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The thought is that which exists through intellectual activity. It is the product of the spirit from the rational process of intellect or imagination abstractions.
The analysis, comparison, generalisation, abstraction and synthesis are part of operations concerning thought, which determines and is reflected in language. It is possible to distinguish between the different types of thought, namely, analytical thinking (that separates all in parts), critical thinking (that tests the knowledge) or systematic thinking (a vision that spans multiple items with its various reports).
In this case, it is the mathematical thought that interests us, which is to systematize and to contextualize knowledge in mathematics. This type of thinking develops from the moment where we know the origin and evolution of the concepts and tools belonging to the field of mathematics.
In developing such a thought, one arrives at a mathematical training more complete which allows us to have a significant range of knowledge which can be useful in obtaining the results.
On the other hand, mathematical thought is to know how a concept or technique is trained. Thus, it is possible to know its inherent difficulties and know how to exploit its use properly.
As a material, mathematical thought includes the study of concepts, techniques and algorithms that occurred in each historical period. However, this does not imply to assess the achievements and mathematical discoveries of antiquity from current knowledge.