The black hole existence and formation have been an unsettled debate, from inception, inviting the attention to look into the matter closely. Despite myriads of evidences for existence, the mathematical possibility of black hole-from Schwarzschild anticipation till the completion of physical structure- continues to be contested among theorists. Various aspects of mathematics involved in theoretical creation of black hole are exposed to question. Also, black holes' overwhelmingly capricious physical nature adds to curiosity of opponents to challenge the underlying theory as doubtful because of its being source of astounding outcomes. In this investigation we aimed at highlighting the conceptual elements in mathematics of black holes that breed the controversy. The reasons that permit the divided view over single physical entity are required to be pointed out in order to bring betterment into the way we run our mathematical investigation. The reasoning supports possibility of creation and existence of black holes along with physical and experimental evidences, would not be undermined here in order to restrict the investigation at finding the prime responsible elements in mathematical track that have potential to bring forth living disputes. The mathematical assumptions that serve as authentication to employ certain mathematical procedure to discuss formation of black holes and the role of mathematics in forming its intuition will be investigated conceptually and possibly philosophically, to reveal the anomalies: yet many other schemes and arguments may exist. This discussion is not aimed at disapproving the existence of black hole but the basic purpose is to reveal how Black Hole's mathematics remains controversial despite assumed evidence for existence