Johann Carl Friedrich Gauss was a German mathemati


cian, physicist and astronomer. He is considered to be the greatest mathematician of his time, equal to the likes of
Archimedes and Isaac Newton. He is frequently called the founder of modern
mathematics. 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 his
extraordinary feats of mental computation. It is said that as an old man, Gauss said
jokingly that he could count before he could talk. Gauss began elementary school at the
age of seven, and his potential was noticed immediately. He so impressed his teacher
Buttner, and his assistant, Martin Bartels, that they both convinced Gausss father that his
son should be permitted to study with a view toward entering a university. Gausss
extraordinary achievement which caused this impression occurred when he demonstrated
his ability to sum the integers from 1 to 100 by spotting that the sum was 50 pairs of
numbers each pair summing 101.

In 1788, Gauss began his education at the Gymnasium with the help of Buttner and
Bartels, where he distinguished himself in the ancient languages of High German and
Latin 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. His
abilities impressed the duke so much that the duke generously supported Gauss until the
dukes death in 1806. Gauss conceived almost all of his fundamental mathematical
discoveries between the ages of 14 and 17. In 1791 he began to do totally new and
innovative work in mathematics. With the stipend he received from the duke, Gauss
entered Brunswick Collegium Carolinum in 1792. At the academy Gauss independently
discovered Bodes law, the binomial theorem and the arithmetic-geometric mean, as well
as the law of quadratic reciprocity. Between the years 1793-94, while still at the
academy, 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 1795
Gauss left Brunswick to study at Gottingen University. His teacher at the university was
Kaestner, whom Gauss often ridiculed. His only known friend amongst the students
Farkas Bolyai. They met in 1799 and corresponded with each other for many years.

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On March 30, 1796, Gauss discovered that the regular heptadecagon, apolygon with
17 sides, is inscriptible in a circle, using only compasses and straightedge – – the first
such discovery in Euclidean construction in more than 2,000 years. He not only
succeeded in proving this construction impossible, but he went on to give methods of
constructing figures with 17, 257, and 65,537 sides. In doing so, he proved that the
constructions, with compass and ruler, of a regular polygon with an odd number of sides
was possible only when the number of sides was a prime number of the series 3,5 17, 257
and 65,537 or was a multiple of two or more of these numbers. This discovery was to be
considered the most major advance in this field since the time of Greek mathematics and
was published as Section VII of Gausss famous work, Disquisitiones Arithmeticae.
With this discovery he gave up his intention to study languages and turned to
mathematics.
Gauss left Gottingen in 1798 without a diploma. He returned to Brunswick where he
received a degree in 1799. The Duke of Brunswick requested that Gauss submit a
doctoral dissertation to the University of Helmstedt, with Pfaff chosen to be his advisor.
Gausss dissertation was a discussion of the fundamental theorem of algebra. He
submitted proof that every algebraic equation has at least one root, or solution. This
theorem, which had challenged mathematicians for centuries, is still called the
fundamental theorem of algebra.

Because he received a stipend from the Duke of Brunswick, Gauss had no need to find
a job and devoted most of his time to research. He decided to write a book on the theory
of numbers. There were seven sections, all but the last section (referred to in the
previous paragraph) being loyal to the number theory. It appeared in the summer of 1801
and is a classic held to be Gausss greatest accomplishment. Gauss was considered to be
extremely meticulous in his work and would not publish any result without a complete
proof. 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 Sir
William Rowan Hamilton in quaternions. Gauss discovered earlier, independent of
Adrien Legendre, the method of least squares.

On January 1, 1801, the Italian astronomer Giusseppe Piazzi discovered the asteroid
Ceres. In June of the same year, Zach, an astronomer whom Gauss had come to know
two 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 disappeared
behind the Sun. Zach published several predictions of it position, including one by Gauss
which differed greatly from the others. Even though Gauss would not disclose his
methods of calculations, it was his prediction which was nearly accurate when Ceres was
rediscovered on December 7, 1801. Gauss had used his least squares approximation
method.

In June of 1802, Gauss visited an astronomer named Olbers who had discovered
Pallas in March of that same year and Gauss investigated its orbit. Olbers was so
impressed with Gauss that he suggested that Gauss be made director of the proposed new
observatory in Gottingen, but no action was taken. It was also around this time that he
began correspondence with Bessel, whom he did not meet until 1825, and with Sophie
Germain. Gauss married Johanna Ostoff on October 9, 1805. It was the first time that he
would 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 Brunswick
and take up the position of director of the Gottingen observatory, a position which he
been suggested for five years earlier. He arrived to his new position in Gottingen in the
latter part of 1807. The following year, 1808, his father died, and a year later his wife
Johanna died after giving birth to their second son, who was to die soon after her. Gauss
was shattered and wrote to Olbers asking him to give him a home for a few weeks. He
remarried Minna, the best friend of Johanna the following year and although they had
three children, this marriage seemed to be one of convenience for Gauss. It is obvious
through many of Gausss accomplishments that his devotion to his work never faltered
even during personal tragic moments.

