cian, physicist and astronomer. He is considered to be the greatest mathematician of his time, equal to the likes ofArchimedes and Isaac Newton. He is frequently called the founder of modernmathematics. It must also be noted that his work in the fields of astronomy and physics(especially the study of electromagnetism) is nearly as significant as that in mathematics. He also contributed much to crystallography, optics, biostatistics and mechanics. Gauss was born in Braunschweig, or Brunswick, Duchy of Brunswick (now Germany)on April 30, 1777 to a peasant couple.
There exists many anecdotes referring to hisextraordinary feats of mental computation. It is said that as an old man, Gauss saidjokingly that he could count before he could talk. Gauss began elementary school at theage of seven, and his potential was noticed immediately. He so impressed his teacherButtner, and his assistant, Martin Bartels, that they both convinced Gausss father that hisson should be permitted to study with a view toward entering a university.
Gausssextraordinary achievement which caused this impression occurred when he demonstratedhis ability to sum the integers from 1 to 100 by spotting that the sum was 50 pairs ofnumbers each pair summing 101. In 1788, Gauss began his education at the Gymnasium with the help of Buttner andBartels, where he distinguished himself in the ancient languages of High German andLatin and mathematics. At the age of 14 Gauss was presented to the duke of Brunswick -Wolfenbuttel, at court where he was permitted to exhibit his computing skill. Hisabilities impressed the duke so much that the duke generously supported Gauss until thedukes death in 1806.
Gauss conceived almost all of his fundamental mathematicaldiscoveries between the ages of 14 and 17. In 1791 he began to do totally new andinnovative work in mathematics. With the stipend he received from the duke, Gaussentered Brunswick Collegium Carolinum in 1792. At the academy Gauss independentlydiscovered Bodes law, the binomial theorem and the arithmetic-geometric mean, as wellas the law of quadratic reciprocity. Between the years 1793-94, while still at theacademy, he did an intensive research in number theory, especially on prime numbers. Gauss made this his lifes passion and is looked upon as its modern founder.
In 1795Gauss left Brunswick to study at Gottingen University. His teacher at the university wasKaestner, whom Gauss often ridiculed. His only known friend amongst the studentsFarkas Bolyai. They met in 1799 and corresponded with each other for many years. On March 30, 1796, Gauss discovered that the regular heptadecagon, apolygon with17 sides, is inscriptible in a circle, using only compasses and straightedge – – the firstsuch discovery in Euclidean construction in more than 2,000 years. He not onlysucceeded in proving this construction impossible, but he went on to give methods ofconstructing figures with 17, 257, and 65,537 sides.
In doing so, he proved that theconstructions, with compass and ruler, of a regular polygon with an odd number of sideswas possible only when the number of sides was a prime number of the series 3,5 17, 257and 65,537 or was a multiple of two or more of these numbers. This discovery was to beconsidered the most major advance in this field since the time of Greek mathematics andwas published as Section VII of Gausss famous work, Disquisitiones Arithmeticae. With this discovery he gave up his intention to study languages and turned tomathematics. Gauss left Gottingen in 1798 without a diploma. He returned to Brunswick where hereceived a degree in 1799. The Duke of Brunswick requested that Gauss submit adoctoral dissertation to the University of Helmstedt, with Pfaff chosen to be his advisor.
Gausss dissertation was a discussion of the fundamental theorem of algebra. Hesubmitted proof that every algebraic equation has at least one root, or solution. Thistheorem, which had challenged mathematicians for centuries, is still called thefundamental theorem of algebra. Because he received a stipend from the Duke of Brunswick, Gauss had no need to finda job and devoted most of his time to research. He decided to write a book on the theoryof numbers.
There were seven sections, all but the last section (referred to in theprevious paragraph) being loyal to the number theory. It appeared in the summer of 1801and is a classic held to be Gausss greatest accomplishment. Gauss was considered to beextremely meticulous in his work and would not publish any result without a completeproof. Thus, many discoveries were not credited to him and were remade by others later,e. g.
– the work of Janos Bolyai and Nikolai Lobachevsky in non-Euclidean geometry,Augustin Cauchy in complex variable analysis, Carl Jacobi in elliptic functions, and SirWilliam Rowan Hamilton in quaternions. Gauss discovered earlier, independent ofAdrien Legendre, the method of least squares. On January 1, 1801, the Italian astronomer Giusseppe Piazzi discovered the asteroidCeres. In June of the same year, Zach, an astronomer whom Gauss had come to knowtwo or three years previously, published the orbital positions of the new small planet. Unfortunately, Piazzi could only observe nine degrees of its orbit before it disappearedbehind the Sun.
Zach published several predictions of it position, including one by Gausswhich differed greatly from the others. Even though Gauss would not disclose hismethods of calculations, it was his prediction which was nearly accurate when Ceres wasrediscovered on December 7, 1801. Gauss had used his least squares approximationmethod. In June of 1802, Gauss visited an astronomer named Olbers who had discoveredPallas in March of that same year and Gauss investigated its orbit. Olbers was soimpressed with Gauss that he suggested that Gauss be made director of the proposed newobservatory in Gottingen, but no action was taken. It was also around this time that hebegan correspondence with Bessel, whom he did not meet until 1825, and with SophieGermain.
Gauss married Johanna Ostoff on October 9, 1805. It was the first time that hewould have a happy personal life. A year later his benefactor, the Duke of Brunswick,was killed fighting for the Prussian army. In 1807, Gauss decided to leave Brunswickand take up the position of director of the Gottingen observatory, a position which hebeen suggested for five years earlier.
