As characteristic of his methodological approach to all subjects, Aristotle carefully defined a few of the limitations of mathematics that ultimately dictated his future studies:
- Although relating geometry to mathematics is supreme, mathematics is limited by precision. A straight line is not one hundred percent straight and a two objects are not technically touching, therefore mathematics cannot always be precise.
- The fact that not everything mathematical that Aristotle studied could not be modeled in the physical world frustrated Aristotle immensely. Therefore, Aristotle offered another limitation or roadblock known as separability: mathematics cannot exist in the physical world and be both separate from from physical matter.