Early Definitions
Aristotle defined mathematics as:
The science of quantity.
In Aristotle's classification of the sciences, discrete quantities were studied by arithmetic, continuous quantities by geometry.
Auguste Comte's definition tried to explain the role of mathematics in coordinating phenomena in all other fields:
The science of indirect measurement.
The "indirectness" in Comte's definition refers to determining quantities that cannot be measured directly, such as the distance to planets or the size of atoms, by means of their relations to quantities that can be measured directly.
Read more about this topic: Definitions Of Mathematics, Survey of Leading Definitions
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