"For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?"

Richard Courant's quote from "What is Mathematics?" stresses the unique and extensive nature of mathematics, recommending that its real essence can only be comprehended through active engagement and experience instead of through philosophical query alone. Courant presumes that both scholars, who approach the subject with a theoretical viewpoint, and laymen, who may not have official training in the field, need to immerse themselves straight in mathematical practice to genuinely grasp its meaning and scope.

By stating that "not philosophy however active experience" is vital in understanding mathematics, Courant challenges the idea that mathematical facts can be totally recorded by philosophical reflection or abstract thinking detached from practical engagement. Mathematics is typically perceived as a simply rational and theoretical discipline; nevertheless, Courant indicates that it is also an experiential one. Solving issues, manipulating numbers, and exploring patterns offer a type of comprehending that abstract thinking alone can not accomplish. Through practice, one encounters the imagination, instinct, and problem-solving aspects intrinsic to mathematics, which reveal its true nature.

Additionally, mathematics as an active experience stresses its dynamic and progressing character. It is not merely a collection of established realities however a living discipline that constantly grows and adjusts through practical engagement. This point of view welcomes people to take part in mathematics as an imaginative and exploratory process, rather than seeing it as an inert body of knowledge.

Eventually, Courant's view lines up with the concept that mathematics is both a science and an art. To ask "What is mathematics?" is to invite individuals to explore its depths through practice, permitting them to witness its charm and reasoning in action. This active participation assists debunk mathematics, transforming it from intimidating concepts into relatable experiences that yield deeper understanding and appreciation.