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Free «Two Mathematicians» Essay Sample

In the history of humanity, there have always been scholars whose contribution to scientific development and progress is an indisputable fact. Despite they were made centuries ago, Isaac Newton’s inventions and discoveries are considered to be seminal milestones in physics, mathematics, mechanics, astronomy, and a wide range of science branches. Although Emil Artin’s scholarly heritage is not as significant as Newton’s achievements, he has greatly contributed to the development of mathematics, as well. Modern researches are conducted in accordance with these scientists’ findings.

            Sir Isaac Newton (1643 – 1726), an outstanding British scientist, made the greatest impact on science development; Newtonian theories and discoveries have survived their demise (Zimba, 2009).

He was born in Woolsthorpe, England, on 25 December 1645. Although Newton’s skills and abilities were obvious since his early childhood, he was not diligent enough while studying at the King’s School, Grantham. Therefore, his mother decided to make a farmer of him. Fortunately, she did not lose her belief about her son’s abilities and Newton entered TrinityCollege, Cambridge, at the age of 18. There, Newton comprehensively studied mathematics, astronomy, mechanics, philosophy, and other natural sciences, and started conducting his own research.

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Newton’s earliest discoveries are frequently associated with the Scientific Revolution in the middle of the XVII century. Encouraging European scientists to pursue scholarly studies and perform experiments, theoretical concepts and advanced ideas promulgated by Francis Bacon and Rene Descartes stipulated the new stage in scientific development.

Newton’s first mathematical discoveries were made during his study at TrinityCollege. Theoretical underpinnings of Newton’s mathematical studies were comprised of works of Schooten, Descartes, Wallis, de Witt, Heuraet, De Beaune, Wren, Halley, Viete, and Huygens. In addition to studying theoretical works of these mathematicians, “Newton encountered the concepts and methods of Ferma and James Gregory” (“Dictionary of Scientific Biography”). The scope of Newton’s mathematical investigations included researches on the calculus and other aspects of analysis, number theory, finite differences, classification of curves, general binomial expansion, infinitesimal calculus, methods of computation and approximation, classical and analytic geometry, etc. Although Newton is primarily known for his works on mechanics and physics, his scholarly investigations and achievements were based on his mathematical findings. Having designed laws of mechanics, Newton utilised a mathematical approach to them. Using mathematical methods, he demonstrated how these laws could be used to solve actual problems of astronomy and mechanics. Planetary motion, elliptical planetary orbits, and gravitation were explained in accordance with Newton’s mathematical formulas and calculations. The general binomial theorem was the first major “step in Newton's creative mathematical life” (“Dictionary of Scientific Biography”). 

Though Copernicus and Galileo Galilei discredited some erroneous concepts of ancient scientists and made a great contribution to the best understanding of laws of the Universe, basic principles, which could connect isolated facts and make relevant scientific forecasting, had not been formulated yet. Newton created such a theory. Although the scientist’s concepts were formulated in the late 1660s, they were published far later. In addition, Newton reluctantly published his works because they induced discussions and burdensome polemic among scientists and even led to scientific opposition. Findings of his investigations and experiments, views, and developed theories were disseminated at meetings of the Royal Society, letters to scientists, and in his books and manuscripts such as “De analysi per aequationes numero terminorum infinitas” (1669), “De motu corporum in gyrum” (1684), book I of the Principia (1684-1685), and “The System of the World” (1687). According to Osler (2000), Newton’s “Principia and Optics are almost universally considered to be the crowning achievements of the Scientific Revolution. Older accounts of Newton concentrated almost exclusively on his mathematics, physics, and optics, the contributions that were taken to embody modern science and its methods” (p. 14). However, Newton’s outstanding discoveries in optics and his telescope were negatively perceived and evaluated by Robert Hook, Huygens, and French Jesuits.

