Carl Friedrich Gauss History 

Carl Friedrich Gauss is probably one of the greatest mathematicians the world has ever known. Many people remember him as a man who knew all mathematics. Gauss can only be paralleled to other renowned icons like Isaac Newton, Archimedes, and Leonhard Euler. Mainly remembered for his remarkable publications that significantly influenced the field of mathematics, Gauss came into limelight at a very tender age.  He was only 21 years old when he came up with a publication on Disquisitiones Arithmeticae, which is often likened to Euclid’s Elements to geometry. Additionally, to his contributions to mathematics, work influenced physical science touching disciplines like astronomy, electricity, optics, statistics, magnetism, and surveying.

Johann Carl Friedrich Gauss was born in Brunswick, Germany on April 30, 1777. His father was Gebhard Dietrich, and his mother was Dorothea Benze. Gauss mother is mostly remembered for her intelligence despite her illiteracy. It is said that she worked as a house cleaner before getting married to Gauss father. Gauss father, on the other hand, was a hardworking man who made end meet by working at different times as a butcher, sales assistant, gardener, bricklayer and treasurer with an insurance company.  Gauss rare talent showed up early in life, as he was found capable of counting even before he learned to speak. According to one well-authenticated record, he corrected an error he identified in his father’s wage calculations when he was barely three years old. He took self-initiative to progress his learning and must have engaged in intensive arithmetical experimentation because during his first arithmetic class he surprised his teacher by promptly solving a busy-work problem of calculating the sum of the first hundred integers. 

Gauss married twice. Aged 28 years, Gauss married Johanna Osthoff in October 1805 and together got three children: Joseph, Wilhelmina, and Louis.  This marriage ended when Johanna died in October 1809, four weeks after Louis’s birth. Luis died later, aged five years. Gauss emarried a year later and got three children. His second wife Wilhelmina happened to be Johanna’s best friend, and together they got Eugene, Wilhelm, and Therese.

Gauss Schooling Years

Gauss began schooling at St. Katherine’s Public School when he was seven years old. It is said that it was during his time in the school that he surprised his teachers, including the better-trained Mr. Büttner by his unmatched ability to perform calculations faster. Mr. Buttner even attempted to bring an advanced arithmetic book which the eight-year-old Carl quickly and completed its exercises.  Moved by the turn of events, Mr. Buttner perceived Gauss potential to become a great scholar if given a chance, a factor that made him seek an audience with Gauss father. When Gauss father appeared in school, it was clear that he had a different opinion on Gauss future as he had hoped that his son would one day become a laborer and help ease the family burden. Gauss father had been blinded by the seemingly limited horizons considering the family position at that moment. Mr. Buttner convinced him that his son’s unique talents would easily attract the attention of a wealthy donor who would readily accept to support his education. With this assurance, Gauss father agreed and even excused the boy from the part-time spinning flax he used to do.

The New Horizons

Carl came under the tutorship of Martin Bartel, a well-educated and gifted mathematician who was older than he was by eight years. Inspired by Carl, Bartel devoted his entire career in mathematics and eventually ended up as a professor. Gauss contribution to mathematics began when he single-handedly derived the binomial theorem at the age of ten. This remarkable feat caused the word about the young genius get to the Duke of Brunswick and attracted his generous support for Gauss Education. Aged 11, Gauss began schooling at Martino-Katharineum grammar school in 1788 and excelled in Mathematics, Latin, Ancient Greek, and Modern Languages.

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In 1792, at the age of 15, Gauss joined Caroline College to further his studies, thanks to the support he received from the Duke. By this time, Gauss was already informed in classical and scientific education far above what is usual for his age at that time. He depicted amazing knowledge in elementary algebra, geometry, and analysis (having invented important theorem that he would encounter in his studies) and possessed a vast wealth of arithmetical insight and much number-theoretic knowledge.  Extensive calculation and analysis of outcomes, often documented in tables, provided an excellent acquaintance with individual numbers and generalizations he used in widening his calculating ability. This period set the roadway for his lifelong heuristic pattern of extensive empirical research culminating in conjectures and new understandings to further investigations and observation. Using this approach, he discovered the binomial theorem for rational exponents, Bode’s law of planetary distances, and the arithmetic-geometric mean.

