6. Carl Friedrich Gauss (1777-1855) was one of
the greatest mathematicians of all time. He combined scientific theory and
practice like no other before him, or since, and even as a young man
Gauss made extraordinary contributions to mathematics. His
Disquisitiones arithmeticae, published in 1801, stands to this day as a true
masterpiece of scientific investigation. In the same year, Gauss gained
fame in wider circles for his prediction, using very few observations, of
when and where the asteroid Ceres would next appear. The method of
least squares, developed by Gauss as an aid in his mapping of the state of
Hannover, is still an indispensable tool for analyzing data. His sextant is
pictured on the last series of German 10-Mark notes, honoring his
considerable contributions to surveying. There, one also finds a bell curve,
which is the graphical representation of the Gaussian normal distribution
in probability. Together with Wilhelm Weber, Gauss invented the first
electric telegraph. In recognition of his contributions to the theory of
electromagnetism, the international unit of magnetic induction is the
gauss.
7.
8. Gauss was born in Brunswick, Germany, on April 30, 1777, to poor,
working-class parents. His father labored as a gardner and brick-layer
and was regarded as an upright, honest man. However, he was a harsh
parent who discouraged his young son from attending school, with
expectations that he would follow one of the family trades. Luckily,
Gauss' mother and uncle, Friedrich, recognized Carl's genius early on and
knew that he must develop this gifted intelligence with education.
While in arithmetic class, at the age of ten, Gauss exhibited his skills as
a math prodigy when the stern schoolmaster gave the following
assignment: "Write down all the whole numbers from 1 to 100 and add
up their sum." When each student finished, he was to bring his slate
forward and place it on the schoolmaster's desk, one on top of the other.
The teacher expected the beginner's class to take a good while to finish
this exercise. But in a few seconds, to his teacher's surprise, Carl
proceeded to the front of the room and placed his slate on the desk.
Much later the other students handed in their slates.
9. At the end of the classtime, the results were examined, with most of
them wrong. But when the schoolmaster looked at Carl's slate, he was
astounded to see only one number: 5,050. Carl then had to explain to
his teacher that he found the result because he could see that,
1+100=101, 2+99=101, 3+98=101, so that he could find 50 pairs of
numbers that each add up to 101. Thus, 50 times 101 will equal 5,050.
At the age of fourteen, Gauss was able to continue his education with
the help of Carl Wilhelm Ferdinand, Duke of Brunswick. After meeting
Gauss, the Duke was so impressed by the gifted student with the
photographic memory that he pledged his financial support to help him
continue his studies at Caroline College. At the end of his college years,
Gauss made a tremendous discovery that, up to this time,
mathematicians had believed was impossible. He found that a regular
polygon with 17 sides could be drawn using just a compass and straight
edge. Gauss was so happy about and proud of his discovery that he gave
up his intention to study languages and turned to mathematics.
Duke Ferdinand continued to financially support his young friend as
Gauss pursued his studies at the University of Gottingen. While there he
submitted a proof that every algebraic equation has at least one root or
solution. This theorem had challenged mathematicians for centuries
and is called "the fundamental theorem of algebra".
10. Gauss' next discovery was in a totally different area of mathematics. In
1801, astronomers had discovered what they thought was a planet, which
they named Ceres. They eventually lost sight of Ceres but their
observations were communicated to Gauss. He then calculated its exact
position, so that it was easily rediscovered. He also worked on a new
method for determining the orbits of new asteroids. Eventually these
discoveries led to Gauss' appointment as professor of mathematics and
director of the observatory at Gottingen, where he remained in his
official position until his death on February 23, 1855.
Carl Friedrich Gauss, though he devoted his life to mathematics, kept his
ideas, problems, and solutions in private diaries. He refused to publish
theories that were not finished and perfect. Still, he is considered, along
with Archimedes and Newton, to be one of the three greatest
mathematicians who ever lived.
11.
12. German mathematician who is
sometimes called the "prince of mathematics." He was a prodigious child,
at the age of three informing his father of an arithmetical error in a
complicated payroll calculation and stating the correct answer. In school,
when his teacher gave the problem of summing the integers from 1 to 100
(an arithmetic series Eric Weisstein's World of Math) to his students to
keep them busy, Gauss immediately wrote down the correct answer 5050
on his slate. At age 19, Gauss demonstrated a method for constructing a
heptadecagon Eric Weisstein's World of Math using only a straightedge Eric
Weisstein's World of Math and compass Eric Weisstein's World of Math
which had eluded the Greeks. (The explicit construction of the
heptadecagon Eric Weisstein's World of Math was accomplished around
1800 by Erchinger.) Gauss also showed that only regular polygons Eric
Weisstein's World of Math of a certain number of sides could be in that
manner (a heptagon, Eric Weisstein's World of Math for example, could
not be constructed.)
