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Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right.[21] Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof. His book, Elements, is widely considered the most successful and influential textbook of all time.[22] The...

The history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, which is shared by many animals,[14] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely the quantity of their members.As evidenced by tallies found on bone, in addition to recognizing how...

Modernism, the idealistic search for truth, gave way in the latter half of the 20th century to a realization of its unattainability. Theodor W. Adorno said in 1970, "It is now taken for granted that nothing which concerns art can be taken for granted any more: neither art itself, nor art in relationship to the whole, nor even the right of art to exist."[45]...