In this paper it will be argued that Ancient Greek Philosophy, seen from the point of view of contemporary science is not only important but also of guiding influence. Many scholars are of the opinion that science has, in many aspects, reached its final success, that the truth has already been attained and further research in all the fields of science is not deemed necessary. The best that may happen is that very small modifications may occur, but still no new substantial discoveries could in principle be made because we have reached the limits of what is to be known. What is more, is that this possible dramatic event, even though far off in time from the the Greeks, may have something important to do with them. In this respect, a few questions will come under consideration such as: Were the basic scientific guidelines that came from the Greeks, ways of thinking which led science to this high mark and end limit? Could it be claimed that the influence on science is in all aspects related to the Greeks? What about so many other cultures and technological civilizations? What would the important influence of Greek thinking be on contemporary scientific thinking? Is it really the case that the Greek influence would bring science to its completion and end? These questions immediately brings two issues to the fore a) the possibility of other technological civilizations that influenced the development of science until today and be the possible end of science. Although these two issues, are distinguishable issues, the first one is a necessary condition for the second one. The article is designed by faking this conditionality into account.