Bourbakisme

Part of speech: noun

Definitions

1. The rigorous, axiomatic and highly abstract approach to mathematics championed by the Bourbaki group of French mathematicians
2. An austere, structure-first style of writing mathematics that builds theories from formal axioms, as advocated by the Bourbaki collective
3. The formalist school of mathematical thought, marked by systematic abstraction and strict logical foundations, that the Bourbaki circle promoted

Etymology: Nicolas Bourbaki was a pseudonym adopted by a group of mostly French mathematicians who, beginning in the 1930s, set out to rebuild mathematics from the ground up. The name came from General Charles-Denis Bourbaki, a real nineteenth-century French army commander, and the choice was a joke that stuck. The collective published a long series of treatises under the name, and the general's name became attached to the whole project. The suffix is the French "-isme," from Latin "-ismus," itself from Greek "-ismos," which marks a doctrine, system or characteristic practice. Combined with the group's name, it labels their approach: presenting mathematics through abstract structures, formal axioms and general theorems, with proofs organised in a tightly numbered, self-contained style. Mathematicians outside France often use the term to describe that formal, structure-first manner, sometimes with praise and sometimes with complaint.