The hand points at the Moon. The dog barks at the hand. Math is confused with arithmetic, which is one tiny subset of math, and notation, which isn't math at a

The hand points at the Moon. The dog barks at the hand. Math is confused with arithmetic, which is one tiny subset of math, and notation, which isn't math at all but is merely a tool mathematicians use to communicate more clearly because some concepts are too bulky when you attempt to express them using words. The essence of math is careful reasoning, following step-by-step processes to derive new truths from existing ones. If you do that, you're doing math, and if you do it without arithmetic or notation, people will say you're doing math without math.