__Carl Friedrich GAUSS
__

Gauss was born in Braunschweig (see map below) on April 1777.

1 : Braunschweig 2 : Göttingen

He studied ancient languages. At the age of 17 he became
interested in mathematics and attempted a solution of the
classical problem of constructing a regular heptagon, or
seven-sided figure, with ruler and compass. He didn’t only
succeed in proving that this construction was impossible, but
went on to give methods of constructing figures with 17, 257 and
65, 537 sides.In so doing he proved that the construction, with
compass and ruler, of a regular polygon with an odd number of
sides was impossible 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. With this discovery he gave up
his intention to study languages and turned to mathematics.

He studied at the University of Göttingen from 1795 to 1798. For
his doctoral thesis he submitted a 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"

"Every polynomial in x can be resoluted in factors from the
first and second degree."

example:

x³ + 4x² + x -6 = (x-1).(x²+5x+6)

The theorem, in its most general form, is equivalent to the statement that every polynomial equation f(z) = 0, where z is a complex number, has at least one root, either real or complex. The coefficients of the polynomial may themselves be either real or complex. At the end of the 18th century (1798) Carl Friedrich Gauss proved this theorem.

By the time of Gauss, algebra had entered its
modern phase. Attention shifted from solving polynomial equations
to studying the structure of abstract mathematical systems whose
axioms were based on the behavior of mathematical objects, such
as complex numbers that mathematicians encountered when studying
polynomial equations. Indeed at the end of the eighteenth century
three men - **Caspard Wessel** (1745-1818), a self-taught **Norwegian**
surveyor, Jean Robert Argand (1768-1822), an equally self-taught
Swiss book-keeper, and Gauss himself - working independently, put
forward geometrical interpretations of complex numbers. But in
the words of G.H.Hardy, 'Gauss was the first mathematician to use
complex numbers in a really confident and scientific way'. He
also took the next step investigating the theory of complex
functions. His volume on the theory of numbers, *Disquisitiones
Arithmeticae *(Inquiries into Arithmetic, 1801), is a classic
work in the field of mathematics.

Gauss next turned his attention to astronomy. A
faint planetoid, Ceres, had been discovered in 1801; and because
astronomers thought it was a planet, they observed it with great
interest until losing sight of it. From the early observations
Gauss calculated its exact position, so that it was easily
rediscovered. He presented his results in a second great work , *Theoria
motus corporum* *coelestium*, which was published in 1809

He also worked out a new method for calculating the orbits of
heavenly bodies. In 1807 Gauss was appointed professor of
mathematics and director of the observatory at Göttingen,
holding both positions until his death there on February 23,
1855.

Although Gauss made valuable contributions to both theoritical
and practical astronomy, his principal work was in mathematics
and mathematical physics. On other example of Gauss' creativity
in the number theory field can be found on the back page of one
of his boyhood tables of logarithms : a shorthand statement of
the prime number theorem. The proof for this theorem was found
later independently by **De la Vallée Poussin (Belgium)** and
Hademard (France).

Gauss' third major treatise is the *Disquisitiones generales
circa superficies curvas* of 1827. In this work he not only
provided the definitive treatment of the differential geometry of
surfaces lying in three-dimensional space, but also advanced the
totally new concept that a surface is a space in itself - an idea
that was generalized further in the context of non-Euclidean
geometry. In the first part of 19th century the German
mathematician Carl Friedrich Gauss, the Russian mathematician
Nikolay Ivanovich Lobachevsky, and Hungarian mathematician Jànos
Bolyai independently demonstrated the possibility of constructing
a consist system of geometry in which Euclid’s postulate of
the unique parallel was replaced by a postulate stating that
through any point not on a given straight line an infinite number
of parallels to the given line could be drawn. But Gauss failed
to publish these important findings because he wished to avoid
publicity.

In probability theory, he developed the important method of least squares and the fundamental laws of probability distribution. The normal probability graph is still called the Gaussian curve.

The figure above represents the graph of the standardized normal Gauss curve with standarddeviation s =1, and the mean m = 0 and z = (X - m )/s according to the formula:

Y = e^{-0.5z²}

He made geodetic surveys, and applied
mathematics to geodesy. With the German physicist Wilhelm Eduard
Weber, Gauss did extensive research on magnetism and electricity.
The *Intensitas vis magneticae terrestris ad mensuram absolutam
revocata* (1832), the *Allgemeine Theorie des Erdmagnetismus*
(1839) and the *Allgemeine Lehrsätze in Beziehung auf die im*
*verkehrten Verhältnisse des Quadrats der Entfernung wirkenden
Anziehungs- und Abstossungskräfte* (1840) are among his most
important works; the unit of intesity of magnetic fields is today
called the gauss.He also carried out research in optics,
particulary in systems of lenses. Scarcely a branch of
mathematics or mathematical physics was untouched by Gauss.

His discoveries and insights pointed the way to much of the best
mathematics of the later nineteenth century. He was indeed, as
his contemporaries styled him, the 'PRINCE OF THE
MATHEMATICIANS'.

*Sources:*

- "Gauss, Carl
Friedrich,","Algebra","Theory of
equations","Geometry"

Microsoft (R) Encarta Copyright (C)1994 Microsoft Corporation

- "Nieuwe Delta 4a", Wolters Leuven

- "Nieuwe Delta 6 analyse en stochastiek", Wolters
Leuven

- "Makers of mathematics" Stuart Hollingdale

- http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Gauss.html