My view is that infinitesimals were a mistake, a long, festering sore in math and some of its applications. Can think intuitively about infinitesimals if you wa

My view is that infinitesimals were a mistake, a long, festering sore in math and some of its applications. Can think intuitively about infinitesimals if you want, but I see no need to mess up the now very clean situation on the foundations of the reals. Indeed, as a grad student, I had some results and went to see a world famous prof to show him what I had and ask him if my work seemed new to him. At one point he suggested an improvement, and, curiously, as a high end pure mathematician in analysis did his first cut, intuitive reasoning in terms of infinitesimals! Fine. But Dedekind cuts, Cauchy sequences, etc. make a rock solid foundation for the reals, and now can we just get on with, say, Fourier theory and the rest of analysis and their applications?