192
Chapter Number and Title
CARL FRIEDRICH GAUSS
The Gaussian Distributions
By age 18,
Carl Friedrich Gauss (1777–1855)
had indepen-
dently discovered the binomial theorem, the arithmetic-
geometric mean, the law of quadratic reciprocity, and the
prime-number theorem. By age 21, he had made one of his
most important discoveries: the construction of a regular 17-sided polygon by ruler
and compasses, the first advance in the field since the early Greeks.
Gauss’s contributions to the field of statistics include the method of least
squares and the normal distribution, frequently called a Gaussian distribution
in his honor. The normal distribution arose as a result of his attempts to
account for the variation in individual observations of stellar locations. In
1801, Gauss predicted the position of a newly discovered asteroid, Ceres.
Although he did not disclose his methods at the time, Gauss had used his
least-squares approximation method. When the French mathematician
Legendre published his version of the method of least-squares in 1805,
Gauss’s response was that he had known the method for years but had never
felt the need to publish. This was his frequent response to the discoveries of
fellow scientists. Gauss was not being boastful; rather, he cared little for fame.
In 1807, Gauss was appointed director of the
University of Göttingen Observatory, where he worked
for the rest of his life. He made important discoveries in
number theory, algebra, conic sections and elliptic
orbits, hypergeometric functions, infinite series, differ-
ential equations, differential geometry, physics, and
astronomy. Five years before Samuel Morse, Gauss built
a primitive telegraph device that could send messages
up to a mile away. It is probably fair to say that
Archimedes, Newton, and Gauss are in a league of their
own among the great mathematicians.
Gauss’s contributions to
the field of statistics
include the method of
least-squares and the
normal distribution,
frequently called a
Gaussian distribution in
his honor.
The Granger Collection, New York