During his three years at the Collegium, continued his empirical arithmetic, on one occasion finding a square root in two different ways to fifty decimal places by ingenious expansions and interpolations. He formulated the principle of least squares, apparently while adjusting different approximations and searching for regularity in the distribution of prime numbers. Before entering the University of Göttingen in 1795, he had rediscovered the law of quadratic reciprocity (conjectured by Lagrange in 1785) and related the arithmetic-geometric mean to infinite series expansions. He also discovered conjectured the prime number theorem (first proved by J. Hadamard in 1896) and found some results that would hold if “Euclidean geometry was not the true one. He later completed his degree in mathematics aged 18 has made an in-depth study that did not only earn him confidence but also trigger his passion on developments made by Leonhard Euler, Newton, and Joseph-Louis Lagrange. Gauss agrees that of all these great people, Archimedes made a significant impact in his life and he considered him a hero.

Beginning October 1795, Gauss enrolled for a doctorate at the University of Göttingen that lasted for the next three years. By this time, he showed greater breadth and depth of expertise as a far as mathematics is concerned when compared to most professors in the same field. Göttingen’s magnificent library collection made a perfect home for the young, ambitious Gauss.  While here, he took much of his time studying modern mathematics and even attended lectures in Physics, linguistics, and astronomy. 

The year 1978 saw Gauss return to Brunswick where he spent his time engaging in an extensive work. In the following year, with the first of his four proofs of the fundamental theorem of algebra, he was awarded a doctorate having been under the nominal supervision of J. F. Pfaff.  Gauss continued with his quest and in the following year justified the previous year’s creativity by his two extraordinary achievements: the calculation of the newly discovered planet Ceres’ orbit and the publication of Disquisitiones arithmeticae.

Gauss Contribution to statistics

Gauss came up with several theorems that have become indispensable in the field of statistics.  Numerical approximations regularly applied in computer programs employ the Law of error propagation. He equally developed the least square method commonly used in the calculation of regression. Gauss is also celebrated for inventing the normal density function, one of the best discoveries he made in this filed

Carl Friedrich Gauss introduced normal distribution in the field of statistics.  Though it has been argued that Pierre Simon was the founder in 1809, Gauss is mostly connected to the discovery on account of him being the earliest publisher of the concept. This controversy has been a subject of study by mathematicians for close to 200 years.  The idea has become widely accepted as “Gaussian Distribution.” One comment from renown.  The study of statistics in its entirety began with Gauss, and it allows statisticians to understand probabilities, prices and markets and many other applications. Contemporary terminology describes the normal distribution as the bell curve with “normal” parameters. Gauss came up with three methods of determining distribution namely mean, median and mode. He got the mean by adding all scores and then diving them by the number of counts to get the average. Median on the other hand was achieved by totaling two central figures of the sample and then dividing them by two or merely picking the central value from an ordinary sequence. The mode was represented by the most frequent of the figure in the distribution of values. Means became the best approach to gaining insight in a number sequence because it averages all the numbers and is thus considered the most reflexive in the entire distribution.This Gaussian approach to statistics found its use in the calculation of standard deviation, Variance, confidence interval, Skew, and Kurtosis.

Carl Friedrich Gauss, Mathematics

Gauss discovered how to make a 17-sided figure (heptadecagon) using a straightedge and compass alone. During his studies at Göttingen, came up with many new ideas that significantly changed the future mathematics. Among the best-known contribution is the Construction of the Heptadecagon. Having been in Göttingen for just six months, came up with a solution to a problem that had troubled mathematicians for the last two centuries- ‘the construction of a regular 17 –sided figure the heptadecagon, by straightedge and compass alone.’ The existing work by ancient Greeks at the time had limited the use of straightedge and compass to the construction of three, five, and fifteen-sided polygons alone. It had proven hard to discover any more such shapes. This discovery became very important in establishing a mathematical formula for finding all regular polygons, which can be constructed by straightedge and compass alone. He found 31 polygons outlined as 51, 85, 255, 257.. and 4,294,967,295-sided figures in addition to the 17-sided figure. Gauss is also remembered for keeping a diary of the remarkable discoveries he made in mathematics, beginning with the heptadecagon.  In 1796, he made 49 entries, some of which present obscurity because of their shortness. Among these entries is the one made on July 10, 1796, that successfully proved discovery on integers. According to this entry, integers can be formed by merely totaling at most three triangular numbers.  

