> When mathematics does not relate to one of the three -- for e.g., in Cantor's theories of "countable" and "uncountable" infinite sets -- it is totally unreal.

> When mathematics does not relate to one of the three -- for e.g., in Cantor's theories of "countable" and "uncountable" infinite sets -- it is totally unreal. I find that to be quite a bold statement. The question as to whether "mathematics is real" feels firmly rooted in philosophy. First, I would question what is meant by real and unreal. Second, I would question if the answer matters whether the existence of the real and the unreal are not yet discovered, or even imagined.