There have always been some curiosities about the accuracy and reliability of philosophical, logical and intellectual foundations of different economic schools. There is no doubt, what is now taught in most of the economics departments all over the world is the tradition of conventional (mainstream) economics, and usually, upon this knowledge, we direct our economic studies and make our policy implications. Now, the question to be asked is that, is this tradition well constructed? Do its explanations of economic phenomena have enough accuracy and reliability? Could the use of formal methods raise explanationary power of mainstream economics and/or orthodox economics? Or, may it be quite the reverse? In other words, is it likely that the use of mathematics has brought some fundamental pitfalls to orthodoxy? In this paper, we will demonstrate that some particular methodological tendencies in mainstream economics, that is, the mathematical-deductive methodology causes some essential pitfalls and shortcomings in this tradition. This is alone a good reason to direct our attention towards heterodoxy and alternative schools, because their approach is less idealistic and more relevant to the ongoing problems of developing countries.