Historical Paradoxes in fundamental of Mathematics and their role in developing branches of Mathematics and rnethods of scientific researches

In this paper, we first define paradoxes and their sources and how they came to existence. Then we classify the different type of paradoxes, describe and explain them and will show that fundarncntal paradoxes (non-removable) exist in mathematical theories inherently. But removable paradoxes are the result of two kinds of mistakes, one is intentional and second is accidental which made by men or mathematicians, Following that, some removable paradoxes will be shown which is resulted from formulizationism and activizationism trends in new age mathematicians. Those which their entrance in mathematics based on somebodies whose their empirical basis and intuitive thought with fundamental concept of mathematics were not so deep.In the main part of the paper we state and describe some fundamental parameters in mathematics which arc the main cases of historical crisis in mathematics and resulted different branches in mathematics and other sciences and moreover they change the mathematical methods and other sciences and consequently change the attitude of physicists and mathematicians toward teaching mathematics and basic sciences and eventually change the way of thought and change the paradigms which govern upon scientific theories.