Pure mathematics

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.

Pure Mathematics Media

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  Pure mathematics studies the properties and structure of abstract objects, such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world.

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  An illustration of the Banach–Tarski paradox, a famous result in pure mathematics. Although it is proven that it is possible to convert one sphere into two using nothing but cuts and rotations, the transformation involves objects that cannot exist in the physical world.