# Carl Friedrich Gauss – The Prince of Mathematicians

 Carl Friedrich Gauß (1777 – 1855)

On April 30, 1777, German mathematician and physical scientist Carl Friedrich Gauß was born. He who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. He is often referred to as Princeps mathematicorum (Latin, “the Prince of Mathematicians”) as well as “greatest mathematician since antiquity”.

Carl Friedrich Gauß grew up as an only child, his mother could barely read but was known to be incredibly intelligent. Rumors about Gauß say that he could calculate before being able to speak and that he corrected his father on his wage accounting at the age of only three. No matter if these rumors are actually true, it indicates that Gauß’ talents and his love for complex calculations were detected very early. At the age of seven, he started to attend school and already designed formulas to easen his calculations during math class.

There is one famous telling about Carl Friedrich Gauss’s boyhood discovery of the “trick” for summing an arithmetic progression. The event occurred when Gauß was seven and attended the Katharina-school in Brunswick. The teacher, one Büttner, had set the class the task of calculating the sum 1 + 2 + 3 + …. + 100 – probably to get a bit of peace for himself, with instructions that each should place his slate on a table as soon as he had completed the task. Almost immediately Gauß placed his slate on the table, saying, “There it is.” The teacher looked at him scornfully while the others worked diligently. When the instructor finally looked at the results, the slate of Gauss was the only one to have the correct answer, 5050, with no further calculation. The ten-year-old boy evidently had computed mentally the sum of the arithmetic progression 1 + 2 + 3 + … + 99 + 100, presumably through the formula m(m+1)/2. His teachers soon called Gauss’s talent to the attention of the Duke of Brunswick [1].

At the age of 14, Gauß was introduced to Duke Karl Wilhelm Ferdinand von Braunschweig, who supported the young Gauß financially and he was able to enroll at the university. Gauß was at the age of 19 the first to prove the possibility to construct a regular heptadecagon, and after earning his doctorate degree, the mathematician began his work on the text book of number theory in Latin language, ‘Disquisitiones Arithmeticae‘.

In the following years, Carl Friedrich Gauß was offered several positions at foreign universities, but in loyalty to the Duke and the hope of getting his own observatory he stayed in Göttingen, where he had to give lectures. Despite the fact that he did not enjoy his teacher occupation, several famous future mathematicians were taught by him, like Richard Dedekind or Bernhard Riemann.

Gauß’ contributions to the field of mathematics are numerous. At the age of only 16, he made first attempts leading to non-Eucleidean geometry. Two years later, Gauß began researching on properties of the distribution of prime numbers, which later on led him to calculate areas underneath graphs and to the Gaussian bell curve. Independent of Caspar Wessel and Jean-Robert Argand, Gauß found the geometrical expression of complex numbers in one plane.

Gauß began working in the field of astronomy after finishing his famous ‘Disquisitiones Arithmeticae‘ and managed to calculate planetary orbits through his method of least squares. He shared his experiences in the work ‘Theoria motus corporum coelestium in sectionibus conicis solem ambientium. His achievements in this field made Gauß internationally famous and several of his astronomical methods are still in use today. Numerous mathematical methods and formulas carry Gauß’ name today and throughout his lifetime and beyond he earned himself the reputation as one of the most genius and productive mathematicians of all times.

At yovisto, you may enjoy a video lecture by Prof. Ramamurti Shankar on Gauss’s Law at Yale University.

References:

• [1] Boyer, Carl B. 1968, 1991. A History of Mathematics. Second edition. Revised by Uta C. Merzbach; foreword by Isaac Asimov. New York: Wiley. (p. 497)