"Multiply a number by the root of 9. If you want to double the root of 9, you can follow the following steps: multiply 2 by 2 to get 4, and multiply 9 by 4 to get 36, which is the root of 36. We know that it is the root of two 9s, which is twice the size of 3. And 3 is the root of 9, and add it to itself to get 6. "This is a quote from a book called Algebra. All the problems in the book and the process of solving them are described in language. Now, with perfect mathematical symbols, we no longer have to read such difficult mathematical books. The use of mathematical symbols makes mathematics more concise and accurate in form, bringing great convenience to the expression and demonstration of mathematical theories.
If expressed in symbols, the main meaning above is that words that appear lengthy in ordinary language become concise and clear after using mathematical symbols. Another advantage of using symbolic representation is that it makes both the problem and the solution more general. For example, the above example is to study "multiplying a number by the root of 9", but due to the lack of symbols, only one special case can be given in Algebra to reflect its general method.
On the one hand, the internal factors in the development of mathematics continue to promote the introduction of symbol systems, and on the other hand, the introduction of symbol systems in turn promote the development of mathematics. The two promote each other, and ultimately make mathematics's dependence on symbols and the importance of symbols to mathematics continue to increase. Appropriate mathematical symbols often become a huge force in promoting the development of mathematics.
The earliest symbol to appear in mathematics is numbers, and its appearance marks the improvement of human understanding of logarithm. The use of the Indo-Arabic numeral system has brought great convenience to all calculations. This is a typical example of "important mathematical results simply due to the choice of appropriate symbols."
Later, with the deepening of the development of mathematics, new mathematical theories accompanied by corresponding mathematical symbols, and both mathematical symbols and mathematics itself entered the fast track. As mathematics becomes more and more abstract and precise, mathematics becomes more and more dependent on symbols. Finally, the introduction of mathematical symbols is not just about making expression concise. In fact, many mathematical theories will be difficult to carry out without appropriate symbols.
Nowadays, the use of mathematical symbols has become one of the most obvious and prominent symbols of modern mathematics. Almost every branch of mathematics has its own symbolic language. At the same time, the mathematical symbol system has also become an internationally accepted and true "Esperanto."