The branch of philosophy that aims to study the foundations, assumptions and the philosophical assumptions of mathematics is called the philosophy of mathematics.
If one considers the historical evidences of thinkers contributing to the ideas that pertain to mathematics, the examples are aplenty. These include two basic categories of philosophers of mathematics: Western Philosophers and Eastern Philosophers.
Western Philosophers have some great names attributed to them such as Plato and Aristotle. Plato concentrated his studies on the mathematical objects, especially their ontological status. Aristotle, on the other hand, contributed to the field of logic of infinity.
It was the great mathematician Leibniz, who focused primarily on the relationship between logic and mathematics.
The study of philosophy of mathematics is made interesting due to the following aspects of mathematics:
o Mathematics is based upon countless number of abstract concepts.
o Wide application of mathematics: It governs many activities of our day-to-day life, besides its application in physics, chemistry and even biology!.
o Infinite: This notion is a peculiar one and has always aroused interest of many philosophers.
The relationship between mathematics and logic is one issue that has been a recurrent one in the philosophy of mathematics. In the 20th century, the philosophy of mathematics revolved around set theory, proof theory, formal logic and other such issues.
Around the break of the 20th century, there were several schools of thought that philosophers of mathematics held. At this time, three schools emerged, namely: intuitionism, logicism and formalism. In the beginning of the twentieth century, there was also an emergence of a fourth school of thought: predicativism. Any issue that would come up at that time, each school would aim to resolve that or claim the fact that mathematics is not as inevitable as opposed to those who believe mathematics to be “the most trusted knowledge”.