The beautiful sentences describing mathematics are as follows:

1. Mathematics is the pursuit of beauty. The harmonious dance between curves and graphics allows us to feel the beauty and infinite possibilities of the universe.

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

3. Although mathematics is complex, its beauty lies in its precision and simplicity. The elegance of mathematical formulas is like poetry.

Mathematics is introduced as follows:

Mathematics is a universal means for humans to strictly describe and deduce the abstract structures and patterns of things. It can be applied to any problem in the real world. All Mathematical objects are essentially artificially defined. In this sense, mathematics is a formal science rather than a natural science. Different mathematicians and philosophers have a range of views on the exact scope and definition of mathematics.

Quantities are introduced as follows:

Due to the need for counting, human beings have abstracted natural numbers from real things, which are the starting point of all "numbers" in mathematics. Natural numbers are not closed to subtraction. To be closed to subtraction, we extend the number system to integers. In order to be closed to division, we extend the number system to rational numbers.

For square root operations that are not closed, we extend the number system to algebraic numbers (actually algebraic numbers are a broader concept). On the other hand, for limit operations that are not closed, we extend the number system to real numbers. Finally, in order to avoid that negative numbers cannot be opened to even powers in the range of real numbers, we extend the number system to complex numbers.

Complex numbers are the smallest algebraic closed fields containing real numbers. We perform four arithmetic operations on any complex numbers, and the simplified results are all complex numbers. Another concept related to "quantity" is the "potential" of infinite sets, which leads to the cardinal number and then another concept of infinity: the Alev number, which allows the sizes of infinite sets to be meaningfully compared. .

The introduction of mathematical famous sayings is as follows:

I am determined to give up that mere abstract geometry. This means that you no longer have to consider problems that are just for thinking. I did this in order to study a different kind of geometry, one whose purpose was to explain natural phenomena.