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**2015**

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Johann Carl Friedrich Gauss was a German mathematician, 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 Gauss’s father that his

son should be permitted to study with a view toward entering a university. Gauss’s

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

duke’s 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 Bode’s 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 life’s 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 Gauss’s 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.

Gauss’s 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 Gauss’s greatest accomplishment. Gauss was considered to be

extremely meticulous in