He arrived to his new position in Gottingen in thelatter part of 1807. The following year, 1808, his father died, and a year later his wifeJohanna died after giving birth to their second son, who was to die soon after her. Gausswas shattered and wrote to Olbers asking him to give him a home for a few weeks. Heremarried Minna, the best friend of Johanna the following year and although they hadthree children, this marriage seemed to be one of convenience for Gauss.
It is obviousthrough many of Gausss accomplishments that his devotion to his work never falteredeven during personal tragic moments. He published his second book, Theoria motus corporum coelestium in sectionibusconicis Solem ambientium, in 1809. The book was a major two volume dissertation onthe motion of celestial bodies. In the first volume he discussed differential equations,conic sections and elliptic orbits, while in the second volume, the main part of the work,he showed how to estimate and then to refine the estimation of a planets orbit.
Gaussscontributions to theoretical astronomy stopped after 1817, although he went on makingobservations until the age of seventy. Gauss produced many publications including, Disquisitiones generales circa serieminfinitam, a treatment of series and introduction of the hypergeometric function,Methodus nova integralium valores per approximationem inveniendi, an essay onapproximate integration, Bestimmung der Genauigkeit der Beobachtungen, a discussionof statistical estimators, and Theoria attractionis corporum sphaeroidicorumellipticorum homogeneorum methodus nova tractata, a work concerning geodesicproblems and concentrating on potential theory. During the 1820s, Gauss found himselfinterested in geodesy. He invented the heliotrope as a result of this interest. The crudeinstrument worked by reflecting the Suns rays using a design of mirrors and a smalltelescope.
Due to inaccurate base lines used for the survey and an unsatisfactory networkof triangles, the instrument was not of much use. He published over seventy papersbetween 1820 and 1830. Since the early 1800s, Gauss had an interest in the possible existence of anon-Euclidean geometry. He discussed this topic in his correspondences with FarkasBolyai and also in his correspondences with Gerling and Schumacher. In a book reviewin 1816, he discussed proofs which deduced the axiom of parallels from the otherEuclidean axioms, suggesting that he believed in the existence of non-Euclideangeometry, although he was rather vague. Gauss confided in Schumacher, telling himthat he believed his reputation would suffer if he admitted in public that he believed inthe existence of such a geometry.
He had a major interest in differential geometry andpublished many papers on the subject. his most renowned work in this field waspublished in 1828 and was entitled Disquisitiones generales circa superficies curva. The paper arose out of his geodesic interests, but it contained such geometrical ideas asGaussian curvature. The paper also includes Gausss famous theorema egregrium: If an area in Ecan be developed (i. e. mapped isometrically) into another area of E, the values of the Gaussian curvatures are identical in corresponding points.
During the years 1817-1832 Gauss again went through personal turmoil. His ailingmother moved in with him in 1817 and remained with him until his death in 1839. It wasalso during this period that he was involved in arguments with his wife and her familyregarding the possibility of moving to Berlin. Gauss had been offered a position at theBerlin University and Minna and her family were eager to move there. Gauss, however,never liked change and decided to stay in Gottingen.
In 1831, Gausss second wife diedafter a long illness. Wilhelm Weber arrived in Gottingen in 1831 as a physics professor filling TobiasMayers chair. Gauss had known Weber since 1828 and supported his appointment. Gauss had worked on physics before 1831, publishing a paper which contained theprinciple of least constraint.
He also published a second paper which discussed forces ofattraction. These papers were based on Gausss potential theory, which proved of greatimportance in his work on physics. He later came to believe his potential theory and hismethod of least squares provided vital links between science and nature. In the six yearsthat Weber remained in Gottingen much was accomplished by his collaborative workwith Gauss. They did extensive research on magnetism. Gausss applications ofmathematics to both magnetism and electricity are among his most important works; theunit of intensity of magnetic fields is today called the gauss.
He wrote papers dealingwith the current theories on terrestrial magnetism, including Poissons ideas, absolutemeasure for magnetic force and an empirical definition of terrestrial magnetism. Together they discovered Kirchoffs laws, and also built a primitive electromagnetictelegraph. Although this period of his life was an enjoyable pastime for Gauss, his worksin this area produced many concrete results. After Weber was forced to leave Gottingen due to a political dispute, Gausss activitygradually began to decrease. He still produced letters in response to fellow scientistsdiscoveries ususally remarking that he had known the methods for years but had neverfelt the need to publish. Sometimes he seemed extremely pleased with advances madeby other mathematicians, especially that of Eisenstein and of Lobachevsky.
From 1845to 1851 Gauss spent the years updating the Gottingen University widows fund. Thiswork gave him practical experience in financial matters, and he went on to make hisfortune through shrewd investments in bonds issued by private companies. Gauss presented his golden jubilee lecture in 1849, fifty years after receiving hisdiploma from Hemstedt University. It was appropriately a variation on his dissertation of1799. From the mathematical community only Jacobi and Dirichlet were present, butGauss received many messages and honors. From 1850 onward, Gausss work was againof nearly all of a practical nature although he did approve Riemanns doctoral thesis andheard his probationary lecture.
His last known scientific exchange was with Gerling. Hediscussed a modified Foucalt pendulum in 1854. He was also able to attend the openingof the new railway link between Hanover and Gottingen, but this proved to be his lastouting. His health deteriorated slowly, and Gauss died in his sleep early in the morningof February 23, 1855.
