An Algorithm in Cognition and Mathematical Insight

Since studying mathematics develops and activates the mental system, it may be claimed that the profound understanding of mathematics can be effective in finding the facts and in true understanding of the phenomena. Thus mathematical understanding can help the individual perform his tasks with better knowledge and insight. In other words, benefitting from mathematical concepts, one can achieve the capability of deducing facts. Having stated the cognitive position of mathematics based on Plato’s and Des cartes’ quotations, the present article introduces a type of mathematical knowledge, which is the outcome of profound understanding of mathematical concepts, as mathematical cognition and insight. Determining the domain of this kind of knowledge based on the concept of the word” algorithm”, it also deals with the quality of the stages of achieving it. The article closes with giving certain examples for the cognitive aspect of the concept of function, and the graph structure in the theory of graphs.