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:: Johann Karl Friedrich Gauss (1777-1855) ::

The DM10 note celebrates the work done by Johann Karl Friedrich Gauss (1777-1855) on error analysis that lead him to formulate the Normal or Gaussian distribution. This distribution plays a central role in statistics, as dictated by the Central Limit Theorem.

Although Gauss made many contributions to applied science, especially electricity and magnetism, pure mathematics was his first love: he called mathematics "the queen of the sciences" and arithmetic "the queen of mathematics." His influence on mathematics was as significant to nineteenth century science as Newton's had been to the science of the eighteenth century, in spite of the fact that he was a perfectionist and did not publish many of his discoveries.

Possibly the best-known anecdote about him happened when his elementary school teacher asked his class to sum the numbers from 1 to 100, and instead he figured out a general formula for summing consecutive integers, which he used to come up with the answer very quickly.

Gauss studied mathematics at the University of Göttingen from 1795 to 1798, and received his doctorate for a proof of an algebraic theorem which had long eluded definitive proof. His Disquisitiones arithmeticae appeared when he was only twenty-four, and in his development of the idea of complex numbers revolutionized number theory and Euclidean geometry.

Although he was certainly brilliant, he was often described as mean by his colleagues and students at Göttingen University, where he spent most of his career. Sometimes when students shared their work with him, he would tell them that he had done it all before. Even if he had, there is no question he dampened many people's enthusiasm for math with his arrogance. One notable exception was the French mathematician Sophie Germain, who corresponded with Gauss under the pen name Antoine-August Le Blanc, because women were not allowed in mathematics. Gauss was very impressed with Germain's work, giving her encouragement throughout her life and even speaking very highly of her when he later found out that she was a woman.

Gauss applied many of his mathematical insights in the field of astronomy by successfully using the method of least squares to predict the location of the asteroid Ceres in 1801. He described his methods at length in Theoria motus corporum coelestium (1809).

In 1820 Gauss made important inventions and discoveries in geodesy, the study of the shape and size of the earth, and in statistics, in which he developed the idea of the Bell Curve and Normal (Gauss) distribution. In the 1830s he developed theories of non-Euclidean geometry and mathematical techniques for studying the physics of fluids, though he never published anything on it for fear of ridicule.

Another one of Gauss' better known results is the Prime Number Theorem, which, given any natural number n, estimates the number of primes below that number as n / log n. When Gauss died, he was widely venerated by his contemporaries and they called him the "prince of mathematics".

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