All of our sensory perceptions and rational cognitions would fall apart like cards in the wind were it not for the glue of intuition holding the house of our lives together. Nor, can we reduce a priori intuitions to the effects of social conditioning. In other contexts, intuition requires, and then adds to, years of experience and training filled with thoughtful reasoning and social conditioning. Virtually every profession distinguishes between the highly intuitive sense of the virtuoso or genius as opposed to the competent, workmanlike performance of other professionals. It is as if, at this level, one's whole being is fully engaged in the apprehension of the nuances and rhythms of the relevant activities, both internal and external.
Intuition is an exquisite sensitivity, within one's deepest being, to the pulses of life's energies.
Mathematical intuition is an interesting case. Yet, one significant aspect of mathematical intuition is the ability to apprehend, and even visualize, this realm. In ancient times, the Pythagoreans, Kabbalists and Neo-Platonists drew comparisons between the intuitions of mathematicians and those of mystics and visionaries. In the nineteenth century, comparison began to take on momentum as mathematicians began exploring the fourth dimension of space. One contemporary writer intrigued by this idea is Martin Gardner.