The concept of ‘ideas’ plays central role in philosophy. The genesis of the idea of continuity and its essential role in intellectual history have been analyzed in this research. The main question of this research is how the idea of continuity came to the human cognitive system. In this context, we analyzed the epistemological function of this idea. In intellectual history, the idea of continuity was first introduced by Leibniz. After him, this idea, as a paradigm, formed the base of several fundamental scientific conceptions. This idea also allowed mathematicians to justify the nature of real numbers, which was one of central questions and intellectual discussions in the history of mathematics. For this reason, we analyzed how Dedekind’s continuity idea was used to this justification. As a result, it can be said that several fundamental conceptions in intellectual history, philosophy and mathematics cannot arise without existence of the idea of continuity. However, this idea is neither a purely philosophical nor a mathematical idea. This is an interdisciplinary concept. For this reason, we call and classify it as mathematical and philosophical invariance.