Another outstanding contribution by Gauss is the publication of the Disquisitiones Arithmeticae. Duke of Brunswick continued support for Gauss’s work made it possible for him to delve into fields that his heart desired.  At the beginning of 1800, Aged 24, he produced one of the most significant works in the history of mathematics and named it Disquisitiones Arithmeticae. This discovery solved the problems arising from the previously discovered Number theory. Number theory or “higher arithmetic,” forms of a branch of mathematics that has existed from early years seen as least amenable to generalities. As late as the eighteenth century, this branch consisted of a large collection of individual results. Gauss, through his Disquisitiones, summarized all the distinct elements of number theory systematically, resolved some of the outstanding complexities and formulated questions and concepts that formed the design for research in the next century and beyond. He made known the congruence of integers that took the form of the modulus (a ≡ b (mod c) if c divides a-b), which became the pioneer algebraic example of today’s ubiquitous idea of an equivalence relation. He provided proof to the quadratic reciprocity law, formulated the theory of composition of quadratic forms and fully examined the cyclotomic equation. Gauss also document important breakthrough that included his formulation of modern modular arithmetic, the law of quadratic reciprocity, and congruence – the notion that supported his integrated method of approaching number theory. This new undertaking left praise in the mouth of his admirers who even suggested, “Gauss had done for number theory what Euclid had done for geometry.” One of his admirers, the great Joseph-Louis Lagrange, whose work formed part of the materials studied at college, commented: “Your [book has] elevated you to the rank of the foremost mathematicians; the last section’s contents are the most beautiful analytical discovery made for a long time.” Gauss work on Disquisitiones almost instantly got him recognition as the prince of the mathematicians, but it was found limited regarding readership. In 1863, another work “Dirichlet’s Vorlesungen über Zahlentheorie” offered an extensive understanding of Gauss work in Disquisitiones and helped in its later development.

The next notable contribution made by Gauss is in the invention of the fast Fourier transform and the method of least squares.Gauss contributed significantly in solving Giuseppe puzzle of a new heavenly body he could not explain. On January 1, 1801, Pizzi discovered a new celestial body that he could only describe as faint, star-like but failed the standards of the stars already discovered. Pizzi took most of the following few nights observing the object as it moved slightly in the background of the stars. This observation made him suggest he might have discovered a comet only to be disappointed later on January 24, by the revelation that the object was moving very slowly and could not be a comet.Gauss continued with his observation in the next six weeks, during which time the object moved drifted across the sky by 3 degrees. Sadly, he fell sick and at the time of his recovery, he found he had lost it. Various astronomers tried to locate it but never succeeded. The quest for an answer led them to ask for mathematical help.

It was at this point that Gauss, who was only 24 years, came into the picture having previously discovered a new approach for calculating orbit from a minimum of observation. His two very powerful discoveries: the fast Fourier transform and the method of least squares were about to land him great fame and remain essential scientific tools for the next two centuries and beyond. Using these robust mathematical methods went beyond the quest to locate the missing body and went ahead to prove that its orbit was nearly circular, just like a planet and calculated how far from the sun the object was located. This object, known as Ceres, ended up being an entirely new category of object that is popularly referred to as an asteroid on the dwarf planet in our modern language.

Gauss early years as a professor saw him release papers addressing a wide range of topics including integrals, series, and statistics. It is also during this time that began working tirelessly on possible theory while at the same time attempted resolving partial differential equations. The effort yielded as these equations found numerous application in physics, including gravitation and electromagnetism.  In 1809, he produced a two- volume publication, which proved helpful in explaining the theory of Motion of the Celestial bodies.  

