Bourbakism

Part of speech: noun

Definitions

1. An approach to mathematics that builds whole fields from axioms and abstract structures, stressing rigorous formal presentation over intuition or examples
2. The formalist, highly abstract manner of writing mathematics pioneered by the collective of French mathematicians who published under the name Bourbaki
3. A style of mathematical exposition that prizes logical rigor, generality and structural axioms, named after the group that championed it in the twentieth century

Etymology: The name Nicolas Bourbaki belongs to no one who ever lived. It was the collective pseudonym of a group of French mathematicians who, from the 1930s onward, set out to rewrite whole branches of mathematics in a rigorous, axiomatic style, publishing their work under a single invented author. The group was a loose, rotating circle, and its members were largely drawn from French academic life, with the pseudonym serving both as a joke and as a way to let the work speak without the authority of any one famous name. "Bourbakism" is simply the French "bourbakisme," built by adding the suffix "-ism" to "Bourbaki." The term names the group's distinctive approach: an insistence on abstract structures, precise definitions, and building mathematics from the ground up. Because the pseudonym was so closely tied to that method, the word became a way of referring to the style itself rather than to the people behind it.