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CHARLES FREDERICK GAUSS was born at Brunswick on the 30th of April, 1777. His father, who was a bricklayer, intended that his son should adopt the same occupation. Accordingly, in the year 1784, young Gauss was sent to the public school of Bütner, in Brunswick, for the purpose of being instructed in the ordinary elements of education. During his attendance at this school, his extraordinary intelligence attracted the notice and procured for him the friendship of Bartels, subsequently Professor of Mathematics in the University of Dorpat, and father-in-law of our celebrated Associate, M. Struve, Director of the Imperial Observatory of Pulkowa. Bartels having kindly represented the merits of young Gauss to Charles William, Duke of Brunswick, he was sent, in the year 1792, to the Collegium Carolinum, very much against the will of his father, who perceived that his own intentions with respect to the future calling of his son would thereby be completely frustrated. In 1794 he entered the University of Göttingen, not yet quite decided whether he should devote his life to the pursuit of mathematics or philology. During his residence here he made several of his greatest discoveries in analysis, which induced him to make the cultivation of mathematical science the main object of his life.
Having completed his studies, he returned to Brunswick, and, in 1798, he repaired to Helmstadt for the purpose of availing himself of the library of that place, having been then engaged in preparing for publication his celebrated work, Disquisitiones Arithmeticae. Shortly after his arrival he was introduced to Pfaff, but he was merely in company with him for an hour or two. Upon his return to Helmstadt, however, in the following year, with the same object in view, he had the opportunity of renewing his acquaintance with Pfaff, which soon ripened into a very intimate friendship. In the course of their evening walks they were in the habit of exchanging their thoughts on mathematical subjects, on which occasions it may be presumed that Gauss communicated quite as much as he received. It has been considered necessary to state these facts in consequence of an erroneous impression which has very extensively prevailed, even in Germany, that Gauss studied mathematics at Helmstadt under the tuition of Pfaff. The Disquisitiones Arithmeticae was published at Brunswick in 1801, under the auspices of the Duke of Brunswick. It immediately stamped its author as one of the most profound and original mathematicians of the age.
The discovery of the planet Ceres by Piazzi on the first day of the present century had the effect of introducing Gauss to the world as a theoretical astronomer of the very highest order. The Italian astronomer not having communicated a sufficient number of his observations of the planet previous to its passing into the rays of the sun, which happened soon after its discovery, there existed no means of ascertaining the form or position of the orbit in which it revolved; and the consequence was, that upon its emerging again from the solar rays in the autumn of the same year, astronomers were totally unacquainted with the precise region of the heavens in which they ought to search for it. Piazzi having at length published his early observations of the planet, Gauss, by a method of his own invention, determined the elements of its orbit, and calculated an ephemeris of its motion, by means of which De Zach succeeded in rediscovering the planet on the 31st of December, exactly after the lapse of a year from the date of its original discovery by Piazzi. The discovery of three other small planets, which soon followed that of Ceres, supplied Gauss with so many occasions for improving his solution of the problem for determining the orbit of a planet from a definite number of observations, and suggested to his inventive mind a variety of beautiful contrivances for computing the movement of a body revolving in a conic section in accordance witin Kepler's laws. These results were finally embodied in his Theoria Motus Corporum Cælestium in Conicis Sectionibus Solem Ambientium, which was published at Hamburgh in 1809. In this celebrated work the author gives a complete system of formulæ and processes for computing the movement of a body revolving in a conic section, and then explains a general method for determining the orbit of a planet or comet from three observed positions of the body. The work concludes with an exposition of the method of least squares, which the author appears to have invented independently of, and even prior to, Legendre, although the latter was the first who communicated it to the world.
The Theoria Motus will always be classed among those great works, the appearance of which forms an epoch in the history of the science to which they refer. The processes detailed in it are no less remarkable for originality and completeness than for the concise and elegant form in which the author has exhibited them. Indeed, it may be considered as the text-book from which have been chiefly derived those powerful and refined methods of investigation by which the German astronomy of the present century is more especially characterised.
It is a curious fact that the date of the preface to this immortal work is exactly two centuries later than the date of Kepler's equally renowned work De Stella Martis. The former is dated March 28, 1809; the latter is dated March 28, 1609.
The other astronomical researches of Gauss are chiefly contained in De Zach's Monatliche Correspondenz, the Transactions of the Royal Society of Göttingen, and the Astronomische Nachrichten. Although not of equal importance with those expounded in the Theoria Motus, they all bear the impress of original genius.
