Algebraic geometry is a branch of
mathematics which, as the name suggests, combines techniques of
abstract algebra, especially
commutative algebra, with the language and the problematics of
geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as
complex analysis,
topology and
number theory. Initially a study of polynomial equations in many variables, the subject of algebraic geometry starts where
equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.
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