Formalism in the History of Philosophical Mathematics: Beyond Logicism and Intuitionism

An examination of the similarities and differences between these three schools may shed light on the richness and variety of mathematical philosophies, as well as the significance of such philosophies to the comprehension and growth of mathematics. Formalism, logicism, and intuitionism are the names of these schools. The purpose of this study is to investigate the three primary schools of thought within the philosophy of mathematics, examine the many ways in which these schools interpret and approach mathematics, and investigate the areas in which these schools share and diverge in their perspectives. All three schools make an effort to present mathematics in a manner that is rigorous and built on a strong foundation, but each of them must also contend with its unique obstacles and challenges. The transcendence of formalism regarding the other two will be shown throughout this investigation with the use of instances such as Godel's incompleteness theorem and infinitesimal quantities.