Carl Gauss Essay, Research Paper
Carl Gauss was a man who is known for making
a great deal breakthroughs in the wide variety of his work in both mathematics
and physics. He is responsible for immeasurable contributions to the fields
of number theory, analysis, differential geometry, geodesy, magnetism,
astronomy, and optics, as well as many more. The concepts that he himself
created have had an immense influence in many areas of the mathematic and
scientific world.
Carl Gauss was born Johann Carl Friedrich
Gauss, on the thirtieth of April, 1777, in Brunswick, Duchy of Brunswick
(now Germany). Gauss was born into an impoverished family, raised as the
only son of a bricklayer. Despite the hard living conditions, Gauss’s brilliance
shone through at a young age. At the age of only two years, the young Carl
gradually learned from his parents how to pronounce the letters of the
alphabet. Carl then set to teaching himself how to read by sounding out
the combinations of the letters. Around the time that Carl was teaching
himself to read aloud, he also taught himself the meanings of number symbols
and learned to do arithmetical calculations.
When Carl Gauss reached the age of seven,
he began elementary school. His potential for brilliance was recognized
immediately. Gauss’s teacher Herr Buttner, had assigned the class a difficult
problem of addition in which the students were to find the sum of the integers
from one to one hundred. While his classmates toiled over the addition,
Carl sat and pondered the question. He invented the shortcut formula on
the spot, and wrote down the correct answer. Carl came to the conclusion
that the sum of the integers was 50 pairs of numbers each pair summing
to one hundred and one, thus simple multiplication followed and the answer
could be found.
This act of sheer genius was so astounding
to Herr Buttner that the teacher took the young Gauss under his wing and
taught him fervently on the subject of arithmetic. He paid for the best
textbooks obtainable out of his own pocket and presented them to Gauss,
who reportedly flashed through them.
In 1788 Gauss began his education at the
Gymnasium, with the assistance of his past teacher Buttner, where he learned
High German and Latin. After receiving a scholarship from the Duke of Brunswick,
Gauss entered Brunswick Collegium Carolinum in 1792. During his time spent
at the academy Gauss independently discovered Bode’s law, the binomial
theorem, and the arithmetic-geometric mean, as well as the law of quadratic
reciprocity and the prime number theorem. In 1795, an ambitious Gauss left
Brunswick to study at Gottingen University. His teacher there was Kaestner,
whom Gauss was known to often ridicule. During his entire time spent at
Gottingen Gauss was known to acquire only one friend among his peers, Farkas
Bolyai, whom he met in 1799 and stayed in touch with for many years.
In 1798 Gauss left Gottingen without a
diploma. This did not mean that his efforts spent in the university were
wasted. By this time he had made on of his most important discoveries,
this was the construction of a regular seventeen-gon by ruler and compasses.
This was the most important advancement in this field since the time of
Greek mathematics.
In the summer of 1801 Gauss published his
first book, Disquisitiones Arithmeticae, under a gratuity from the Duke
of Brunswick. The book had seven sections, each of these sections but the
last, which documented his construction of the 17-gon, were devoted to
number theory.
In June of 1801, Zach an astronomer whom
Gauss had come to know two or three years before, published the orbital
positions of, Ceres, a new “small planet”, otherwise know as an asteroid.
Part of Zach’s publication included Gauss’s prediction for the orbit of
this celestial body, which greatly differed from those predictions made
by others. When Ceres was rediscovered it was almost exactly where Gauss
had predicted it to be.
Although Gauss did not disclose his methods
at the time, it was found that he had used his least squares approximation
method. This successful prediction started off Gauss’s long involvement
with the field of astronomy.On October ninth, 1805 Gauss was married to
Johana Ostoff. Although Gauss lived a happy personal life for the first
time, he was shattered by the death of his benefactor, The Duke of Brunswick,
who was killed fighting for the Prussian army.