In 1807 Gauss was appointed Professor of Mathematics at Göttingen, where he continued to reside during the remainder of his life. Latterly he devoted considerable attention to the subject of terrestrial magnetism, and in concert with Professor Weber made some very important improvements in that branch of science. He died on the 23d of February, 1855. His remains were accompanied to the grave by a vast multitude of persons, including the entire corps of the University of which he was so distinguished an ornament.
Gauss was one of the leading mathematicians of the age, and was the last of the powerful school which is headed by Lagrange; but he lived to an age which made him the survivor of many who must be said to belong to a later epoch. His researches are of the most abstruse character, and turn much on the theory of number and its applications. The Disquisitiones Arithmeticae is one of the standard works of the century. But though the character of his subjects tempts few readers – though his own severe brevity renders these subjects even more difficult than they need be – yet the young reader of Euclid may be brought into contact with Gauss, so as to understand the tone of his genius in a manner which would be utterly impossible in the case of Newton, or Lagrange, or Euler.
It had always been supposed that Euclid had attained the boundary of what is possible in geometrical construction, with the allowance of constructive means to which he limits himself by the three first postulates. Two thousand years had past without any construction being achieved of which a geometer would have supposed Euclid or Archimedes incapable, had the attention been turned that way. But when Gauss, by the highest algebra applied to numerical considerations, showed that a regular polygon of 17 sides (or of any number which is prime, and also one more than a power of 2) can be inscribed in a circle under Euclid's restriction as to means, he made the first advance upon Euclid, and established the connexion of trains of thought so widely different in character, in subject-matter, and in difficulty, that his theorem is of a most useful application. It is the most remarkable standing proof that every part of mathematics must be looked into for the progress of every other; and we have no doubt that this theorem has very much encouraged research into the hidden points of relation between the different branches of pure science.
It was reserved to Gauss to open that extension of plane geometry which consists in transferring the field of reasoning from a plane to any surface whatever. Every surface has its shortest line, as a plane has its straight line; and a triangle drawn upon a surface, bounded by shortest lines, such as the common spherical triangle on the surface of a sphere, has close analogies with the rectilinear triangle in a plane. Gauss showed how the sum of the three angles of such a triangle is connected with the constitution of the area inclosed; thus extending to all surfaces the well-known theorem which Roy and Legendre applied in geodetical calculation. The time may come when the advance of mathematical reasoning shall convert plane geometry into a geometry of all surfaces, in such manner that any theorem which is established on one surface shall immediately be read off on every other. Should this time ever arrive, it will be remembered that Gauss first opened the career, and suggested the possibility of the extension, by giving some of the principal theorems.
Having completed his studies, he returned to Brunswick, and, in 1798, he repaired to Helmstadt for the purpose of availing himself of the library of that place, having been then engaged in preparing for publication his celebrated work, Disquisitiones Arithmeticae. Shortly after his arrival he was introduced to Pfaff, but he was merely in company with him for an hour or two. Upon his return to Helmstadt, however, in the following year, with the same object in view, he had the opportunity of renewing his acquaintance with Pfaff, which soon ripened into a very intimate friendship. In the course of their evening walks they were in the habit of exchanging their thoughts on mathematical subjects, on which occasions it may be presumed that Gauss communicated quite as much as he received. It has been considered necessary to state these facts in consequence of an erroneous impression which has very extensively prevailed, even in Germany, that Gauss studied mathematics at Helmstadt under the tuition of Pfaff. The Disquisitiones Arithmeticae was published at Brunswick in 1801, under the auspices of the Duke of Brunswick. It immediately stamped its author as one of the most profound and original mathematicians of the age.
