  An apparent problem with naturalism is that there do not seem to be sharp boundaries between science and non-science and between mathematics and non-mathematics. For example, the transition from physics to philosophy of physics to physics-heavy metaphysics to common-or-garden metaphysics seems to be gradual. When a mathematician writes a research article, an undergraduate textbook, a popular book on mathematics, a book expounding his personal philosophy of mathematics and his psychological associations with various mathematical theories, at what point exactly has he stopped doing mathematics? When research mathematicians get together after the seminar and agree over coffee that the Riemann Hypothesis is the most important outstanding problem in mathematics, is this a strictly mathematical claim or a personal judgement recognised by mathematicians as outside the province of mathematics proper?