Inventing the Heliotrope

By 1817, Gauss had begun developing an interest in geodesy, which became his preoccupation in the next eight years. The push had a long-standing history having worked on a surveying problem as early as 1796. He also participated in a survey with F. X. G. von Zach in 1802. Gauss time in Göttingen was greatly marked by his concern for accurate location of the observatory. In the year 1812, He visited Seeberg observatory and discussed matters relating to see levels only to find himself further stimulated to engage in problems that are more general. Moved by the unfolding events, Gauss approached Schumacher and asked him about the possibility of including Hannover in a letter addressing the survey of Denmark. Gauss did this with an understanding that the work would provide a new filed to exercise his calculating abilities. Additionally, he knew this project would complement his positional astronomy, compete for efforts by the French to calculate the arc length of one degree on the meridian and provide some extra money in his pocket.

Gauss contribution in physics is further made evident by his application of a long-standing knowledge in physical literature and his handling of problems in theoretical physics particularly in capillarity, mechanics, acoustics crystallography and optics. This result yielded the first fruit that he entitled Über ein neues allgemeines Grundgesetz der Machanik (1829). This work contained the law of constraint stated as: “the motion of a system departs as little as possible from free motion, where departure, or constraint, is measured by the sum of products of the masses times the squares of their deviations from the path of free motion.” Gauss presented this work as a new formulation similar to the renowned principle d’Alembert.  In 1830, He made a contribution capillarity entitled generalia theoriae figurae fluidorum in statu aequilibrii. Also seen as an important paper in calculus of variation, this work offered the first solution of a variational problem characterized by double integrals, variable limits and boundary conditions.

In 1840, towards the end, his physical research Gauss produced a publication entitled   Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungsund Abstossungskräfte. This work was a product of his previous magnetic work and was linked hisTheoria attractionis of 1813. The work became the first methodical treatment of perspective theory as a mathematical topic.  It recognized the importance of existence theorems in physics and got to a level of thoroughness that remained unmatched for more than a century. Gauss used the same period to complete another work entitled Dioptrische Untersuchungen (1841) that used a system to lenses to analyze the path of light. This work showed that among other things, any system is equal to a properly chosen single lens. Even  Gauss argued that he had kept the theory for about forty years unpublished on the ground of it being too elementary, upon its publication one of his scientific biographers labeled it his most excellent work. In fact, it became his last significant scientific contribution.

Triangulation of Hannover remained unapproved until it 1820 although Gauss had already begun a strenuous surveying activity on the same in 1818.   This surveying program ran throughout the summer and ran into winter when it involved data reduction. Gauss completed the fieldwork single-handedly in eight years. By 1825, he had limited his work to supervision and calculation and progressed with triangulation of Hannover to its completion in 1847. The end of this program meant greater experience since he had worked on a million plus numbers single-handedly. This project also led him to invent Heliotrope, an “instrument for reflecting the sun’s rays in a measured direction.”  Gauss disappointment triggered this invention with the existing inferior techniques of using lamps and powder flares at night to observe distant points. While thinking about the possibility of using a beacon with the brightness needed to be observed in the daytime, Gauss landed on the idea of employing reflected sunlight. This approach led him to revisit the optical theory, which later culminated in the design of the instrument and development of the first model in 1821. This tool composed of a mirror, which reflects sun’s rays over very long distances, found its use in the survey.  It is said that his interest in this invention came after being involved in the land survey, particularly for map making. While engaged in this undertaking, he saw the need to record far separated locations with high accuracy, a factor that led him to begin working on Heliotrope. This instrument’s only limitation came to be in its application: can only work in the bright sunshine. Heliotropes have been used in both Germany and USA in the past years. The invention brought forward much success in the practical work, now that it had the brightness likened to that of a first-magnitude star observed at a distance of fifteen miles. Although there are records of a similar instrument (heliostats) in an earlier period (possibly unknown to Gauss), heliotrope provided the precision needed by coupling mirrors with a small telescope. Heliotrope became widely accepted as standard equipment for use in large-scale triangulation until 1840 when improved models and aerial surveying in later years. 

