# Carl Friedrich Gauss

Carl Gauss was born in Braunschweig (commonly known as Brunswick) Germany. The date was April 30, 1777 and he came from a nominally poor family. His parents were hard-working people that would have differing ideas on the path that young Carl should take. His father was a man that believed in the hard work that came from working with your hands. As a bricklayer and a gardener, he did not put much stock in book-learning and hoped to have his son learn a trade. He purposely tried to dissuade Carl from following a formal education and would seek one of the trades he was involved in.

However, his mother was more of a gentile quality and felt that her son had greater potential than mere trade work. She believed her only child deserved to benefit from a proper education. Carl’s uncle Friedrich also saw the potential in his gifted nephew.

Apparently, the main reason the birthdate of Carl Friedrich Gauss is even known is due to the work of Gauss himself. At the time of his birth, no one had recorded the date; even his mother had not written it down. Young Carl gathered certain bits of information from his mother and figured out the probable date of his arrival.

Carl Gauss apparently was displaying his genius with numbers at a young age. What his mother and uncle saw in him came out in a couple of instances. There is a story that while looking some of his father’s pay records, at the young age of three years old, young Gauss found an error in the math and corrected the mistake. His father was not one to take lightly this situation and had his son handling the family books within a couple years.

Another time, when Gauss was about 9 years old, he displayed his prowess as a mathematical genius once again. During a time in class, the teacher instructed the class “write” out all whole numbers that were between 1 and 100; then add everything up to get the final sum. When finished they were to bring their completed work up to his desk for marks. While it took the majority of the class a normal length of time to bring up their completed answers; Carl Gauss placed his answer on the desk in short order before anyone else was done.

The teacher was surprised to see that young Gauss had only placed one number on his slate, “5,050”. He asked Carl how he came to that conclusion, the young boy simply said he could get two whole numbers, representing for example 1+100, 2+99, etc. would add up to 101. He deduced that 101 times 50 would equal 5,050. The teacher was spellbound by this display of quickness and accuracy.

Because he came from a poor family, the idea of a high caliber education seemed out of the question. But luck would have it that the Duke of Brunswick, Carl Wilhelm Ferdinand appreciated what he saw in young Gauss with his keen intellect and fervent desire to learn. He made Carl his personal mission to make sure the boy received a higher education and provided the finances for such a purpose.

It is believed that one other major reason that the Duke was so interested in the young boy’s education was the fact young Gauss had a keen photographic memory. He believed this advantage for the lad would be a great benefit to the Carl’s future. As timewould tell, the Duke would be proven correct.

Beginning in 1792 at the age of 15, Carl Gauss began attending Collegium Carolinum, where he would spend the next three years. After those intro years of college, he transferred to University of Gottingen and spent another three years in those Ivy walls. Gauss became more fascinated by the world of mathematics and algebra.

While at Gottingen, Gauss postulated the idea that there is a root to every algebraic equation. This concept had been bane in the world of algebra for many famous mathematicians and is the modern basis for fundamental algebra. Out This would be the first out of the box discovery or postulation to come from young Gauss.

Another idea that came to the mind of young Gauss in regards to the concept of prime numbers. For centuries., mathematicians had been struggling with the idea of how often a prime number occurred or in any type of known pattern. Gauss deliberated the idea that if prime numbers could be looked at by graphing their occurrences, a more complete pattern could be reached. His concept was that the probability of primes coming up would be reduced by a factor of 2 as the numbers grew at a rate for every 10. However, he did not immediately disclose his findings until many years later. His reason was that his idea was sound, but it lacked evidence.

In 1796 Carl Gauss astounded many in the field of mathematics when he proved that by simply using a compass and ruler, a 17-sided regular polygon could be created. It is considered that this construction of a 17-sided polygon by this method was a major find in that particular field and one of the biggest since early times of the Greeks.

Other discoveries made by Gauss while at Gottingen consisted of:

- Binomial Theorem
- Law of Quadratic reciprocity

These were just a few of the algebraic formulas that young Gauss put into public discussion. His discovery of the compass and ruler construct of a 17-sided polygon is found in his famous book,*Disquisitiones Arithmeticae. *

Although Gauss made the polygon construct discovery at Gottingen, he left the university without receiving a diploma. One thing that stands out about Gauss at university is his disdain for those that taught but did not have his mental equivalency or better. His was a precocious nature and he tended to make note of his own intellect as compared to those were supposed to be his teachers.

The Duke of Brunswick continued to provide financially for young Gauss. Once Carl did go back to receive his delayed diploma from Gottingen, he made his way to the University of Helmstedt. Here he would seek his doctorate, at age 23. His dissertation for the doctorate was on “The Fundamental Theorem of Algebra”.

