**Carl Fredrich Gauss**

1777 -1855
By: Professor Doug Jones

This month we are meeting Carl Fredrich Gauss. You can see from the timeline that he was a contemporary of André Ampère. Carl Gauss was born April 30, 1777, in Brunswick, which is now part of Germany. His parents were very poor. His mother had no education at all and was completely illiterate. His father was a simple

craftsman, also with very limited education. According to Gauss, his mother could not tell him the date of his birthday other than it was on a Wednesday, eight days before the Feast of Ascension. At an early age Gauss figured out the formula for determining the day that Easter falls on in any given year. Armed with that data, and the fact that Ascension is 40 days after Easter, he figured out his birthday. Gauss often said that he could count before he could talk. There are many stories of young Gauss doing remarkable things. It is clear that he was a child prodigy when it came to mathematics. There is a story which appears in some very early biographical sources that has Gauss at age 3 correcting some arithmetic errors in his fathers’ accounts.

[1] Another oft-recounted story happened when Gauss, at age seven, started school. On the first day of Mathematics class, the teacher gave the class the assignment to add all the integers between 1 and 100. Gauss immediately saw the solution and solved the problem in no time while the rest of the class slogged through the problem. His teacher, of course, was very impressed and quickly realized that Gauss was no ordinary student. The teacher's assistant was a man named Johann C M Bartels, who was a rising star himself in the world of mathematics. He tutored Gauss for a few years, introducing his young charge into number theory and analysis. In a few years, at age eleven, Gauss entered the “Gymnasium” which in his day was a sort of advanced prep school. In addition to continuing to show promise in mathematics, he demonstrated a remarkable ability in ancient languages.

Gauss was an only child. It must have been difficult for his working class, uneducated parents to let him go to pursue advanced education, especially since they had no way of supporting him. Some sources say that Gauss had a somewhat difficult relationship with his father, but eventually, his father realized that he must let his extraordinarily gifted son go. Gauss’s father died in 1808. Gauss’s mother lived to be 97, and for the last 22 years of her life, Gauss cared for her in his home. But, back to the storyline…

At age 15, Gauss had attracted the attention of the Duke of Brunswick, who became his sponsor. So, in 1792 with the support of the Duke, Gauss entered Collegium Carolinium, a very prestigious technical university. During this time Gauss discovered a sort of pattern in the occurrence of prime numbers, a problem that had been vexing mathematicians for centuries. Gauss decided to keep this to himself for many years until he had developed a more rigorous proof of his discovery.

[2] A few years later, Gauss moved to the University of Gottingen. At this point, Gauss was torn between a career in mathematics or the study of ancient language, as he expressed an equal fascination with both. In 1792, Gauss made a discovery that nudged him towards mathematics as his life’s work. He discovered that one could create a 17-sided polygon inside a circle using a straight edge and a compass.

[3] Later on, Gauss would say that this may have been his most important discovery. Even though it seems to pale in comparison to his lifelong series of amazing contributions to the field of mathematics, he was apparently the first one in about two thousand years of recorded geometry to notice that this was even possible. Secondly, the proof he wrote supporting his observation was groundbreaking and opened the door for other significant discoveries. In 1797, at age 20, he wrote his doctoral thesis with an impossibly long Latin title,

*Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse*. For those of you who are a tad rusty in Latin, it means “New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors (i.e., polynomials) of the first or second degree.” Did that help at all?

A few years later, in 1801, Gauss published two works that garnered significant attention. The first was a textbook on algebraic number theory, the very first of its kind. This book became the standard resource for number theory for the 19

^{th} century and beyond. The second publication in 1801 was Gauss’s “re-discovery” of the asteroid Ceres. Ceres had been discovered a year earlier by an Italian astronomer and that discovery was significant in the astronomical world of the day. However, Ceres disappeared behind the sun before anyone could take enough observations to accurately map the asteroid's orbit. Since the orbit had not been calculated, no one knew where to look for the asteroid’s reappearance.

