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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