Once he received his doctorate, Carl Gauss set about using his time to the research of mathematics since his financial needs were being met by the Duke. It was during this time of life that Gauss set about writing his book mentioned earlier, *Disquisitiones Arithmeticae. *

Gauss surprised again many during the summer of 1801. An astronomer that Gauss had met before published a work that detailed the orbit positions of an asteroid, named Ceres, that had been discovered by an Italian astronomer. The Italian had been tracking the orbit of this “small planet” it before it went behind the sun. Gauss managed to use a method known as “least squares approximation” to detail where the planet would reappear. His conclusion matched pretty close to accurate versus the predictions of his acquaintance astronomer Zach. His Theory of motion of the celestial bodies moving in conic sections around the Sun came from this prediction about Ceres.

This fascination for astronomy continued for Carl Gauss. The next summer of 1802 visited another astronomer friend named Olbers. Olbers had made a discovery of a body called Pallas and asked Gauss to deliberate on its orbit. During this time a new observatory was being opened in Gottingen and Gauss was requested to be its new curator.

By October of 1805, Carl Gauss met and married a young lady named Johanna Ostoff. But his marriage was short-lived as she would soon die after having given birth to their second child. (This child would succumb to illness soon after as well.) It was during this period of his happiness and tragedy that Gauss had taken up position as Director of the Gottingen Observatory.

The tragic loss of his wife and child would soon be compounded by the deaths of others dear to the mathematician. The Duke of Brunswick, which had taken an interest in Carl’s education years before was killed in fighting for the Prussians. This was a particularly heavy burden upon Carl as he grown close to his benefactor and friend. A year later in 1808, Carl’s father passed away.

The heaviness in his heart for all these deaths caused Gauss to seek the asylum of himself for a periodof time with his friend Olbers. He believed that by being in close connection with a good friend, he could pass through the grief and still be a good father for is remaining child. It was important to Gauss that he be a good father.

Gauss would marry again to a young lady that had been a close friend of Johanna. This marriage was not as much as of love as it seemed to meet a need for each of them. From this marriage three children would be born to Carl Gauss.

In 1809, Carl Gauss had his second work published that came from his earlier experience with the Cere’s prediction. *Theoria motus corporum coelestium in sectionibus conicis Solem ambientium*was its title. The first part of the work detailed conics and orbits, the more geometry of the of orbits. The second half focused on the estimations involved in figuring the possibilities and refinement of the orbit of a celestial body. For another ten years Gauss would continue to be involved in the math of astronomy.,

Other aspects of Gauss’s life at this time centered around the area of probability and statistics. He developed a way to show or display probability by means of geometric shapes. By using a bell-shaped curve, data could be displayed statistically. This creation came to be known as the Gaussian Function or Gaussian Distribution.

Through these years, Gauss spent a considerable amount of time with the observatory which was finally being opened. His passion for the facility was only muted by his continued research into other arenas. He was completing other works which included a thesis on hypergeometric function. Other works corresponded with a work that is practical in modern equations of fluid flow and electricity known as potential theory. Gauss was the Avant garde of his day in dealing with a myriad of studies that involved different aspects of physics, geometry and algebra.

In 181m Gauss participated in a geodesic survey that was to coordinate with the Danish grid. This look at the state of Hanover was a 24-hour obsession for Gauss. He would make measurements and then use his knowledge of calculus to continue the work in the evening. Fellow astronomers were constantly communicated with to deliberate his findings.

From his work with the survey, Gauss created the heliotrope. Although he spent considerable time on the project and the heliotrope aided him significantly, Carl Gauss felt his findings might have been less than accurate due to certain details in his conclusions. But his work also developed a number of publications that were rooted in the geodesic accomplishment.

Another area that was significant to Carl Gauss was his work with maps. His work on the theory of map projections using angles brought him considerable attention again. This discovery and work was honored with the Copenhagen University Prize in 1823. This work had some connections to his earlier look at the mapping orbit of Ceres.

Carl Friedrich Gauss continued to make discoveries that would aid in various disciplines of study. Many in the remaining years of his life felt that Gauss was a genius but his writings were simplistic in content. Some even referred to them as “gruel”. However, Gauss was not one to be hindered or ashamed in what he accomplished.

By the time Carl Gauss passed away in 1855, much of his unpublished works began to become public. The same “experts” that denigrated his work, started to fully appreciate the brilliance of the man. Today, Carl Gauss is put on the same playing field as great mathematicians as Archimedes and Pascal.