intuitionism (mathematics)

Intuitionism is a philosophical approach to mathematics that emphasizes the construction of mathematical objects and the mental processes involved in understanding them. Founded by mathematician L.E.J. Brouwer, it argues that mathematics is not an objective discovery but a human creation. In intuitionism, a mathematical statement is considered true only if it can be constructively proven, meaning there must be a method to demonstrate its validity. This contrasts with classical mathematics, which accepts the law of excluded middle (either a statement is true or false) without requiring explicit proof. Intuitionism thus prioritizes intuition and constructiveness in mathematical reasoning.