He published his second book, Theoria motus corporum coelestium in sectionibus
conicis Solem ambientium, in 1809. The book was a major two volume dissertation on
the 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. Gausss
contributions to theoretical astronomy stopped after 1817, although he went on making
observations until the age of seventy.
Gauss produced many publications including, Disquisitiones generales circa seriem
infinitam, a treatment of series and introduction of the hypergeometric function,
Methodus nova integralium valores per approximationem inveniendi, an essay on
approximate integration, Bestimmung der Genauigkeit der Beobachtungen, a discussion
of statistical estimators, and Theoria attractionis corporum sphaeroidicorum
ellipticorum homogeneorum methodus nova tractata, a work concerning geodesic
problems and concentrating on potential theory. During the 1820s, Gauss found himself
interested in geodesy. He invented the heliotrope as a result of this interest. The crude
instrument worked by reflecting the Suns rays using a design of mirrors and a small
telescope. Due to inaccurate base lines used for the survey and an unsatisfactory network
of triangles, the instrument was not of much use. He published over seventy papers
between 1820 and 1830.
Since the early 1800s, Gauss had an interest in the possible existence of a
non-Euclidean geometry. He discussed this topic in his correspondences with Farkas
Bolyai and also in his correspondences with Gerling and Schumacher. In a book review
in 1816, he discussed proofs which deduced the axiom of parallels from the other
Euclidean axioms, suggesting that he believed in the existence of non-Euclidean
geometry, although he was rather vague. Gauss confided in Schumacher, telling him
that he believed his reputation would suffer if he admitted in public that he believed in
the existence of such a geometry. He had a major interest in differential geometry and
published many papers on the subject. his most renowned work in this field was
published in 1828 and was entitled Disquisitiones generales circa superficies curva.

The paper arose out of his geodesic interests, but it contained such geometrical ideas as
Gaussian 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 ailing
mother moved in with him in 1817 and remained with him until his death in 1839. It was
also during this period that he was involved in arguments with his wife and her family
regarding the possibility of moving to Berlin. Gauss had been offered a position at the
Berlin 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 died
after a long illness.

Wilhelm Weber arrived in Gottingen in 1831 as a physics professor filling Tobias
Mayers chair. Gauss had known Weber since 1828 and supported his appointment.
Gauss had worked on physics before 1831, publishing a paper which contained the
principle of least constraint. He also published a second paper which discussed forces of
attraction. These papers were based on Gausss potential theory, which proved of great
importance in his work on physics. He later came to believe his potential theory and his
method of least squares provided vital links between science and nature. In the six years
that Weber remained in Gottingen much was accomplished by his collaborative work
with Gauss. They did extensive research on magnetism. Gausss applications of
mathematics to both magnetism and electricity are among his most important works; the
unit of intensity of magnetic fields is today called the gauss. He wrote papers dealing
with the current theories on terrestrial magnetism, including Poissons ideas, absolute
measure for magnetic force and an empirical definition of terrestrial magnetism.
Together they discovered Kirchoffs laws, and also built a primitive electromagnetic
telegraph. Although this period of his life was an enjoyable pastime for Gauss, his works
in this area produced many concrete results.
After Weber was forced to leave Gottingen due to a political dispute, Gausss activity
gradually began to decrease. He still produced letters in response to fellow scientists
discoveries ususally remarking that he had known the methods for years but had never
felt the need to publish. Sometimes he seemed extremely pleased with advances made
by other mathematicians, especially that of Eisenstein and of Lobachevsky. From 1845
to 1851 Gauss spent the years updating the Gottingen University widows fund. This
work gave him practical experience in financial matters, and he went on to make his
fortune through shrewd investments in bonds issued by private companies.
Gauss presented his golden jubilee lecture in 1849, fifty years after receiving his
diploma from Hemstedt University. It was appropriately a variation on his dissertation of
1799. From the mathematical community only Jacobi and Dirichlet were present, but
Gauss received many messages and honors. From 1850 onward, Gausss work was again
of nearly all of a practical nature although he did approve Riemanns doctoral thesis and
heard his probationary lecture. His last known scientific exchange was with Gerling. He
discussed a modified Foucalt pendulum in 1854. He was also able to attend the opening
of the new railway link between Hanover and Gottingen, but this proved to be his last
outing. His health deteriorated slowly, and Gauss died in his sleep early in the morning
of February 23, 1855.

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