In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.

十九世纪的代数学知识体系庞大，它包含置换群、矩阵、代数数论、代数几何等多个分支。

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Diophantine equation is an important subject in number theory and closely connected with algebraic number theory, combinatorics, algebraic geometry and computer science etc.

丢番图方程是数论中一个十分重要的研究课题，与代数数论、组合数学、代数几何等有密切联系。

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Mr Weil's advances in algebraic geometry and number theory which in 1994 helped him win the equivalent of the Nobel prize in mathematics, the Kyoto prize in basic science are so abstruse they are inaccessible to the layman.

ECONOMIST: Andr�� Weil