Difference between pure and applied mathematics
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The main differences
The easiest way to think of it is that pure maths is maths done for its own sake, while applied maths is maths with a practical use. But in fact, it’s not that simple, because even the most abstract maths can have unexpected applications. For example, the branch of mathematics known as “number theory” was once considered one of the most “useless”, but now plays a vital part in computer encryption systems. If you’ve ever bought something online, you can thank number theorists for letting you do it safely.
You could also think about how maths relates to other subjects and to the real world. Applied maths tries to model, predict and explain things in the real world: for example, one area of applied mathematics is fluid mechanics, which analyses how fluids are affected by forces. Other examples of applied maths might be statistics or probability theory.
Pure maths, on the other hand, is separate from the physical world. It solves problems, finds facts and answers questions that don’t depend on the world around us, but on the rules of mathematics itself.
Unfortunately, there is no perfect way to decide what pure maths is and what applied maths is. Even mathematicians can’t agree on it! If you’re thinking of studying for a maths degree and there are separate courses or departments for pure and applied maths at the university you’re applying to, then get in touch and find out exactly what the courses involve.
The easiest way to think of it is that pure maths is maths done for its own sake, while applied maths is maths with a practical use. But in fact, it’s not that simple, because even the most abstract maths can have unexpected applications. For example, the branch of mathematics known as “number theory” was once considered one of the most “useless”, but now plays a vital part in computer encryption systems. If you’ve ever bought something online, you can thank number theorists for letting you do it safely.
You could also think about how maths relates to other subjects and to the real world. Applied maths tries to model, predict and explain things in the real world: for example, one area of applied mathematics is fluid mechanics, which analyses how fluids are affected by forces. Other examples of applied maths might be statistics or probability theory.
Pure maths, on the other hand, is separate from the physical world. It solves problems, finds facts and answers questions that don’t depend on the world around us, but on the rules of mathematics itself.
Unfortunately, there is no perfect way to decide what pure maths is and what applied maths is. Even mathematicians can’t agree on it! If you’re thinking of studying for a maths degree and there are separate courses or departments for pure and applied maths at the university you’re applying to, then get in touch and find out exactly what the courses involve.
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