  There are two important senses in which Aristotle never presents a philosophy of mathematics. Aristotle considers geometry and arithmetic, the two sciences which we might say constitute ancient mathematics, as merely the two most important mathematical sciences. His explanations of mathematics always include optics, mathematical astronomy, harmonics, etc. Secondly, Aristotle, so far as we know, never devoted a treatise to philosophy of mathematics. Even Metaphysics xiii and xiv, the two books devoted primarily to discussions of the nature of mathematical objects, are really concerned with diffusing Platonist positions that there are immutable and eternal substances over and beyond sensible substances and Pythagorean positions that identify numbers with sensible substances.