1. Mathematics is the pursuit of beauty. The harmonious dance of curves and figures makes us feel the beauty and infinite possibilities of the universe.

2. Mathematics, the eternal temple, contains endless wisdom and beauty. It is like a harmonious movement, leading us to explore the mysteries of the universe.

Although mathematics is complex, its beauty lies in its accuracy and conciseness. The elegance of mathematical formulas is like poetry.

Mathematics is introduced as follows:

Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.

The quantity is introduced as follows:

Due to the need of counting, human beings abstract natural numbers from physical objects, which is the starting point of all "numbers" in mathematics. Natural number does not close subtraction. For closed subtraction, we extend the number system to integers. In order not to close division, but to close division, we extend the number system to rational numbers.

For open root operation, we extend the number system to algebraic number (in fact, algebraic number is a broader concept). On the other hand, for the limit operation is not closed, we extend the number system to real numbers. Finally, in order to prevent negative numbers from operating to even powers in the real number range, we extend the number system to complex numbers.

A complex number is the smallest algebraic closed field containing real numbers. We perform four operations on any complex number, and the simplification results are all complex numbers. Another concept related to "quantity" is the "potential" of infinite sets, which leads to cardinality and another infinite concept: Alev number, which allows meaningful comparison between the sizes of infinite sets.

The famous mathematical sayings are introduced as follows:

I am determined to give up the only abstract geometry. In other words, I don't think about the problems that are only used to practice my thoughts. I did this to study another kind of geometry, that is, geometry aimed at explaining natural phenomena.