# Gauss: Great Mathematician or the Greatest Mathematician?

Today (April 30) is the birthday of Carl Friedrich Gauss (1777-1855), a German mathematician, considered by some to be the greatest mathematician in history. Gauss influenced many fields, including number theory, algebra, differential geometry, geophysics, electrostatics, astronomy, and optics.

Gauss was born to poor working-class parents in Brunswick, Germany. His mother, who was illiterate, never recorded his birthday, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension. To solve the puzzle of his birthdate, Gauss had to derive methods to compute a date in past and future years.

Gauss’ genius was evident at an early age, and there are several anecdotes about his precocity. According to one legend, at age 3 he corrected, in his head, an error his father had made while calculating finances. According to another famous story, one of his primary school teachers gave him the task of adding the numbers 1 to 100, as a punishment for misbehavior. The teacher was astonished when Gauss produced the answer a few seconds later. Gauss realized that he could add the numbers as pairs from opposite ends of the list (1+100, 2+99, 3+98, etc.), and that each of these pairs equals 101. Since there are 50 of these pairs, the addition of all numbers from 1 to 100 must equal 50 x 101 or 5,050.

Some of Gauss’ contributions:

• He proved the fundamental theorem of algebra, which states that every polynomial has a root of the form a+bi. (Although his proof had a gap that was filled in 1920 by Alexander Ostrowski.)
• In 1801, he proved the fundamental theorem of arithmetic,  which states that every natural number can be represented as the product of primes in only one way.
• At age 24 (in 1801), Gauss published Disquisitiones Arithmeticae, considered one of the most brilliant achievements in mathematics. In this publication, Gauss systematized the study of number theory (properties of the integers), proved that every number is the sum of at most three triangular numbers, and developed the algebra of congruences.
• Also in 1801, G Piazzi, an Italian astronomer, discovered Ceres, a dwarf planet. Piazzi had only been able to observe 9 degrees of its orbit before it disappeared behind the Sun. When Ceres was rediscovered later that year, it was almost exactly where Gauss had predicted. Gauss made the prediction based on his least squares method of approximation. Gauss published a theory of the motion of planetoids disturbed by large planets in 1809. His work was such an improvement over the cumbersome mathematics of 18th century orbital prediction that his work remains a cornerstone of astronomical computation.

Things named in honor of Gauss include:

• Degaussing, the process of eliminating a magnetic field
• The CGS unit for magnetic field was named gauss
• The crater Gauss on the Moon
• Asteroid 1001 Gaussia
• The ship Gauss, used in the Gauss expedition to the Antarctic
• Gaussberg, an extinct volcano discovered by the above mentioned expedition
• Gauss Tower, an observation tower in Dransfeld, Germany

Sources:

Carl Friedrich Gauss. Wikipedia. Retrieved April 30, 2013, from http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

Gauss, Karl Friedrich. Scienceworld.Wolfram.com. Retrieved April 30, 2013, from http://scienceworld.wolfram.com/biography/Gauss.html

Johann Carl Friedrich Gauss. Retrieved April 30, 2013, from http://www-groups.dcs.st-and.ac.uk/history/Biographies/Gauss.html

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