science: The Abstraction of Mathematics

The Abstraction of Mathematics

In mathematics a movement toward the abstract, axiomatic approach began early in the 19th cent. with the discovery of two different types of non-Euclidean geometries and various abstract algebras, some of them noncommutative. While there has been a tendency to consolidate and unify under a few general concepts, such as those of group, set, and transformation, there has also been considerable research in the foundations of mathematics, with a close examination of the nature of these and other concepts and of the logical systems underlying mathematics.

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