The ignorance of bourbaki

Abstract

If one looks at the history of mathematics, one sees periods of bursting creativity, when new ideas are being developed in a competitive and therefore very hasty spirit, and periods when people find that the ideas so recently in vogue are inexact, incoherent, and possibly inconsistent. In the latter periods there is an urge to consolidate past achievements. I said "the history of mathematics," but mathematics is a complex sociological organism, and its growth takes place in different branches and in different countries, even different universities, in different ways and at different speeds. Sometimes national groups feel that mathematics in their country is in a bad way: You find an expression of that in the "Introduction" to later editions of Hardy's Pure Mathematics, where he remarks that it was written with an enthusiasm intended to combat the insularity of British mathematics of the turn of the century, which had taken no account of the development of mathematics in France in the 19th century. Indeed, in 1910 France could be proud of her succession of mathematicians such as Legendre, Laplace, Lagrange, Fourier, Cauchy, Galois, Hadamard, Poincar4--a most impressive list of scholars of the highest distinction. But after the first World War, the feeling in France changed, and the young French mathematicians of the day began to consider that the torch of mathematical research had passed to Germany--where there were many great mathematicians building on the past work of Riemann, Frobenius, Dedekind, Kummer, Kronecker, Minkowski, and Cantor , such as Klein, Hilbert, Weyl, Artin, Noether, Landau, and Hausdorff and that French mathematics had gone into a decline.