What is abstract mathematics?
In order to give full play to the advantages of symbols such as standard numbers, plus signs and brackets, people often write written narratives into a formal system represented by a series of symbols. However, these symbols were not necessary features of mathematics at that time. Although written narrative is also used to represent plums, bananas, apples and oranges, at that time, mathematical narrative (composed of arbitrary symbols) became more and more obvious as a simple and accurate structural model of mathematics. Soon, a few far-sighted figures began to understand the characteristics of mathematical narrative, among which Godel was the best. This way of looking at things opens up a new branch of mathematics-abstract mathematics. The commonly used mathematical analysis methods are related to the imitation-germination stage of abstract mathematics, which forms the essence of formal system-mathematics itself is assumed to be the original sample of abstract mathematics. In this way, mathematics is like a snake that has eaten itself. It turns its head to catch itself. Godel shows that the strange conclusion comes from the focusing process when looking at mathematics itself through the mathematical lens. One way to understand this conclusion is to imagine that on a distant planet (such as Mars), all the symbols used to write legendary works happen to be the Arabic numerals from 0 to 9 that we usually use. So Martians will discuss a famous discovery in textbooks. They will find that we are related to Euclid on earth, and at the same time we will say "their works", and what they write will be like this: "44454087666 is 46 digits in our view. For Martians, it is not a number at all, but a statement. Indeed, for them, the prime numbers they wrote represent 34 letters, 6 words and a few lines, just like I used English letters with you. Now let's imagine discussing the universal properties of all mathematical theorems.