Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All proposed definitions are controversial in their own ways. See more

Most contemporary reference works define mathematics by summarizing its main topics and methods:
The abstract … See more

• Mathematics portal
• Philosophy of mathematics
• Foundations of mathematics See more

• Courant, Richard; Robbins, Herbert (1996), What Is Mathematics? (2nd ed.), Oxford University Press, ISBN 978-0-19-510519-3
• Gowers, Timothy; Barrow-Green, June; Leader, Imre, … See more

Pythagoras stated "All is number. Number rules the universe", paraphrased by Plato, from which Platonism historically was the main mathematics … See more

In the 19th century, as mathematics branched out into abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, … See more

Bertrand Russell wrote this famous tongue-in-cheek definition, describing the way all terms in mathematics are ultimately defined by reference to undefined terms:
The subject in which we never know what we are talking … See more