In 1807 Gauss left Brunswick to take up
the position of director of the Gottingen observatory. This was a time
of many changes for Carl Gauss. Gauss had made his way to Gottingen by
late 1807. The following year his father died, and a year following that
tragedy, his wife Johanna died giving birth to their second son, who was
to die shortly after her. Understandably Gauss’s life was shattered, he
turned to his friends and colleagues for support. The next year, Gauss
was married a second time. His new wife was named Minna, she was the best
friend of Johanna. Although the couple had three children, this second
marriage seemed to be somewhat of a expedience for Gauss.
Gauss’s work was not visibly affected by
these life altering events. In 1809, he went on to publish his second book
Theoria motus corporum coelestium in sectionibus conicis Solem ambientium.
This publishing was a profound two volume thesis on the motion of celestial
bodies. Gauss’s contributions in the field of theoretical astronomy continued
until the year 1817. Gauss himself continued making observations until
the age of seventy.
In 1818, Gauss was asked to carry out a
geodesic (a study in which predictions are made of exact points or area
sizes of the earth’s surface) survey of the state of Hanover, to link with
the existing Danish grid. Gauss eagerly accepted the job, and took personal
charge of the survey. He made his measurements by day, and reduced them
by night, using his incredible mental ability for calculations. To aid
him in his survey, Gauss invented the heliotrope, which worked by reflecting
the Sun’s rays using a design of mirrors and a small telescope. But inaccurate
base lines used for the survey and an unsatisfactory network of triangles.
Gauss often doubted his work in the profession,
but over the course of ten years, from 1820 to 1830, published over seventy
papers. From the early 1800’s Gauss had had an interest in the question
of the possible existence of a non-Euclidean geometry. In a book review
of 1816 Gauss discussed proofs which suggested and supported his belief
in non-Euclidean geometry (which was later proved to exist), though he
was quite vague. Gauss later confined in one of his fellow theoreticians
that he believed his reputation would suffer if he admitted to the public
the existence of such a geometry.
The period of time from 1817 to 1832 was
a particularly hard time for Gauss. He took in his sick mother, who stayed
with him until her death twenty-two years later. At the same time he was
in a dispute with his wife and her family about whether they should move
to Berlin, where Gauss had been offered a job. Minna, his wife, and hr
family were enthusiastic about the move, but Gauss, who did not like change,
decided to stay in Gottingen. Minna died in 1831 after a long illness.
In 1832, Gauss and a colleague of his,
Wilhelm Weber, began studying the theory of terrestrial magnetism. Gauss
was quite enthusiastic about this prospect and by 1840, had written three
important papers on the subject. These papers all dealt the current theories
on terrestrial magnetism, absolute measure for magnetic force, and an empirical
definition of terrestrial magnetism.
Gauss and Weber achieved much in their
six years together. The two discovered Kirchoff’s laws, as well as building
a primitive telegraph device. However, this was just an enjoyable hobby
of Gauss’s. He was more interested in the task of setting up a world wide
net of magnetic observation points. This vocation produced a great deal
of concrete results. The Magnetischer Verein and its journal were conceived,
and the atlas of geomagnetism was published.
From 1850 onwards Gauss’s work was that
of nearly all practical nature. He disputed over a modified Foucalt pendulum
in 1854, and was also able to attend the opening of the new railway link
between Hanover and Gottingen, but this outing proved to be his last. The
health of Carl Gauss deteriorated slowly and he died in his sleep early
in the morning of February 23, 1855.
Carl Gauss’s influence in the worlds of
science and mathematics has been immeasurable. His abstract findings have
changed the way in which we study our world. In Gauss’s lifetime he did
work on a number of concepts for which he never published, because he felt
them to be incomplete. Every one of these ideas (including complex variable,
non-Euclidean geometry, and the mathematical foundations of physics) was
later discovered by other mathematicians. Although he was not awarded the
credit for these particular discoveries, he found his reward with the pursuit
of such research, and finding the truth for its own sake. He is a great
man and his achievements will not be forgotten.
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