Gauss applied a new mathematical method of his own design to deal with errors in observation and he predicted exactly where and when the asteroid would reappear. These two accomplishments solidified his position in the academic community, not only as a preeminent mathematician but as an astronomer as well. Gauss accepted a position of astronomer at Gottingen and published a very important work on the computation of orbits, facilitated of course, by his remarkable ability as a mathematician. By 1806, Gauss, now married to his first wife, Johanna, had a son, Joseph. Gauss accepted a professorship at Gottingen, which he held for the rest of his life. In 1808, their daughter Minna was born. A year later Johanna died along with their third child an infant named Louis. The following year Gauss remarried and had 3 more children with his second wife, also named Minna. His marriage to Minna lasted 21 years until her death in 1831.

Gauss never traveled much, preferring to stay at the University in Gottingen. He became a very popular professor, attracting some of the great minds of his day to study with him. He did not permit his students to take notes in class, insisting instead that they follow him point by point through the highly detailed logic of his thesis. It is ironic since one of the criticisms of Gauss’s written work is a certain lack of detail in his explanations!

[4] One of his most famous students was George Friedrich Bernhard Riemann (1826-1866), who, in his own right, was to become one of the great mathematicians.

Gauss made his mark as the preeminent mathematician of his day with significant contributions to many fields in math, including probability and statistics (the Gaussian Curve). His accomplishments place him among the top mathematicians of all time. But it seems that Gauss had an insatiable curiosity, as we see him exploring many different disciplines. In 1810, Gauss began studying optics and dioptrics, which is the study of refraction. In 1818, Gauss accepted a contract to survey the Kingdom of Hannover. This process lasted until 1832. Some have suggested that this was a waste of time for a man of such genius, however, in the course of undertaking this task, Gauss invented the heliotrope, which focuses the sun’s rays into a beam that can be seen from long distances making the surveying process much more precise. It was during this time that he developed a way to think about the curvature of a surface. He showed that a cylinder and a flat sheet of paper share an intrinsic property, which is why images can be transferred from one to the other without distortion. Whereas a globe and a flat plane do not share the same intrinsic property, which is why it is impossible to ever have a perfect 2-dimensional map of a globe.

[5]
It wasn’t until 1830 when Gauss was in his fifties, that he took interest in magnetism. He became fascinated with the earth’s magnetic field and participated in the very first worldwide magnetic survey. There was no way to measure the earth’s magnetic field at the time, so Gauss invented the magnetometer! He also teamed up with a colleague from Gottingen and actually made the first working electromagnetic telegraph. His version used induced current to move a compass needle instead of using long and short clicks like the system eventually developed by Morse. But instead of pursuing the telegraph as a business venture, he took what he learned from his work on the telegraph and used it to contribute to the broader field of mathematical physics.

Many biographers describe Gauss as a shy man, probably what we would call an introvert in today's language. Unfortunately, as he aged, his personality seemed to suffer and by many accounts, he became arrogant, bitter and unpleasant.

[6] And yet, even though by many accounts old age was not kind to him, he remained a student, teaching himself Russian at age 62.

Gauss was a man of faith and in his biographies, there are numerous private letters where Gauss reveals his faith and what his convictions meant to him.

In a letter to a friend he wrote, “There is in this world a joy of the intellect, which finds satisfaction in science, and a joy of the heart, which manifests itself above all in the aid men give one another against the troubles and trials of life. But for the Supreme Being to have created existences, and stationed them in various spheres in order to taste these joys for some 80-90 years - that was surely a miserable plan.' . . . 'Whether the soul was to live for 80 years or for 80 million years, if it were doomed in the end to perish, such an existence would only be a respite. In the end, it would drop out of being. We are thus impelled to the conclusion to which so many things point, although they do not amount to a coercive scientific proof, that besides this material world there exists another purely spiritual order of things, with activities as various as the present, and that this world of spirit we shall one day inherit.”

[7]
The gauss is the CGS unit for magnetic flux density or magnetic induction. We use the gauss in audio when we measure or specify how strong the magnetic field is in the gap in which the voice coil sits in a driver. Interestingly, CGS, which stands for the centimeter – gram – second, representing the 3 fundamental units of length, mass and time, was a system actually proposed by Gauss in 1832.

Carl Fredrich Gauss died of a heart attack at the age of 77 on Feb 23, 1855.