Eli5: what is pure mathematics and why is it important?
In: Mathematics
Pure mathematics is math for the sake of mathematics without an application in mind.
Some people will probably say that pure math is important because a lot of it ends up being useful down the line. For example, number theory was very pure initially but ended up being very useful for cryptography and computer programing.
However, while it’s true that a lot of the ideas do end up being useful later, pure mathematicians would probably tell you that their work is important even if it was guaranteed to never be useful. It’s important in the same way that philosophy, poetry, or art is important. It’s human discovery and expression. It’s expanding human knowledge.
Pure mathematics is defined as the study of mathematics without consideration for practical application outside of mathematics.
The point of it is to push the boundaries of what we can know to be necessarily true laws of mathematics. If you can come with with more laws like that, you give other people more tools to use in future problems involving math.
Much of our math formula, theorems, and algorithms come as products of pure mathematics, without which we would have a hard time getting a lot of things done efficiently.
Math is like a hefty toolbox. To every real-world application, there is a set of tools in that box that is used for it.
Pure mathematics is like making tools for the sole purpose of making new tools or improving the already existent yet unhandy ones.
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