The years he spent in survey worked to see Gauss develop ideas on least squares. Ha also discovered new solutions to the general problems commonly referred to as mathematical statistics. The later years saw him unravel his mature expository ideas in the Theoria combinationis obseruationum erroribus minimis obnoxiae (1823, with supplement in 1828). Another publication of 1828, entitled the Bestimmung des Breitenunterschiedes zwischen den Sternwarten uon Göttingen and Altona durch Beobachtungen am Ramsdenschen Zenithsector offered a summary of his previous ideas on instrumental errors, figure of the earth, and the calculus of observations.  The greatest contribution of that period which also became his last breakthrough in a significant direction of mathematical research came through Disquisitiones generates circa superficies curvas (1828).  This work developed from a geodesic meditation that had taken three decades and served as the foundation of differential geometry in the century.

Gauss in 1931 invented the first organized use of absolute units (mass, distance and time) to calculate a non-mechanical quantity. By 1931, Gauss had begun applying potential mathematical theory in the real world. During this period Gauss, a 54-year-old mathematician, worked alongside a 27-year-old physicist named Weber at Gottingen to develop something on electricity and magnetism.  During the entire period of their collaboration, Gauss led took the lead in Theoretical capability while Weber handled experimental capabilities despite the latter showing high theoretical competence and novelty. Their collaborative efforts soon bore fruit as in 1832 Gauss presented the Intensitas uis magneticae terrestris ad mensuram absolutam reuocopjata (1833) that offered the first organized use of absolute units( mass, distance and time) to calculate a non-mechanical quantity. The also worked collaboratively on several experiments that allowed define the earth’s magnetic field using grams, millimeters and seconds. Simply put, the two proved that mass, length and time, which are mostly mechanical dimensions could be used to define earth’s magnetic field. This discovery provided a strong impetus for the application of SI units.

Gauss developed a binary alphabet code that was instrumental in the later invention of telegraph systems. Gauss and Weber’s collaboration continued and in 1833 realized the invention of the world’s pioneer telegraph systems. They additionally developed a binary alphabet code that served to allow communication between Gauss’s astronomical observatory and Weber’s physics building about 1.5 miles (2.5 km) apart. By 1835, their work had been widely accepted allowing their telegraph lines to be installed alongside Germany’s first railroad.

Gauss working alongside Webner invented the Kirchoff’s Circuit Laws.Inspired by Faraday’s findings on the induced current in 1831, Gauss and Webner undertook a determined investigation of electrical phenomena.  Their investigation led to the discovery of how current and voltage are distributed in branches of the electric circuit.  Their work concluded that current is governed by the law of conservation of charge and voltage by the law of conservation of energy. Later in 1845, Gustav Kirchoff rediscovered the same laws that now bear his name. The two also anticipated various discoveries in thermal, static, and frictional electricity but never publish their findings, probably because their attention was much on terrestrial magnetism.

Gauss’s Law & Gauss’s Law for Magnetism

Gauss exceptional talent mathematics led him to analyze the behavior of magnetic and electric fields. In 1835, using his divergence theorem at he had discovered without the help of Joseph-Louis Lagrange, he came up with two laws.  

Gauss’s Law, which states an electric field, is equal to the distribution of electric charges that cause it Gauss’s Law for Magnetism, which says that magnetic monopoles do not exist. When presented mathematically, these laws contribute two of the four equations used to combine magnetic and electric fields into a single electromagnetic field.  This unification came into place in 1864, thanks to James Clerk Maxwell

