Johann Karl
Friederich Gauss
(Born
April 30, 1777 - Died February 23, 1855)
“the prince of mathematicians”
Johann Gauss was born in
Brunswick, Germany in 1777 to a poor, uneducated family. He started elementary school at age seven
and showed great promise even at that age.
His instructors Buttner and Bartels were impressed by his ability to
evaluate the sum of integers from 1 to 100 by recognizing that the sum was 50
pairs of numbers summing 101. Gauss
went to secondary school in 1788 with the help of Buttner and Bartels. Bartels would later be the teacher of
Lobachevsky. In 1792 Gauss received a
stipend from the Duke of Brunswick-Wofenbuttel to attend Brunswick Collegium
Carolinum. He discovered Bode’s law of
planetary distances, the binomial theorem for rational exponents, and the
arithmetic-geometric mean. He attended
Brunswick Collegium until 1795.
From 1795 to 1798 Gauss attended
the University of Gottingen. In 1796 he
invented modular arithmetic, rediscovered quadratic reciprocity and developed
the prime number theorem. While
studying the cycoltomic equation (whose solution has the geometric counterpart
of dividing a circle into equal arcs) he conceived of the construction of a
regular 17-gon by ruler and compass.
This was the first major advance in this field in 200 years. Gauss was so elated he requested that a
heptadecagon be placed on his tombstone.
It is here at the University of Gottingen that he became friends with
another student, Farkas Bolyai. Farkas
Bolyai’s son would later develop the idea of non-Euclidian Geometry. Gauss left the University of Gottingen
without receiving a diploma. He later
returned to Brunswick and received his degree in 1799. The Duke of Brunswick-Wofenbuttel continued
to give Gauss a stipend and this enabled Gauss to continue his research without
finding a job. His dissertation was a
proof of the fundamental theorem of algebra.
In 1801 he published a
book Disquisitiones Arithmeticae. It
included modular arithmetic and the first proof of the quadratic
reciprocity. In 1801 G. Piazzi
discovered the planetoid Ceres. Piazzi
was only able to track its orbit for nine degrees. But Gauss after three months of work was able to predict where it
would be. Zach later rediscovered Ceres
very near to where Gauss had predicted.
Gauss had used his least squares approximation method to make his
prediction. A few years later he
published the Theory of Celestial Movement and it included the gaussian
gravitational constant and the method of least squares.
In 1805 Gauss married
Johanna Ostoff and had a happy marriage.
He and his wife had three children.
Shortly after, the Duke of Brunswick was killed while he was in the
Prussian army fighting against Napoleon.
Gauss needed to find employment and became the Director of the Gottingen
observatory. He held this position for
the rest of his life. Gauss’s wife
died in 1809 and he never recovered from this loss. However, he married Friederica Wilhelmine Waldeck, the best
friend of his wife Johanna in 1810.
This was said to be a marriage of convenience and they also had three
children together.
In 1818 Gauss performed
a geodesic survey of the state of Hanover and linked it with the existing
Danish grid. It is during this time
that he invented the heliotrope (reflects sunlight over great distances to mark
the position of participants in a land survey). This survey also led to the Gaussian distribution and his
interest in differential geometry was inspired. He developed the theorem says the curvature of a surface can be
determined by measuring angles and distances on the surface, it does not depend
on how the surface might be imbedded in 3-dimmensional space. Gauss also
developed a method for measuring the horizontal intensity of the magnetic
field. He also developed the
mathematical theory for separating the inner and outer sources of the Earth’s
magnetic field.
Gauss followed his motto
pauca sed matura (few, but ripe). He
did not publish often; he preferred to wait until they were complete and beyond
reproach. Gauss typically worked
independently through his life. His
work as found in his personal diaries has shown that he had discovered several
mathematical concepts many years before his contemporaries had published
them. Non-Euclidian geometry is an
example of this. He worked on it prior
to 1800 but did not publish it. His
students included noted mathematicians Richard Dedekind, Moritz Cantor and
Bernhard Riemann. Gauss died in 1855 in
Gottingen, Germany, and left a long legacy of contributions to many fields
including mathematics, magnetism, geodesy, optics and astronomy. Because of his contributions to astronomy
Gauss had a crater named after him called the Gauss crater and also an asteroid
1001 Gaussia. His inventions included
the magnometer, the heliotrope, the telegraph and the photometer.
Quotations of Gauss:
Gauss
Quotations
Some of Gauss’s Work:
Gauss's
Hypergeometric Theorem
Gauss-Bolyai-Lobachevsky
space
Gaussian
Interpolation Formula
Gauss’s
Law for a Magnetic Medium
Gauss's
Law of Normal Gravitational Force