"Analysis grew and grew, not heeding the warnings of the critics, constantly forging ahead and conquering new domains. First geometry and mechanics, then optics and acoustics, propogation of heat and thermodynamics, electricity and magnetism, and finally even the laws of the Chaos came under its direct sway. ...And yet this magnificent structure was created by the mathematicians... without much thought of the foundations on which it rested. Is it not remarkable then, that in spite of all the loose reasoning, all the vague notions and unwarranted generalization, so few serious errors had been committed? ...Then came the critical period: Abel and Jacobi, Gauss, Cauchy and Weierstrass, and finally Dedekind and Cantor, subjected the whole structure to a searching analysis, eliminating the vague and ambiguous. And what was the net result of this reconstruction? Well, it condemned the logic of the pioneers, but vindicated their faith."