Hello, mathematics is a book that starts with mathematics and interprets the truth of the world. Mr. Azuma Tani profoundly analyzed the importance of mathematics in the fields of nature, social science and humanities, and comprehensively expounded the future development of mathematics.
After reading "Hello, Mathematics", I immediately put forward profound thinking: Why is mathematics a part of human beings? How does the development of mathematics promote the development of other fields? As a math and science lover, I am eager to know the scientific knowledge covered in this book.
"Hello, Mathematics" unveiled the mystery of the mathematical world to me. Our commonly used definitions, theorems and equations are all produced to solve practical problems.
definition
Aristotle defined mathematics as "quantitative mathematics", which lasted until18th century. /kloc-since the 0/9th century, mathematical research has become more and more rigorous, and it has begun to involve abstract topics such as group theory and projection geometry that have no clear relationship with quantity and measurement. Mathematicians and philosophers have begun to put forward various new definitions.
Some of these definitions emphasize the deductive nature of a lot of mathematics, some emphasize its abstraction, and some emphasize some themes in mathematics.
Even among professionals, the definition of mathematics has not been reached. Whether mathematics is an art or a science has not even been decided. Many professional mathematicians are not interested in the definition of mathematics or think it is undefined. Some just say that mathematics is done by mathematicians.
structure
Many mathematical objects, such as numbers, functions, geometry, etc., reflect the internal structure of continuous operation or the relationships defined therein. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations.
In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.
Therefore, we can learn abstract systems such as groups, rings and domains. These studies (structures defined by algebraic operations) can form the field of abstract algebra.