Unifying Theories in Mathematics - Bourbaki

Bourbaki

The cause of axiomatic development was taken up in earnest by the Bourbaki group of mathematicians. Taken to its extreme, this attitude was thought to demand mathematics developed in its greatest generality. One started from the most general axioms, and then specialized, for example, by introducing modules over commutative rings, and limiting to vector spaces over the real numbers only when absolutely necessary. The story proceeded in this fashion, even when the specializations were the theorems of primary interest.

In particular, this perspective placed little value on fields of mathematics (such as combinatorics) whose objects of study are very often special, or found in situations which can only superficially be related to more axiomatic branches of the subject.

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