The article examines philosopher Charles Sanders Peirce's views on the role of poetic creation in mathematical reasoning. In his manuscript entitled "The Essence of Mathematics," Peirce defines mathematics as the science which draws necessary conclusions. He also defines it as the study of what is true of hypothetical states of things. The article notes that Peirce himself acknowledges that it is difficult to decide between the two definitions of mathematics, the one by its method, that of drawing necessary conclusions, and the other by its aim and subject matter, as the study of hypothetical states of things.