Newton’s "Mathematical Principles of Natural Philosophy" or the Principila consists of three books published in 1687. The first book, headed “De motu cortorum” (“On the motion of bodies”), determines the basic definitions of motion, dynamics, mass, centripetal, inverse-square central, and radial forces and provides mathematical explanation of their interconnections. The second book investigates bodies’ motion through resisting media. Book 3, entitled “De mundi systemate” (“On the system of the world”), clarifies reasons and consequences of gravitation and substantiates the law of universal gravitation. Gravitation was the first natural interaction provided by scientifically relevant mathematical grounding. This Newton’s work demonstrates possibilities of accurate predictions of planetary motion.

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Although research on these laws took Newton approximately two years, which he spent in the country escaping from the epidemic of bubonic plague, they greatly contributed to the development of science. Application of Newton’s laws allows solving a wide range of scientific and technical problems (osler, 2000; Zimba, 2009; “Dictionary of Scientific Biography”). Newton’s "Mathematical Principles of Natural Philosophy" was intensively debated and caused enormous disputes among scholars despite the fact that the scientist provided scientific explanation for almost all concepts of physics and mechanics.

Newton’s mathematical studies were stipulated by requirements for new calculative techniques. Demands for development of new mathematics, mathematics of variables, were extremely essential. However, almost all Newton’s publications and discoveries led to acute debates initiated by his opponents. Robert Hooke, Huygens, Wallis, Leibniz, members of the Royal Society, churchmen, and several foreign scholars were among them. Moreover, he was accused of plagiarism by Robert Hooke concerning the theory of gravitation.

Development of infinitesimal calculus involving concepts of standard and non-standard calculus, tangents, curves, maxima, and minima caused debates with Gottfried Leibniz and new accusations of academic dishonesty. Leibniz developed a similar mathematical method, which differentiated from Newton’s one in specific designations. Leibniz’s designations appeared to be more convenient and are still applied today. Newton explained geometrical lemmas by the method of limits; his substantiation was logically faultless though too tedious and complicated. The matter was investigated by the committee appointed by the Royal Society; Newton’s priority over the discovery of infinitesimal calculus was estimated. Nevertheless, it is still a controversial issue if to take into consideration the fact that Isaac Newton was the president of the Royal Society then.

Constant critical discussions, offensive conclusions, invidious claims, scientific contradictions, theological debates, and intense political conditions caused Newton’s nervous breakdowns and made a deleterious impact on his nature and attitude to younger scientists. He died at the age of eighty-five on March 20, 1727. Although his discovery of universal gravitation contained several wrong assumptions, Newton’s contribution to science cannot be overemphasized. “Historians have privileged Newton's mathematical physics because, as Westfall asserts, that is the field of greatest prominence in their intellectual world” (Osler, 2000, p. 17). Scientific and technological development, numerous achievements in mathematics, physics, mechanics, space exploration, and even information technology are inextricably linked with inventions and discoveries made by Newton centuries ago. 

Although Emil Artin’s mathematical findings and discoveries were made approximately two centuries later than those of Newton and he is less known than Isaac Newton, the significance of his findings is justified by their wide applications in modern mathematical studies. Emil Artin is one of founders of geometric and axiomatic algebra; he is famous for his research studies of Galois Theory, field theory, number theory, Hilbert's problem number 17, the reciprocity law, L-functions, rings, and the conjectures (Brauer, 1967; MacCaull, 1988; Rosen, 2007). “He was a renowned research mathematician, one of the most important algebraists and number theorists of the twentieth century” (Rosen, 2007, p. 1).

 
 
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Emil Artin (1898 -1962) was brought up in the family of an art dealer and an opera singer. He spent his childhood and adolescence in Reichenberg, Bohemia. He had a passion for music during all his life. Mathematics became the essential part of his life, as well.

