A question like this certainly demands that the meaning of the word "exists" must be examined. That doesn't make me imnpatient with the question per se. Just with discussions about it that overlook that point. —Dan Allan Wechsler wrote: ----- Questions like this tend to make me impatient, because it seems to me that when one person says, "it's obvious that math is real," and another "it's obvious that math is fiction", they must be disagreeing on the definition of one of the terms. Most likely, they are tacitly differing over what it means to say "X is real". It is likely that they would also lock horns over whether liberty, altruism, evil, or frustration are "real". The discussion isn't fruitful unless we settle in advance what we mean by "reality" when applied to abstract contexts. Most likely when we say "real", we actually mean one of a half-dozen vaguely-related predicates, some of which apply to mathematical truth, and some of which don't. -----