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.

• 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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