My theorem: There are no uninteresting numbers. Assume that there are. Then there is a lowest uninteresting number. That would make that number very interesting. Which is a contradiction.
A number of readers have objected that "numbers" in the above theorem should be "natural numbers" (non-negative integers). My reply to one reader was this:
Yes, but I wanted to keep it simple and quotable. And the proof that all numbers are interesting should not be boring. From natural numbers, it can be generalized to rationals, as fractions with interesting numerators and denominators are obviously interesting. And what could be more interesting than an irrational that cannot be formed from any finite combination of rationals? I see that David Wells' book Curious and Interesting Numbers has something similar: "39 ... seems to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number having the property of being uninteresting."
Also "uninteresting" is not well-defined. Several mathematics teachers have asked permission to quote my theorem.
http://www.nezperce.com/~jimloy/math/math.htm
