The real founder of modern German mathematics is Carl Friedrich Gauss 1, one of the many mathematicians who rose to highest eminence from very humble birth. The son of a day laborer, his abilities showed themselves so early as to attract attention, and he was sent to the Carolineum at Braunschweig (1792-1795) and thence to the University of Gottingen (1795-1798). During his university career he conceived the idea of the theo ry of least squares 2, discovered the celebrated proposition that a circle can be divided into 17 equal arcs by Euclidean methods, and began his great work on the theory of numbe rs 3. Thereafter he devoted his attention largely to the problems of astronomy, geodesy, and electricity 4, but found time to write on the theory of surfaces, complex numbers, least squares, congruences, hyperbolic geometry, and substantially every leading field of mathematics. He was among the first to give serious thought to the question of a non-Euc lidean geometry. He asserted that "mathematics is the queen of the sciences, and the theory of numbers is the queen of mathematics." His first work on celestial mechanics 5 led Laplace to recognize him as the leading mathematician of Europe, and this recognition was general from that time until his death 6. Kronecker said of him that "almost everythin g which the mathematics of our century has brought forth in the way of original scientific ideas, is connected with the name of Gauss," and it was only with such exaggeration as is entirely excusable that the elder Bolyai spoke of him as "the mathematical giant who from his lofty heights embraces in one view the stars and the abysses."

(Smith, pp. 502-504)