What is Mathematics?
Different schools of thought, particularly in philosophy, have put forth radically different definitions of
mathematics. All are controversial and there is no consensus.
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
, 1851. 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.