The paper examines the beingness of mathematical science from various aspects. The fires of them ist the uncovering of the beingness of science through its intrinsic reason of its existence, through its entelecheia as its inner active principle. The fundamental question then is: What is the bytostné what, i. e. the essence of science? The first aspect is closely related to the second one, i. e. the problem of natural/ordinary world. Patočka argues, that philosophy as well as science, which since antiquity are the seeing of the invisible, have their roots in the natural habitual human attitude, in a visible world accessible to natural/ordinary inquiry. The third problem Patočka paid attention to is the interconnectedness of philosophy and mathematical science. He points out, that in the name of the fight against metaphysics the modern science rejected the traditional philosophy and its metaphysics, replacing it with the second metaphysics with its mechanistic and causal determination of the whole reality. This often leads to radical scientism and also to interconnection between science and so called science technology. Patočka also shows the ideological and political consequences of the whole issue, resulting from contemporary predominating understanding of the beingness of the mathematical science.