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　　Mathematician, born in Brunswick, Germany. A prodigy in mental calculation, he conceived most of his mathematical theories by the age of 17, and was sent to study at Brunswick and G ttingen. He wrote the first modern book on number theory, in which he proved the law of quadratic reciprocity, and discovered the intrinsic differential geometry of surfaces. He also discovered, but did not publish, a theory of elliptic and complex functions, and pioneered the application of mathematics to such areas as gravitation, magnetism, and electricity. In 1807 he became professor of mathematics and director of the observatory at G ttingen, and in 1821 was appointed to conduct the trigonometrical survey of Hanover, for which he invented a heliograph. The unit of magnetic induction has been named after him

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