Pure mathematics

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Pure mathematics is a field of mathematics. Other fields of mathematics are driven and motivated by applications, they can be used to solve real-world problems, for example mathematical physics in physics or engineering. In contrast, pure mathematics studies abstract ideas or it tries to make proofs more beautiful or easier to understand.

Examples

Generalizing theorems: Finding a more general theorem can lead to a better understanding of mathematics.
Generality can also shorten proofs: There no longer is a need to handle special cases. This makes proofs shorter, simpler, and easier to follow or explain.

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