Leibniz in 1686 in his Discours de mtaphysique points out that if an arbitrarily complex theory is permitted then the notion of theory" becomes vacuous because there is always a theory. This idea is developed in the modern theory of algorithmic information, which deals with the size of computer programs and provides a new view of Gdel's work on incompleteness and Turing's work on uncomputability.This will be a first-person account of some doubts and speculations about the nature of mathematics that I have entertained for the past three decades.