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<Carl Friedrich Gauss

BIOGRAPHY 10.1 Carl Friedrich Gauss (1777 -1855)

Carl Friedrich Gauss was born in Brunswick, Germany, where he grew up in humble circumstances. His father was a bricklayer and gardener; his mother had no schooling and could not even write. Yet Gauss grew up to become one of the greatest mathematicians of all time. His precocity was extraordinary and probably unequaled. Before he was three, while watching his father's wage calculations, he detected an error and announced the correct result. At school, the speed and accuracy of his mental calculations astonished his beginning teacher in arithmetic; once, he summed all the numbers from 1 to 100 in no time at all by inventing the formula for doing so. Before long, Gauss mastered the best available textbooks and went beyond his teachers. Gauss's amazing powers came to the attention of the Duke of Brunswick who became his patron, sending him to the University of Göttingen. While a student there, Gauss discovered that a regular polygon of 17 sides is amenable to straightedge-and-compass construction; such a feat had eluded mathematicians for 2,000 years. Shortly thereafter, in 1801, Gauss published Disquisitiones Arithmeticae, a masterpiece that took the theory of numbers far beyond its earlier state and established Gauss as a mathematical genius of the first rank, equal to Archimedes and Newton. This great work was followed by another in 1809, the Theoria Motus Corporum Coelestium, in which Gauss developed methods for calculating the orbits of heavenly bodies. It was here that he made first use of two of the most common tools of all sciences today, the theory of least squares (discussed in Chapter 16) and the normal curve (discussed in Chapter 10). Although Gauss acknowledged the priority of Laplace (Biography 8.1) with respect to the normal curve, it soon came to be known as the Gaussean curve, and it is still known as such in many countries today. Gauss, apparently, was the first to view the bell-shaped curve as a model for depicting random error (as noted in Application 10.1). Writing in the context of his book on celestial mechanics, he said:

The investigation of an orbit having, strictly speaking, the maximum probability, will depend upon a knowledge of the law according to which the probability of errors decreases as the errors increase in magnitude: but that depends upon so many vague and doubtful considerations--physiological included--which cannot be subjected to calculation, that it is scarcely, and indeed less than scarcely, possible to assign properly a law of this kind in any case of practical astronomy. Nevertheless, an investigation of the connection between this law and the most probable orbit, which we will undertake in its utmost generality, is not to be regarded as by any means a barren speculation. Let fD be the probability to be assigned to each error D. Now although we cannot precisely assign the form of this function, we can at least affirm that it should be a maximum for D = 0, equal, generally, for equal opposite values of D, and should vanish, if, for D is taken the greatest error, or a value greater than the greatest error.

By age 30, Gauss was director of the Göttingen observatory, where he stayed for the rest of his life. He contributed mightily not only to astronomy but also to every branch of mathematics and physics. Hundreds of publications testify to a man who combined in a most unusual way a pure mathematician's interest in abstract ideas and logical rigor, a theoretical physicist's interest in the creation of mathematical models of the physical world, an astronomer's talent for keen observation, and an experimentalist's skill in the application and invention of methods of measurement. Among other things, Gauss invented the heliotrope, the magnetometer, the photometer, and, some 5 years before Samuel Morse, the telegraph.

Source: Adapted from Helen M. Walker, Studies in the History of Statistical Method (Baltimore: Williams and Wilkins, 1929), p.23.

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