This study of Leibniz’s philosophical views on mathematics starts from the rank he assigned to them in the encyclopedia of knowledge. Mathematics, in many Leibnitian writings, is proposed to other disciplines as an example to follow: they are an essential component of the new, at the same time encyclopaedic and demonstrative knowledge he is advocating. If we then consider the object of mathematics and their foundations, we see that Leibniz grants an ideal existence to mathematical notions; an algorithmic existence, via their definition or thanks to procedures; and a kind of Pythagorean existence which is based on the intrinsic rationality of the natural order. On this tripod (either ontological or epistemological) mathematical objects base their existence, which depends in the end on relations between real-world entities, harmony relationships and finality.