Karl Friedrich Gauss

Karl Friedrich Gauss (1777-1855) kept an amazingly rich scientific activity. An early passion for numbers and calculations extended to the first theory of numbers, to algebra, analysis, geometry, probability, and the theory of errors. At the same time, he carried on an intensive empirical and theoretical research in many branches of science, including observational astronomy, celestial mechanics, surveying, geomagnetism, electromagnetism, mechanism optics, and actuarial science. His publications, abundant correspondence, notes, and manuscripts show him to have been one of the greatest scientific virtuosos of all time.

Reporter: You're known as the prince of mathematics. You've invented countless mathematical theorems and you're reputed to have a brilliant mind. Can you tell me about your educational career?

 

Gauss: My childhood was very simple. However, I showed extraordinary for having been brought up in an austere childhood in a poor and uneducated family. At the age of 14, I received a stipend from the duke of Brunswick, which allowed me to devote my tie to my studies for 16 years. Before my 25th birthday, I was already famous for my work in mathematics and astronomy. When I turned 30, I went to Gottingen to become director of the observatory. I rarely left the city except on scientific business. From there, I worked for 47 years until my death at 78 years old.

Reporter: When did you first show signs of your mathematical inclination?

Gauss: At the age of three, I informed my father of an arithmetical error in a complicated payroll calculation, and told him the correct sum. Often in school, our teachers had to grade papers and such, and would give us "busy work." Once, my teacher gave our class the problem of summing all the integers from 1 to 100. I immediately wrote down the correct answer, 5050, on my slate.

Reporter: How did you find the solution so easily?

Gauss: Well, there are 50 pairs of numbers that add up to 101; 1+100, 2+99, 3+98...49+52, 50+ 51. 50 multiplied by 101 is 5050.

Reporter: What else did you accomplish in your earlier years?

Gauss: At 19 years old, I proved that the heptadecagon, a regular polygon of 17 sides, could be made with a compass and straightedge, known as a construction. While constructions for regular 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, etc, sided polygons, had been given by Euclid, constructions based on the Fermat primes were unknown to the ancients.  My proof relies on the property of irreducible polynomial equations that roots composed of a finite number of square root extractions only exist when the order of the equation is a product in the form of Fermat's primes. I also showed that only a certain number of regular polygons could be constructed with a compass and straightedge. These proofs appear in my monumental work, Disquisitiones Arithmeticae.

Reporter: Can you describe your personal life?

Gauss: My personal life was tragic and complicated. Due to the French revolution, the Napoleonic period and the democratic revolutions in Germany, I suffered from political turmoil and financial insecurity. I found no fellow mathematical collaborators and worked alone for most of my life. An unsympathetic father, the early death of my first wife, the poor health of my second wife, and terrible relations with my sons denied me family sanctuary until my late life.

Reporter: In Disquisitiones Arithmeticae, heralded as one of the greatest achievements in mathematics, you published number theories and developed the algebra of congruences. But what brought you to the hands of future generations was the Gaussian curve, appearing on the German bill. Could you briefly describe the Gaussian curve?

Gauss: The Gaussian curve, sometimes called the normal or bell curve, illustrates the distribution of a random population. What makes a curve a Gaussian curve is the relative height of the curve at different locations. All Gaussian curves have certain properties: 1) the total area under the curve and above the x-axis is one 2) the curve is bell shaped 3) the curve is symmetrical about the mean of the distribution. Every Gaussian curve encompasses 68% of the area of the curve in +1 and –1 Standard Deviation along the x-axis.

Gaussian distributions have many convenient properties. Random variates with unknown distributions are often Gaussian, especially in physics and astronomy. Many common attributes such as SAT and IQ scores, height, and even radio waves from space as detected by the SETI organization (Search for Extra-Terrestrial Intelligence) follow Gaussian distributions, with few samples at the high and low ends and many in the middle.

Reporter: Any last comments?

Gauss: Astronomy and mathematics are the magnetic poles toward which the compass of my mind ever turns.

 

Works Cited


http://www.willamette.edu/~mjaneba/help/normalcurve.html

Give a pragmatic introduction to the Gaussian Curve.

http://psy.ucsd.edu/~rdbeer/GaussCurve.htm

Presents the full view of a 10 Deuschmark and a close up of the Gaussian Curve.

http://scienceworld.wolfram.com/biography/Gauss.html

Succinctly describes the mathematical achievements, publication, and life of Gauss.

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Gauss.html

Offers specific information about Gauss's educational life.

http://www.geocities.com/RainForest/Vines/2977/gauss/english.html

Vast database of Gauss's life, from detailed biography to quotes.