  I'll discuss how Goedel's paradox "This statement is false/unprovable" yields
his famous result on the limits of axiomatic reasoning. I'll contrast that with
my work, which is based on the paradox of "The first uninteresting positive
whole number", which is itself a rather interesting number, since it is
precisely the first uninteresting number. This leads to my first result on the
limits of axiomatic reasoning, namely that most numbers are uninteresting or
random, but we can never be sure, we can never prove it, in individual cases.
And these ideas culminate in my discovery that some mathematical facts are true
for no reason, they are true by accident, or at random. In other words, God not
only plays dice in physics, but even in pure mathematics, in logic, in the
world of pure reason. Sometimes mathematical truth is completely random and has
no structure or pattern that we will ever be able to understand. It is NOT the
case that simple clear questions have simple clear answers, not even in the
world of pure ideas, and much less so in the messy real world of everyday life.
