The Bourbaki project was implemented in the period of very rapid progress in mathematics. Many books of the treatise became obsolete at the exact moment of publication.
In particular, functional analysis had been developing contrary to what one might imagine reading the book Topological Vector Spaces.
But to a failure was doomed the heroic and ambitions plan of Bourbaki to present the elements of the whole mathematics of the twentieth century in a single treatise along the methodological lines of Euclid.
Mathematics renews and enriches itself with outstanding brilliant achievements much faster than the books of Bourbaki’s treatise were compiled.
There is no wonder that the mathematical heroes who create the twentieth century mathematics have distinctly and immediately scented the shortcomings of Bourbaki. The treatise encountered severe criticism and even condemnation since it omits many important topics.
As usual, this serious criticism convened all sorts of educationists, would-be specialists in “propaedeutics” and “methodology” who are hardly aware of what is going on in the real mathematics.
Everyone knows that to criticize a book for incompleteness is a weak argument since it is strange to judge an article for what is absent in this article.
Grudges against the content of the treatise transform by necessity to the criticism of its form. The terseness, conciseness, and lapidary of the style of exposition fall victim to criticism and even ostracism by the adversaries of the malicious “bourbakism” in education.
