have story to tell and has each creatively constructed their own works within the diameters of their era.
Euler was one of the mathematical giants of the 18th Century. Leonard Euler (1707-1783) was born in Basel, Switzerland. His father was a Lutheran minister and wanted him to follow his path. Euler’s interest was different however, he was a natural mathematician. Johann Bernoulli helped Euler pursue his path by convincing his father of his mathematical abilities. Bernoulli became Euler’s teacher at the St. Petersburg Academy of Science. Euler’s personal life was more on the tragic side. He married and had 13 children, but only 5 survived their infancy. It is said that Euler made some of his greatest discoveries while holding his baby
"We could describe (Heinrich) Schliemann's excavations on the hill of Hissarlik and consider their results without speaking of Troy or even alluding to it," Georges Perrot wrote in 1891 in his Journal des Savants. "Even then, they would have added a whole new chapter to the history of civilization, the history of art" (qtd. in Duchêne 87). Heinrich Schliemann's life is the stuff fairy tales are made of. A poor, uneducated, and motherless boy rises through his hard work and parsimonious lifestyle to the heights of wealth (Burg 1,2). He travels the world and learns its languages ("Heinrich Schliemann"), takes a beautiful Greek bride, and together they unearth the treasures of Troy and the citadel of Agamemnon, thereby fulfilling the dream he has chased since childhood (Calder 18,19; Burg 8). Indeed, by presenting his life in romantic autobiographies as a series of adventures, starring Heinrich Schliemann as the epic hero (Duchêne 14), he ensured his status as a lasting folk hero and perennial bestseller (Calder 19).
...Optica and Dioptrice, laying the groundwork for all future optical discoveries to come. After him came Newton, who questioned the commonly held belief about light and discovered a fundamental property of how light worked and what prisms did. Fraunhofer had spent his whole life working with the same optical principles as Kepler. He performed the same experiment as Newton, but he explored further, and opened up whole new worlds of discovery. Today, we still use spectroscopy and Fraunhofer lines to determine what far off planets and stars are made of, and if it would be possible for life to exist on them. Thanks to the discovery of Fraunhofer lines, Niels Bohr was able to come up with his model of the atom, expanding our knowledge of how the universe works. All of these scientific discoveries were built on top of one another, and who knows what we will discover next?
One of the greatest figures of 19th century European art, Wilhelm Richard Wagner, is most commonly recognized in the world by his outstanding operas. However, the legacy he left for the future generations goes far beyond his music. Wagner’s personal philosophy, controversial ideas, progressive vision, and most of all, his enigmatic personality still evokes interest among both his admirers and critiques. Addressing the composer’s musical heritage, it is probably the legendary opera Parsifal that is just as much disputed over as its creator. The significance of this work, as well as its controversy, seems to reflect Wagner’s complicated personality, and thus is worth studying even in more than a century after the composer’s death.
Johannes Kepler was a German astronomer and mathematician ho discovered that planetary motion is elliptical. Early in his life, Kepler wanted to prove that the universe obeyed Platonistic mathematical relationships, such as the planetary orbits were circular and at distances from the sun proportional to the Platonic solids (see paragraph below). However, when his friend the astronomer Tycho Brahe died, he gave Kepler his immense collection of astronomical observations. After years of studying these observations, Kepler realized that his previous thought about planetary motion were wrong, and he came up with his three laws of planetary motion. Unfortunately, he did not have a unifying theory for these laws. This had to until Newton formulated his laws of gravity and motion.
Isaac Newton’s story of how an apple falling from a tree that hit his head inspired him to formulate a theory of gravitation is one that all school children grow up hearing about. Newton is arguably one of the most influential scientific minds in human history. He has published books such as Arithmetica Universalis, The Chronology of Ancient Kingdoms, Methods of Fluxions, Opticks, the Queries, and most famously, Philosophiæ Naturalis Principia MathematicaHe formulated the three laws of gravitation, discovered the generalized binomial theorem, developed infinitesimal calculus (sharing credit with Gottfried Wilhelm Von Leibniz, who developed the theory independently), and worked extensively on optics and refraction of light. Newton changed the way that people look at the world they live in and how the universe works.
Born on May 7, 1833, Johannes Brahms is regarded as the foremost romantic composer of instrumental music in classical forms. He composed virtually every variety of music except opera. Although his music was the object of attacks by followers of Richard Wagner, and Franz Liszt, his popularity grew over time as a great composer of unique individuality (Weinstock 456). His life, influences on him and his music, and his outstanding musical works all take a part in the history of this famous composer.
Gustav Stresemann Gustav Stresemann was given the job of German Foreign Minister during the six years commencing 1923. A foreign policy was needed. The German Nationalists needed to be given confidence in the Republic as it was not happy with the Republic's acceptance of the VersaillesTreat. Throughout the time of 1923 to 1929 Stresemann had certain choices to make which question whether he was acting as a 'Good German' or a 'Good European' There are arguments for both sides to the question.
Albrecht Ritschl was one of the most pivotal theologians in the history of Christianity. While many charge him with introducing ideas that led to a more liberal theology, his intentions were nevertheless honorable. Ritschl lived in a time where Christianity was no longer considered relevant or feasible, and his reinterpretations were an attempt to keep Christianity applicable to modern society. His defenses, however, often resulted in a corruption of doctrine and left Christianity open to attack. Thus Ritschl was an extremely influential theologian, though many question how positive that influence may have been.
Furthermore, during 1619 he invented analytic geometry which was a method of solving geometric problems and algebraic geometrically problems. After, Rene worked on his method of Discourse of Mindand Rules for the Directions of th...
.... People wanted to hear what he had to say. People respected him as a person and his knowledge so much that Queen Christina of Sweden wanted to know what he knew. Sadly she wanted the study sessions to be held at five a.m. These study sessions eventually led to his death in 1650 of pneumonia. He probably could’ve lived a lot longer and had a bigger influence of more people if he didn’t die in 1650. As a mathematician he invented and perfected analytical geometry. As a scientist he told everyone about light reflection and refraction. He also talked about space, the moon, the stars and Earth. As a philosopher he inspired people he never even knew with his wise sayings. He gave people a new view on how everything worked. He described the mind being separate from matter simply because it could think. He was truly a great thinker and a great influence to everyone today.
Carl Friedrich Gauss was born April 30, 1777 in Brunswick, Germany to a stern father and a loving mother. At a young age, his mother sensed how intelligent her son was and insisted on sending him to school to develop even though his dad displayed much resistance to the idea. The first test of Gauss’ brilliance was at age ten in his arithmetic class when the teacher asked the students to find the sum of all whole numbers 1 to 100. In his mind, Gauss was able to connect that 1+100=101, 2+99=101, and so on, deducing that all 50 pairs of numbers would equal 101. By this logic all Gauss had to do was multiply 50 by 101 and get his answer of 5,050. Gauss was bound to the mathematics field when at the age of 14, Gauss met the Duke of Brunswick. The duke was so astounded by Gauss’ photographic memory that he financially supported him through his studies at Caroline College and other universities afterwards. A major feat that Gauss had while he was enrolled college helped him decide that he wanted to focus on studying mathematics as opposed to languages. Besides his life of math, Gauss also had six children, three with Johanna Osthoff and three with his first deceased wife’s best fri...
already formulated calculus conclusions of his own. It is also worth mentioning that many of the concepts of calculus were invented as a result of their collaboration during their letter correspondents; important discoveries such as the power series.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.