Carl Friedrich Gauss was a German mathematician and scientist who
dominated the mathematical community during and after his lifetime. His
outstanding work includes the discovery of the method of least squares,
the discovery of non-Euclidean geometry, and important contributions to
the theory of numbers.
Born in Brunswick, Germany, on April 30, 1777, Johann Friedrich
Carl Gauss showed early and unmistakable signs of being an extraordinary
youth. As a child prodigy, he was self taught in the fields of reading
and arithmetic. Recognizing his talent, his youthful studies were
accelerated by the Duke of Brunswick in 1792 when he was provided with a
stipend to allow him to pursue his education.
In 1795, he continued his mathematical studies at the University
of Gottingen. In 1799, he obtained his doctorate in absentia from the
University of Helmstedt, for providing the first reasonably complete
proof of what is now called the fundamental theorem of algebra. He
stated that: Any polynomial with real coefficients can be factored into
the product of real linear and/or real quadratic factors.
At the age of 24, he published Disquisitiones arithmeticae, in
which he formulated systematic and widely influential concepts and
methods of number theory -- dealing with the relationships and
properties of integers. This book set the pattern for many future
research and won Gauss major recognition among mathematicians. Using
number theory, Gauss proposed an algebraic solution to the geometric
problem of creating a polygon of n sides. Gauss proved the possibility
by constructing a regular 17 sided polygon into a circle using only a
straight edge and compass.
Barely 30 years old, already having made landmark discoveries in
geometry, algebra, and number theory Gauss was appointed director of the
Observatory at Gottingen. In 1801, Gauss turned his attention to
astronomy and applied his computational skills to develop a technique
for calculating orbital components for celestial bodies, including the
asteroid Ceres. His methods, which he describes in his book Theoria
Motus Corporum Coelestium, are still in use today. Although Gauss made
valuable contributions to both theoretical and practical astronomy, his
principle work was in mathematics, and mathematical physics.
About 1820 Gauss turned his attention to geodesy -- the
mathematical determination of the shape and size of the Earth's surface
-- to which he devoted much time in the theoretical studies and field
work. In his research, he developed the heliotrope to secure more
accurate measurements, and introduced the Gaussian error curve, or bell
curve. To fulfill his sense of civil responsibility, Gauss undertook a
geodetic survey of his country and did much of the field work himself.
In his theoretical work on surveying, Gauss developed results he needed
from statistics and differential geometry.
Most startling among the unpublished discoveries of Gauss is that
of non-Euclidean geometry. With a fellow student at Gottingen, he
discussed attempts to prove Euclid's parallel postulate -- Through a
point outside of a line, one and only one line exists which is parallel
to the first line. As he got closer to solving the postulate, the closer
he was to non-Euclidean geometry, and by 1824, he had concluded that it
was possible to develop geometry based on the denial of the postulate.
He did not publish this work, conceivably due to its controversial
nature.
Another striking discovery was that of noncommutative algebras,
which has been known that Gauss had anticipated by many years but again
failed to publish his results.
In the 1820s, in collaboration with Wilhelm Weber, he explored
many areas of physics. He did extensive research on magnetism, and his
applications of mathematics to both magnetism and electricity are among
his most important works. He also carried out research in the field of
optics, particularly in systems of lenses. In addition, he worked with
mechanics and acoustics which enabled him to construct the first
telegraph in 1833.
Scarcely a branch of mathematics or mathematical physics was
untouched by this remarkable scientist, and in whatever field he
labored, he made unprecedented discoveries. On the basis of his
outstanding research in mathematics, astronomy, geodesy, and physics, he
was elected as a fellow in many academies and learned societies. On
February 23, 1855, Gauss died an honored and much celebrated man for his
accomplishments.
|