The discovery of the planet Ceres by Piazzi on the first day of the present century had the effect of introducing Gauss to the world as a theoretical astronomer of the very highest order. The Italian astronomer not having communicated a sufficient number of his observations of the planet previous to its passing into the rays of the sun, which happened soon after its discovery, there existed no means of ascertaining the form or position of the orbit in which it revolved; and the consequence was, that upon its emerging again from the solar rays in the autumn of the same year, astronomers were totally unacquainted with the precise region of the heavens in which they ought to search for it. Piazzi having at length published his early observations of the planet, Gauss, by a method of his own invention, determined the elements of its orbit, and calculated an ephemeris of its motion, by means of which De Zach succeeded in rediscovering the planet on the 31st of December, exactly after the lapse of a year from the date of its original discovery by Piazzi. The discovery of three other small planets, which soon followed that of Ceres, supplied Gauss with so many occasions for improving his solution of the problem for determining the orbit of a planet from a definite number of observations, and suggested to his inventive mind a variety of beautiful contrivances for computing the movement of a body revolving in a conic section in accordance witin Kepler's laws. These results were finally embodied in his Theoria Motus Corporum Cælestium in Conicis Sectionibus Solem Ambientium, which was published at Hamburgh in 1809. In this celebrated work the author gives a complete system of formulæ and processes for computing the movement of a body revolving in a conic section, and then explains a general method for determining the orbit of a planet or comet from three observed positions of the body. The work concludes with an exposition of the method of least squares, which the author appears to have invented independently of, and even prior to, Legendre, although the latter was the first who communicated it to the world.
The Theoria Motus will always be classed among those great works, the appearance of which forms an epoch in the history of the science to which they refer. The processes detailed in it are no less remarkable for originality and completeness than for the concise and elegant form in which the author has exhibited them. Indeed, it may be considered as the text-book from which have been chiefly derived those powerful and refined methods of investigation by which the German astronomy of the present century is more especially characterised.
It is a curious fact that the date of the preface to this immortal work is exactly two centuries later than the date of Kepler's equally renowned work De Stella Martis. The former is dated March 28, 1809; the latter is dated March 28, 1609.
The other astronomical researches of Gauss are chiefly contained in De Zach's Monatliche Correspondenz, the Transactions of the Royal Society of Göttingen, and the Astronomische Nachrichten. Although not of equal importance with those expounded in the Theoria Motus, they all bear the impress of original genius.
In 1807 Gauss was appointed Professor of Mathematics at Göttingen, where he continued to reside during the remainder of his life. Latterly he devoted considerable attention to the subject of terrestrial magnetism, and in concert with Professor Weber made some very important improvements in that branch of science. He died on the 23d of February, 1855. His remains were accompanied to the grave by a vast multitude of persons, including the entire corps of the University of which he was so distinguished an ornament.
Gauss was one of the leading mathematicians of the age, and was the last of the powerful school which is headed by Lagrange; but he lived to an age which made him the survivor of many who must be said to belong to a later epoch. His researches are of the most abstruse character, and turn much on the theory of number and its applications. The Disquisitiones Arithmeticae is one of the standard works of the century. But though the character of his subjects tempts few readers – though his own severe brevity renders these subjects even more difficult than they need be – yet the young reader of Euclid may be brought into contact with Gauss, so as to understand the tone of his genius in a manner which would be utterly impossible in the case of Newton, or Lagrange, or Euler.
It had always been supposed that Euclid had attained the boundary of what is possible in geometrical construction, with the allowance of constructive means to which he limits himself by the three first postulates. Two thousand years had past without any construction being achieved of which a geometer would have supposed Euclid or Archimedes incapable, had the attention been turned that way. But when Gauss, by the highest algebra applied to numerical considerations, showed that a regular polygon of 17 sides (or of any number which is prime, and also one more than a power of 2) can be inscribed in a circle under Euclid's restriction as to means, he made the first advance upon Euclid, and established the connexion of trains of thought so widely different in character, in subject-matter, and in difficulty, that his theorem is of a most useful application. It is the most remarkable standing proof that every part of mathematics must be looked into for the progress of every other; and we have no doubt that this theorem has very much encouraged research into the hidden points of relation between the different branches of pure science.
It was reserved to Gauss to open that extension of plane geometry which consists in transferring the field of reasoning from a plane to any surface whatever. Every surface has its shortest line, as a plane has its straight line; and a triangle drawn upon a surface, bounded by shortest lines, such as the common spherical triangle on the surface of a sphere, has close analogies with the rectilinear triangle in a plane. Gauss showed how the sum of the three angles of such a triangle is connected with the constitution of the area inclosed; thus extending to all surfaces the well-known theorem which Roy and Legendre applied in geodetical calculation. The time may come when the advance of mathematical reasoning shall convert plane geometry into a geometry of all surfaces, in such manner that any theorem which is established on one surface shall immediately be read off on every other. Should this time ever arrive, it will be remembered that Gauss first opened the career, and suggested the possibility of the extension, by giving some of the principal theorems.
Carl Frederick Gauss's obituary appeared in Journal of the Royal Astronomical Society 16:4 (1856), 80-83.