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A lot of things. For example: partial differential equations are used to find weak points in aircraft before they fly, group theory is used to encrypt data over the internet, multi-particle stochastic processes, can tell us how diseases will spread, and how traffic behaves on roads, as well as how an economy works.

Maths is also used in all sciences - everything scientists do they could not do without mathematics.

On a lower level, it allows us to count how many things we have, and to decide for instance that 3 loaves of bread is better than 2.

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Q: What is mathematics for?
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