Random talk on mathematics is such a book as a gift from academician and Professor Ren to middle school students. With the popular language and the standard way of thinking of middle school students, this paper expounds the subject background, historical origin, content and thought of advanced mathematics such as geometry, function, calculus, mathematical logic, statistics, set theory and information cryptography. People who have read her don't need to wonder why the language of Random Talk on Mathematics is not so professional and the reasoning is not so accurate, and then question her mathematical professionalism. Because mathematics is difficult, it is a mathematician's life partner, and the mathematics that the public likes must be alive and kicking.

For example: which came first, the chicken or the egg? If this question is put on biologists, it will definitely be a headache, because it seems that both answers are reasonable. But from a mathematical point of view, the question becomes extremely simple and the answer is easy to determine. According to the thinking habit of solving mathematical problems, we should first define "eggs". As long as we define "eggs are eggs laid by chickens" or "eggs laid by chickens are eggs", the result of the problem will be obvious.

This example is given to show the unique charm of mathematical logic. The reason is that mathematics is a purely "abstract" logic system based on definitions and axioms, and the most obvious difference between mathematics and other subject systems is that it is developed purely through the mutual deduction and deduction of theorems. As long as the problem itself is given a definite definition, any problem will have a definite result according to this definition.

Throughout the history of mathematics, the two development ideas of mathematics have been induction and deduction, from special induction to general, from complex uncertainty to simple certainty. The purpose of "Random Talk on Mathematics" is to summarize and deduce the complex and interlaced mathematical system and present it to readers in simple and understandable language.