Gauss

Carl Friedrich Gauss (1777-1855)

Carl Friedrich Gauss has born in Braunschweig, Germany. His parents were poor. His father Gerhard, a labourer, canal tender and bricklayer, encouraged him only to what he saw as useful, labouring tasks.

His mother, Dorothea, who herself had a talented younger brother Friedrich, recognised his talents and encouraged him to pusrue them. In return Gauss looked after her, especially in her later years after she had become blind and until her death in 1839.

Gauss' talents came to the notice of a school master when he quickly solved the task of adding the numbers from 1 to 100 and later he received the sponsorship of the Duke of Braunschweig to study at College, where he maintained an interest in Philology as well as Mathematics.

He later studied at the University of Göttingen, where he now focussed on Mathematics.

As a student he made major discoveries, including the Method of Least Squares and the discovery of how to construct the regular 17-gon. The latter result was highly significant. Since the time of Euclid mathematicians had known only how to construct with compass and straight-edge regular n-gons in which n was a multiple of 3, 5 powers of 2 or combinations thereof. Gauss' discovery added to these numbers prime numbers of the form 2^(2^n)+1. For n=0 and 1 this included 3 and 5 but for n=2, 3 and 4 this added 17, 257 and 65,537 to the list.

In later life, after having a profound influence on mathematics, Gauss still regarded this as one of his greatest achievements and asked that a regular 17-gon be placed on his tombstone (unsuccessfully, as it happened).

Gauss went on to be awarded a Doctorate in Philosophy at the University of Helmstedt in 1799, with a thesis which proved that every rational integer function of one variable can be resolved into real factors of the first or second degree. This was a major unsolved problem, commonly known as the Fundamental Theorem of Algebra, and had been believed to be true by Euler.

Gauss in 1801 published a major work in Number Theory, "Disquisitiones arithmeticae" which recast much of 18th century Number Theory, but many of his own discoveries, including the Law of Quadratic Reciprocity, for which he found independent proofs.

For some years Gauss lived in Braunschweig and had six children from two marriages. He is believed to have many descendants in Germany and the United States. He was supported by the Duke of Braunschweig until his death and in 1807 received a flattering offer from St Petersbourg, which had never satisfactorily replaced Euler.

The Baron Alexander von Humboldt, an amateur patron of the sciences managed to get him appointed as Professor of Mathematics at Göttingen, and Director of the Göttingen Observatory, posts which he held to his death.

It is impossible in a short resume to refer to all of his discoveries, not only to mathematics, but also physics, statistics (he introduced the normal distribution), astronomy and geodesy.

As an analyst, he was the first to develop adequate standards of proof of results involving infinitely many numbers. He anticipated the development of non-Euclidean geometries.

For a great mathematician, Gauss published very little, sometimes having his results independently discovered by others. He kept a methodical diary which recorded his results, but applied to himself the strictest standards about the way in which his work would be published.

Gauss asserted that "Mathematics is the Queen of Sciences, and the Theory of Numbers is the Queen of Mathematics".

Written by Peter Taylor, June 1998.

This T Shirt, which celebrates the 17-gon which Gauss said could be on his tombstone, is available from the AMT.