Discussion on the fundamentals of mathematics on formalist and intuitive approaches an investigation

Against the applied mathematics tendency, which was effective in mathematics until the 19th century, the abstract (pure) mathematics tendency gained strength towards the end of the 19th century. Again, since the end of the 19th century, the world of mathematics felt the need to find a solid foundation that would save the basic concepts and principles of mathematics from uncertainty, clear them from contradictions, and prevent possible philosophical discussions and intra-scientific debates that may arise in the future. This requirement has generated heated debate in the mathematical community. One of the results of these discussions, was the increase in the intrection of the mathematical community with philosophy and another results wasthe development of various philosophical approaches that offer a number of changes in mathematics as a result of this interection. Especially at the beginning of the 20th century, logicism, formalism and intuitionism, among these approaches, gathered important supporters in the world of mathematics and led to the formation of a serious literature on philosophy of mathematics Your master's thesis first discussed the important developments that took place in the 18th and 19th centuries and that led to the growth of the problem of the foundations of mathematics, and then structured it in a way that makes clear the approaches of formalist and intuitionist philosophies of mathematics to the problem of foundations of mathematics. While the debate on the foundations of mathematics continued, the debates of David Hilbert and L.E.J. Brouwer in the background were influenced by the political atmosphere of the period. The direct impact of this debate, which has turned into a political crisis, on the debate on the foundations of mathematics will also be revealed. Keywords: Philosophy of Mathematics, David Hilbert, Formalism, Luitzen Egbertus Jan Brouwer, Intuition, Logicism