Norman Wildberger is a mathematician against the ambiguous rules of infinity and limits, and is against the real numbers in their entirety. AFAIK he is trying to create an alternative to analysis that uses only rationals. I'm currently under the impression that his criticisms are sound but moot in practice. Some people think he is out of his mind, but on the face of things, I can't help but side with Wildberger in his sentiment in the spirit of Bertrand Russell. Here is a sample video: What does pf think? Please tell me I'm not drinking cool aid.