All disciplines have a theoretical guidance, that is, philosophy, and so does mathematics. Let's look at the set theory in mathematics. After Cantor developed the simple set theory, many paradoxes appeared, such as Russell Paradox. This problem was solved by determining the difference between class and set in the philosophical sense. Some basic problems in mathematics, such as axiom of choice and continuum hypothesis, are different dividing points based on philosophical cognition of different schools.
Regarding the concept of infinity, the transformation from the potential infinity in ancient Greece to the real infinity now makes the concept of continuity developed. These are the dependence of mathematics on philosophy. In mathematical logic, Godel's theorem shattered people's belief in mathematical certainty, and the duality of logic was also questioned. In a sense, it actually implied that law of excluded middle was unreliable, which was a breakthrough in philosophical cognition.
From the perspective of practical mathematics, we can also see that, for example, the familiar central limit rule in probability theory is quite philosophical in both proof and conclusion. Mathematics has developed from the earliest study of numbers and shapes to the present study of the abstract structure of space and the motion mode of objects in it. Behind it are profound philosophical cognitive theories and changes in categories.
Introduction to mathematics:
Mathematics (hanyu pinyin: shùXué；; ; Greek: μ α θ η μ α κ; English: mathematics or maths), whose English comes from the ancient Greek word μθξμα(máthēma), has the meaning of learning, learning and science. Ancient Greek scholars regarded it as the starting point of philosophy and the basis of learning. In addition, there is a narrow and technical meaning of "mathematical research". Even in its etymology, its adjective meaning is used to refer to mathematics whenever it is related to learning.
Its plural form in English and the plural form in French plus -es form mathématiques, which can be traced back to the Latin neutral plural (mathematica), and Cicero from the Greek plural τ α μ α θ ι α ι κ? (Tamatika). In ancient China, mathematics was called arithmetic, also called arithmetic, and finally it was changed to mathematics. Arithmetic in ancient China was one of the six arts (called "number" in the six arts).
Mathematics originated from the early production activities of human beings, and the ancient Babylonians had accumulated some mathematical knowledge, which could be applied to practical problems. As far as mathematics itself is concerned, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof, but their contribution to mathematics should also be fully affirmed.
The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be found in ancient mathematical documents of ancient Egypt, Mesopotamia and ancient India. Since then, its development has continued to make small progress. But algebra and geometry at that time were still independent for a long time.