A mathematical concept is a general idea behind an equation, problem or formula in math. In contrast to a math fact, which must be committed to memory, a math concept explains why math works in a certain way.
A student who understands mathematical concepts advances to a higher level of learning involving abstract thinking. Understanding math concepts often negates the need to memorize answers to problems. Mathematicians use abstract thinking to formulate new theories, which they test by mathematical proof. Mathematical practices such as counting and measurement developed from initial abstraction and logical thinking. Math arises from thinking abstractly about many kinds of practical problems in disciplines such as architecture, astronomy and business.