I found this quote by Stephen Wolfram on page 1177 of his book A New Kind of Science.
Yet of the limited set of people exposed to higher mathematics, different ones often seem to think in bizarrely different ways. Some think symbolically, presumably applying linguistic capabilities to algebraic or other representations. Some think more visually, using mechanical expirience or visual memory. Others seem to think in terms of abstract patterns, perhaps sometimes with implicit analogies to musical harmony. And still others—including some of the purest mathematicians—seem to think directly in terms of constraints, perhaps using some kind of abstraction of everyday geometrical reasoning.
I understand what he means by algerberic and visual, but the other two are less clear to me, especially the part about "directly in terms of constraints". Can anyone shed some light on what he means by this?