The final stage is known as the formal operational stage (adolescence and into adulthood, roughly ages 12 to adulthood): Intelligence is demonstrated through the logical use of symbols related to abstract concepts. This form of thought includes “assumptions that have no necessary relation to reality.” At this point, the person is capable of hypothetical and deductive reasoning. During this time, people develop the ability to think about abstract concepts. Piaget stated that “hypothetico-deductive reasoning” becomes important during the formal operational stage. This type of thinking involves hypothetical “what-if” situations that are not always rooted in reality, i.e., counterfactual thinking. It is often required in science and mathematics.