Contribution to terrestrial magnetism

The period marking the 1930s saw Gauss take a new turn to study terrestrial magnetism, which led him to take part in the first global survey of the Earth magnetic field. It is during this period that he invented the magnetometer.  Working alongside Wilhelm Weber, a physicist and Göttingen colleague he developed the first electric telegraph. Unfortunately Gauss spirited effort in his new invention grew cold due to certain parochialism. Despite the setback Gauss still made the best of the experience he had acquired while pursuing this invention the case has it that during the same period he developed key mathematical consequences from the work that he named potential theory. As an important branch of mathematical physics, potential theory arises from the study of gravitation and electromagnetism.  It is also during his pursuit of the magnetic field subject that he concluded, “principal dipolar component had its origin inside the Earth instead of outside.” Here, Gauss demonstrated that “dipolar element was a diminishing function inversely proportional to the square of earth’s radius.”  Gauss new conclusion led speculations by scientists on the subject of the origin of earth’s magnetic field with regard to ferromagnetism, various dynamo theories and various rotation theories. Rotation theories and Ferromagnetism were later discredited. Rotational theories disapproval followed the revelation that no fundamental connection existed between an associated magnetic field and the mass in motion. Ferromagnetism on the other hand faced the same fate on grounds that the temperature at which ferromagnetism is demolished(the Curie point)  is achieved only 20 or so kilometers or about 12 miles beneath the surface. Geoemagneticians generally concentrate on different dynamo theories, which address the occurrences where a source of energy at the center of the earth realizes a self-sustaining magnetic field.

Contribution to the subject of Cartography

Gauss is also remembered for his writings on the subject of Cartography where he developed the theory of map projections.  This theory refers to “a systematic conversion of latitudes and longitudes of position on the surface of the earth to a flat sheet of paper, a map.” More precisely, a map estimate call for a conversion from a set of two self-determining points on the model of the earth ( the longitude and the latitude) to  a set of two self-determining points on the map ( the Cartesian points x and y). In 1823, Gauss was given the reward of the Danish Academy of Sciences for his work on angle-preserving maps. This work almost suggested that multipart functions of intricate variables   are largely angle –preserving, however Gauss position stopped him from making such fundamental insight explicit.  Bernhard Riemann, a strong supporter of gauss work, later made more development on this work. In addition to this work, Gauss is remembered for many other unpublished insights relating to the “nature of complex functions and their integral.”  Gauss work on cartography obviously served as a foundation for the modern day cartography, which largely employ aerial and satellite photographs as the basis for the desired chart or map. Modern procedure for converting photographs data into charts or maps are governed by photogrammetry principles and often produce a degree of accurateness that was previously unachievable. Later improvements in the field of satellite photography in the late 20th century and the availability of satellite images on the internet have realized the creation of Google earth and other related databases, which are readily available online. Satellite photography has also made it possible to develop comprehensive maps detailing features of the moon and other planets making our solar system.  Additionally, the use of geographic information system (GIS) has been developed which in turn has helped in expanding the scope of study in cartographic subjects.

Contribution to the work on elliptic functions

Another work on which Gauss made a significant contribution although it is least known to his contemporaries was the work on elliptic functions. In 1812, he published an account of an interesting infinite series.  This work, which was never published, addressed the subject of differential equation and how it satisfies the infinite series. Here he successfully showed how the series, better known as hypergeometric series, could play a part in definition known and many new functions. Luckily, gauss was already acquainted with the idea of using the differential equation to establish a general theory of elliptic function. This allowed him to free the theory from its reliance in the theory of elliptic integrals. Termed a major breakthrough, Gauss work proved helpful in understanding his previous work in 1790s. During his first discovery, Gauss found that elliptic function naturally considers hypergeometric series as complex –valued functions linked to the complex variable; however, his new discovery established that the present theory of complex integrals fell short of the task.  When Norwegian Niels Abel and the German Carl Jacobi later published some of this theory in 1930, Gauss remarked to one of his friend that Abel had discovered 1/3 of the whole theory. Although gauss comment was found to be true, it is sad that he could opt to withhold such important information, thanks to his personality.

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Conclusion 

Gauss considered one of the greatest in the history of mathematics is not just remembered for his contributions but also his brilliance. Having had a simple life, spending the better part of his childhood in poverty with his unlettered family, Gauss unique precocity never died. Gauss began schooling at St. Katherine’s Public School when he was seven years old. It is said that it was during his time in the school that he surprised his teachers, including the better-trained Mr. Büttner by his unmatched ability to perform calculations faster. Mr. Buttner even attempted to bring an advanced arithmetic book which the eight-year-old Carl quickly and completed its exercises.  Moved by the turn of events, Mr. Buttner perceived Gauss potential to become a great scholar if given a chance, a factor that made him seek an audience with Gauss father. When Gauss father appeared in school, it was clear that he had a different opinion on Gauss future as he had hoped that his son would one day become a laborer and help ease the family burden. Gauss father had been blinded by the seemingly limited horizons considering the family position at that moment. Mr. Buttner convinced him that his son’s unique talents would easily attract the attention of a wealthy donor who would readily accept to support his education. With this assurance, Gauss father agreed and even excused the boy from the part-time spinning flax he used to do.

