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.
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