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 of our own epoch. In him that abundant fertility of invention, displayed by mathematicians of the preceding period, is combined with an absolute rigorousness in demonstration which is too often wanting in their writings, and which the ancient Greeks might have envied. Unlike Laplace, Gauss strove in his writings after perfection of form. He rivals Lagrange in elegance, and surpasses this great Frenchman in rigour. Wonderful was his richness of ideas; one thought followed another so quickly that he had hardly time to write down even the most meagre outline. At the age of twenty Gauss had overturned old theories and old methods in all branches of higher mathematics; but little pains did he take to publish his results, and thereby to establish his priority. He was the first to observe rigour in the treatment of infinite series, the first to fully recognise and emphasise the importance, and to make systematic use of determinants and of imaginaries, the first to arrive at the method of least squares, the first to observe the double periodicity of elliptic functions. He invented the heliotrope and, together with Weber, the bifilar magnetometer and the declination instrument. He reconstructed the whole of magnetic science.

Carl Friedrich Gauss[47] (1777–1855), the son of a bricklayer, was born at Brunswick. He used to say, jokingly, that he could reckon before he could talk. The marvellous aptitude for calculation of the young boy attracted the attention of Bartels, afterwards professor of mathematics at Dorpat, who brought him under the notice of Charles William, Duke of Brunswick. The duke undertook to educate the boy, and sent him to the Collegium Carolinum. His progress in languages there was quite equal to that in mathematics. In 1795 he went to Göttingen, as yet undecided whether to pursue philology or mathematics. Abraham Gotthelf Kästner, then professor of mathematics there, and now chiefly remembered for