13. Gauss proved the fundamental theorem of algebra, Eric Weisstein's World of
Math which states that every polynomial Eric Weisstein's World of Math has
a root of the form a+bi. In fact, he gave four different proofs, the first of
which appeared in his dissertation. In 1801, he proved the fundamental
theorem of arithmetic, Eric Weisstein's World of Math which states that
every natural number Eric Weisstein's World of Math can be represented as
the product Eric Weisstein's World of Math of primes Eric Weisstein's World
of Math in only one way.
At age 24, Gauss published one of the most brilliant achievements in
mathematics, Disquisitiones Arithmeticae (1801). In it, Gauss systematized
the study of number theory Eric Weisstein's World of Math (properties of the
integers Eric Weisstein's World of Math). Gauss proved that every number is
the sum of at most three triangular numbers Eric Weisstein's World of Math
and developed the algebra Eric Weisstein's World of Math of congruences.
EricWeisstein'sWorld of Math
14. In 1801, Gauss developed the method of least squares fitting, Eric
Weisstein's World of Math 10 years before Legendre, but did not publish
it. The method enabled him to calculate the orbit of the asteroid Eric
Weisstein's World of Astronomy Ceres, which had been discovered by
Piazzi from only three observations. However, after his independent
discovery, Legendre accused Gauss of plagiarism. Gauss published his
monumental treatise on celestial mechanics Theoria Motus in 1806. He
became interested in the compass through surveying and developed the
magnetometer and, with Wilhelm Weber measured the intensity of
magnetic forces.WithWeber, he also built the first successful telegraph.
Gauss is reported to have said "There have been only three epoch-making
mathematicians: Archimedes, Newton and Eisenstein" (Boyer 1968, p.
553). Most historians are puzzled by the inclusion of Eisenstein in the
same class as the other two. There is also a story that in 1807 he was
interrupted in the middle of a problem and told that his wife was dying.
He is purported to have said, "Tell her to wait a moment 'til I'm through"
(Asimov 1972, p. 280).
15. Gauss arrived at important results on the parallel postulate, Eric Weisstein's World
of Math but failed to publish them. Credit for the discovery of non-Euclidean
geometry Eric Weisstein's World of Math therefore went to Janos Bolyai and
Lobachevsky. However, he did publish his seminal work on differential geometry
Eric Weisstein's World of Math in Disquisitiones circa superticies curvas. The
Gaussian curvature Eric Weisstein's World of Math (or "second" curvature) is
named for him. He also discovered the Cauchy integral theorem Eric Weisstein's
World of Math
for analytic functions, Eric Weisstein's World of Math but did not publish it. Gauss
solved the general problem of making a conformal map Eric Weisstein's World of
Math of one surface onto another.
Unfortunately for mathematics, Gauss reworked and improved papers incessantly,
therefore publishing only a fraction of his work, in keeping with his motto "pauca
sed matura" (few but ripe). Many of his results were subsequently repeated by
others, since his terse diary remained unpublished for years after his death. This
diary was only 19 pages long, but later confirmed his priority on many results he
had not published. Gauss wanted a heptadecagon Eric Weisstein's World of Math
placed on his gravestone, but the carver refused, saying it would be
indistinguishable from a circle. The heptadecagon Eric Weisstein's World of Math
appears, however, as the shape of a pedestal with a statue erected in his honor in
his home town of Braunschweig.
18. Carl Friedrich Gauss (1777-1855) is considered to be the greatest German
mathematician of the nineteenth century. His discoveries and writings
influenced and left a lasting mark in the areas of number theory, astronomy,
geodesy, and physics, particularly the study of electromagnetism.
20. Ball, W.W. Rouse. (1960). A Short Account of the History of
Mathematics. New York, NY: Dover Publications Inc.
Bell, Eric T. (1937). Men of Mathematics. New York, NY: Simon and
Schuster.
"Gauss, Carl Friedrich," Microsoft (R) Encarta. Copyright (c) 1994
Microsoft Corporation. Copyright (c) 1994 Funk & Wagnalls
Corporation.
Hall, Tord. (1970). Carl Friedrich Gauss. Cambridge, MA: The MIT
Press.
Reimer, Luetta. (1990). Mathematicians Are People, Too. Palo Alto,
CA: Dale Seymour Publications.
