(1) Pythagoras is the founder of the theory that everything has a number. He said, "Numbers rule the universe". This statement has been agreed by many people for a long time. Socrates even emphasized that learning mathematics is "learning for the soul itself". Plato called "God is a geometer", and he wrote on the gate of his school: "People who don't know geometry are not allowed to enter."
(2) Philosophical Theory Since the ancient Greeks began to engage in philosophy, mathematics has become an important source of philosophical problems. Almost all the great philosophers in ancient Greece were great mathematicians. No wonder they defined mathematics more easily from philosophy. Aristotle said: "Although new thinkers study mathematics for other things, they regard mathematics and philosophy as the same."
In the preface to the first edition of Mathematical Principles of Natural Philosophy, Newton said that he regarded this book as a book on the mathematical principles of philosophy, and "put forward mathematical problems within the scope of philosophy as much as possible." Russell is more direct. He said, "In order to create a healthy philosophy, you should abandon metaphysics and become an excellent mathematician." He regards mathematical literacy as the basic condition for creating a healthy philosophy.
(3) Symbolic mathematics is recognized as a high-level language and a world of symbols. Galileo's words are widely circulated, that is, "the universe is a big book that is always in front of us, and philosophy is written in this book." However, you can't understand it unless you master its language and symbols first. This book is written in mathematics. Its symbols are triangles, circles and other figures. Without them, you can't understand a word. Without them, you will only wander in the dark maze. "
(4) Science says that mathematics is a science. "Mathematics, the queen of science; Arithmetic, the queen of mathematics. " (Gauss) "Mathematics is the door and key to science." (Bacon) "Mathematics is an influential science of our time, which has quietly expanded the fields it conquered; People who don't use mathematics to serve themselves will find that mathematics is used by others against themselves "(Herr Paris).
In the Encyclopedia of China, mathematics is defined as: "Mathematics is the study of quantitative relations and spatial forms in the real world, in short, it is the science of studying numbers and shapes." (Wu Wenjun) This authoritative assertion was born out of Marx and Engels' generalization of mathematics. Engels pointed out that "mathematics is a quantitative science" and "the object of pure mathematics is the spatial form and quantitative relationship of the real world". According to Engels' point of view, it is more accurate to say: mathematics-a science that studies the quantitative relationship and spatial form of the real world.
M Klein said: "Mathematics is not only a method, an art or a language, but also a rich knowledge system, which is very useful for natural scientists, social scientists, philosophers, logicians and artists, and influences the theories of politicians and theologians; Satisfied human curiosity to explore the universe and meditation on beautiful music; Sometimes it may even subtly affect the process of modern history. " "In fact, in modern empirical science, the acceptability of mathematical methods is increasingly becoming the main criterion for the success of this discipline." (collected works of Einstein. )
We are familiar with the question "What is mathematics?" The answer is: "Mathematics is the science of model". "Mathematics is science, mathematics is the art of creation", "Mathematics is science, and mathematics is technology." "Mathematics is a language." "Mathematics is a kind of culture." "Mathematics is the language of science, the gymnastics of thinking, the need of life, and the magic weapon of ultimate victory" and so on.
Mathematics is the product of diversification and integration. It is not easy to give an appropriate answer to "what is mathematics" in a few sentences. The key is to look at the problem. Our understanding of "mathematics" should move from monism to pluralism. Coulant, an American mathematician, said in his book What is Mathematics: "... For scholars and ordinary people, the answer to this question depends more on their own mathematical experience than philosophy: What is mathematics?"