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.

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.