I believe that reality is something both mental and physical, and far more wonderful than anything the mind can conceive or the eye can ever see. However, when this reality manifests in the consciousness of the mathematician, it does so in the beautiful forms and shapes that I have attempted to describe in this book; in the external world, it appears in the diverse forms of living nature. When we bring these two realms together as manifestations of the same reality, we find that they coincide and fit together. And when we bring them together - provided we have the will and the mental faculties to proceed in the right way - we stand at the gateway (note: only at the gateway) of knowledge.