contents

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.

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.

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".

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.

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.)

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.

Eric Weisstein's World of Math

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. With Weber, 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).

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.

CONCLUSION

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.

REFERENCES

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.

THE END