Eric Temple Bell on Foundations of mathematics

“Fourier's analytical theory of heat (final form, 1822), devised in the Galileo-Newton tradition of controlled observation plus mathematics, is the ultimate source of much modern work in the theory of functions of a real variable and in the critical examination of the foundation of mathematics.”

“These doubts did not halt mathematical creation. Technicians working on the superstructure did not drop their tools and scurry down to the basement because some of their underpinning needed reinforcing. Continuing their own highly specialized labors, they left the necessary task to experts who understood what they were about. The building had not collapsed as late as 1940; and while those engaged in elaborating the superstructure but seldom concerned themselves with what the consolidators of the foundations were doing, they had at least come to tolerate their presence in the building. The misconceptions and recriminations of the 1900's gave way in the 1930's to a first crude approximation to harmony. It was as if the American Federation of Labor and the Committee for Industrial Organization had at last decided to bury the hatchet elsewhere than in either's skull, and get on with the job.”