maths and language are abstracted symbols

--for memory of theoretical physics

The above formula means that internal energy of ideal gas is not a funtion of the volume of the ideal gas, in other words, the internal energy of ideal gas will not change if only the volume of the ideal gas changes. It is a direct application of the first law thermodynamics in ideal gas.

In the above paragraph, I use one sentence, 42 words, to explain briefly what the equation means. But from another point of view, I used 42 words to explain the result of direct application of the first law of thermodynamics to ideal gas. And the same application (or fact) can be described by only one equation.

Of course, the letters U, V and T need definitions before the equation, or any combination of them, has any meaning. But is the 42-word sentence self-contained or self-sufficient? No, what is ideal gas, what is internal energy, what is volume, what is temperature and what is function. Even what is "change"?

In maths, definitions are like building blocks, one upon another, which form the mansion of maths. I try to find out what is at the bottom of this mansion. I look at numbers: 1 to 9 and the 0. They are abstracted symbols of the things in real world. 1 apple, 2 apples...From the real things, we get the idea of 1 and 2 and so on.

Language more or less serves the same function: to describe the real things. But a big difference between maths and language is that too many words in a language do not have clear definition. And it seems that people do not care about whether they have clear definitions or not.