He studied at the University of Vienna until his service in the army within World War I; then, in 1919, Artin entered the University of   Leipzig, where he received his doctorate in 1921. He continued his academic career as an educationalist at the University of Hamburg lecturing on mathematics, mathematical physics, mechanics, and the theory of relativity. Artin was promoted to the post of a full Professor at the University of Hamburg in 1925 (Rosen, 2007). He had a wide range of scientific interests including history of music, astronomy, biology, chemistry, biochemistry, and mechanics.  

Rosen (2007) identifies the period of 1921-1931 as the most productive for Artin’s mathematical investigations. The discovery of the Artin reciprocity law, the introduction of new types of zeta and L-functions, the invention of Artin L-functions and their properties, the development of the theory of braids, and advances in topology and algebraic geometry are Artin’s major achievements within this period. He conducted research on the theory of hypercomplex systems (associative algebras). His numerous conjectures greatly contributed to the development of mathematics (Rosen, 2007). Artin’s achievements were acknowledged and highly evaluated by more experienced mathematicians such as Herbrand, Iyanaga, Zassenhaus, van der Waerden, Chevalley, and Witt (Brauer, 1967). He edited the scholarly journal “Communications on Pure and Applied Mathematics”. Collaborating with Scherk, Whaples, Ankeny, R. H. Fox, and Chowla, Artin published several joint articles on real quadratic field, the theory of simple rings, algebraic number theory, topology, and the field theory.

However, his further life and scientific activities were dramatically transformed by political circumstances. When Hitler came to power and the Civil Service Law was passed in 1933, Emil Artin had to leave Germany. The situation was aggravated by the fact that his wife, Natalie Jasny, was half-Jewish. Therefore, in order to avoid political repressions or other life-threatening circumstances, Artin and his family moved to the United States in 1937.

 During his life in the United Sates, Artin gave lectures at Notre Dame in South Bend, Indiana, Indiana University at Bloomington, and Princeton University. “At Princeton, he became interested once again in the foundations of class field theory. A new approach was afforded by the use of group cohomology, which was introduced into the subject by Gerhardt Hochschild, Tadashi Nakayama, and Andr´e Weil” (Rosen, 2007, p. 3). Artin’s ideas influenced his students; later, his investigations of reciprocity were developed and generalized by his tutees Serge Lang and John Tate. Artin’s theoretical elaborations on class field theory were summarized in the Artin-Tate notes entitled Class Field Theory.

In spite of inspiring scientific atmosphere, brilliant students, and efficient collaboration with such outstanding mathematicians as Nesbitt, Thrall, Weil, and Nakayama, Artin made a decision to return to Germany. He moved there in 1958.  He gave lectures on algebraic number theory at Göttingen, and, then, “in 958 he accepted a Professorship at the University of Hamburg. There he remained for the rest of his life” (Rosen, 2007, p. 3).

Emil Artin died suddenly at the age of 64 on December 20, 1962. His unexpected death was caused by a heart attack. Artin’s scientific contributions into mathematics were illuminated in the articles of Richard Brauer and Hans Zassenshaus. Emil Artin’s books “Galois theory”, “The gamma function”, “Geometric algebra”, and “Theory of algebraic numbers”, as well as his lectures, comprise invaluable scientific heritage. Several Artin’s articles were published in German; his adherents translated them into English in order to make his prominent findings and discoveries available to the wide public. Disseminating Artin’s mathematical findings, van der Waerden published the textbook of “Modern algebra”, which was based on lectures of Emil Artin (Rosen, 2007).

To conclude, in spite of differences in their life circumstances, specific characteristics, historical conditions, scholarly interests, achievements, and scope of work, both Isaac Newton and Emil Artin greatly contributed to the development of science in general and mathematics in particular. They made mathematics serve people. Their findings are widely applied in modern research studies testifying to their high scientific value. For Newton and Artin, “to be a mathematician meant to participate in a great common effort, to continue work begun thousands of years ago, to shed new light on old discoveries, to seek new ways to prepare the developments of the future” (Brauer, 1967, p. 40).

   

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