Mathematics has become a vastly diverse subject over history, and there is a corresponding need to categorize the different **areas of mathematics**. A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve. In addition, as mathematics evolves, these classification schemes must evolve as well to account for newly created areas or newly discovered links between different areas. Classification is made more difficult by some subjects, often the most active, which straddle the boundary between different areas.

A traditional division of mathematics is into pure mathematics, mathematics studied for its intrinsic interest, and applied mathematics, mathematics which can be directly applied to real world problems. This division is not always clear and many subjects have been developed as pure mathematics to find unexpected applications later on. Broad divisions, such as discrete mathematics and computational mathematics, have emerged more recently.

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