This page is a sub-page of our page on What is Mathematics?
The sub-pages of this page are:
The impossibility of teaching mathematics
Mathematics can never be taught. It can only be given the opportunity to grow. Mathematics is a feeling, a sensitivity and an awareness of structure, which is planted in each and every one of us, like a seed of the cosmic consciousness. To practice the art of mathematics is to be involved in a purely mental process, which has surprisingly strong connections with the surrounding physical reality.
When you are developing your mathematical understanding, both halves of your brain work together in the process of constructing combinations of mental fantasies that are tested for logical consistency. The right half of the brain is fantasizing, and the left part is analyzing and testing the logic of the suggested ideas. Only the ideas that survive the logical examination are elevated to the status of mathematical truths.
Mathematics can therefore be described as logically tested fantasies. It offers powerful means for its devotees to overcome some of their sensory limitations and contemplate the inner profundity of the structure of the universe.