Pure mathematics deals with discovering about the ideas we sense, while applied mathematics means modeling real-world phenomena using a mathematical theory.
As an example, developing (the story of) Euclidean geometry, i.e. intellectually discovering the properties of and relationships between ideas like points, straight lines and planes, is pure mathematics. On the other hand, modeling shapes and trajectories of physical objects by means of Euclidean geometry, with the aim of making measurable predictions about them, is applied mathematics.(10)
Another example of applied mathematics is to model asset prices as continuous quantities, while knowing that real prices have a finite number of decimal places, given e.g. in cents.
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(10) Is "applied mathematics" mathematics at all?
Yes, because in the models we work with mathematical ideas. However, the application of a model is unlikely to yield deep mathematical discoveries, for the aim is to solve problems of another discipline, not that of mathematics.