Beginning at age fourteen, thanks to the generous support advanced by the duke of Brunswick, Gauss started the journey of building his intellectual interest that took the next sixteen years. By the time he was twenty-five years, he had already gained fame as a mathematician and astronomer. At age, thirty Gauss moved to Göttingen where he worked as a director of the observatory. His early years at Göttingen was marked with numerous achievements since it was during this period that he developed some ideas and publications in the different fields of mathematics. Among the well-known publications are several outstanding papers resulting from his work on tiny planet Palls, disconcerted by Jupiter. The first article was termed “Disquisitlones generates circa seriem infrnitam (1813), first rigorous treatment of series and introduction of the hypergeometric functions, ancestors of the “special functions” of physics and Methodus nova inregralium valores per approximationem invenlendi (1816), an important contribution to approximate integration. The second is Bestimmung der Genauigkeit der Beobachtungen (1816), an early investigation of the effectiveness of statistical estimators. The next is Determinatio attractionis quam in punctum quodvis positionis datae exerceret planeta si eius massa per totam orbitam ratione temporis quo singulae partes describuntur uniformiter esset dispertita (1818). Thia artilcle exhibited that the disconcertion caused by a planet is similar to that of an equivalent mass spread along its orbit in proportion to the time spent on an arc.” The year 1978 saw Gauss return to Brunswick where he spent his time engaging in an extensive work. In the following year, with the first of his four proofs of the fundamental theorem of algebra, he was awarded a doctorate having been under nominal supervision of J. F. Pfaff. Gauss early years as a professor saw him release papers addressing a wide range of topics including integrals, series, and statistics. It is also during this time that began working tirelessly on possible theory while at the same time attempted resolving partial differential equations. Gauss early years as a professor saw him release papers addressing a wide range of topics including integrals, series, and statistics. It is also during this time that began working tirelessly on possible theory while at the same time attempted resolving partial differential equations. The effort yielded as these equations found numerous application in physics, including gravitation and electromagnetism. Gauss effort yielded as these equations found numerous application in physics, including gravitation and electromagnetism.  In 1809, he produced a two- volume publication, which proved helpful in explaining the theory of Motion of the Celestial bodies.   Gauss contribution in mathematics is made evident by his application of a long-standing knowledge in mathematical literature and his handling of problems in theoretical physics particularly in capillarity, mechanics, acoustics crystallography and optics. This result yielded the first fruit that he entitled Über ein neues allgemeines Grundgesetz der Machanik (1829). This work contained the law of constraint stated as: “the motion of a system departs as little as possible from free motion, where departure, or constraint, is measured by the sum of products of the masses times the squares of their deviations from the path of free motion.”In 1840, towards the end, his physical research Gauss produced a publication entitled   Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse des Quadrats der Entfernung wirkenden Anziehungsund Abstossungskräfte. This work was a product of his previous magnetic work and was linked hisTheoria attractionis of 1813. The work became the first methodical treatment of prospective theory as a mathematical topic.

Gauss came up with several theorems that have become indispensable in the field of statistics.  Numerical approximations regularly applied in computer programs employ the Law of error propagation. He equally developed the least square method commonly used in the calculation of regression. Gauss is also celebrated for establishing the normal density function, one of the best discoveries he made in this filed. Gauss married twice. Aged 28 years, Gauss married Johanna Osthoff in October 1805 and together got three children: Joseph, Wilhelmina, and Louis.  This marriage ended when Johanna died in October 1809, four weeks after Louis’s birth. Luis died later aged five years. Remarried a year later and got three children. His second wife Wilhelmina happened to be Johanna’s best friend, and together they got Eugene, Wilhelm, and Therese.

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