Supplementary mathematics/Philosophy of mathematics

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique.

Questions about:

1. the mode of being of the mathematical objects: do they exist "really" and independently of a concrete use, and if so, in what sense? What does it even mean to refer to a mathematical object? What is the character of mathematical propositions? What are the relationships between logic and mathematics? – These are ontological questions .
2. the origin of mathematical knowledge : what is the source and essence of mathematical truth ? What are the conditions of mathematical science? What are your basic research methods? What role does human nature play in this? – These are epistemological questions .
3. the relationship between mathematics and reality : What is the relationship between the abstract world of mathematics and the material universe? Is mathematics anchored in experience , and if so, how? How is it that mathematics “fits the objects of reality so perfectly” ( Albert Einstein ) ? In what way do concepts like number , point , infinity gain their meaning beyond the inner-mathematical realm?

The starting point is almost always the view that mathematical propositions are apodictically certain, timeless and exact and that their correctness depends neither on empirical results nor on personal opinions. The task is to determine the conditions for the possibility of such knowledge, as well as to question this starting point.