It is common to get stuck in a transitional link in the process of solving problems. At this time, you can admit the intermediate conclusion first, and then push it backwards to see if you can draw a conclusion. If there are two questions and the question of 1 can't be figured out, then we can treat the question of 1 as "known", do the second question first and jump to the answer.

When thinking in a positive way is blocked, we can often use the method of reverse thinking to explore new ways to solve the problem, so as to make breakthrough progress. If it is difficult to push forward, we will push back, and if it is difficult, we will directly disprove it.

"Retreat for progress" is an important problem-solving strategy. For a relatively general problem, if it can't be solved for a while, we can retreat from the general to the special, from the abstract to the concrete, from the complex to the simple, from the whole to the local, from the parameters to the constant, and from the strong conclusion to the weak conclusion.

In short, you need to retreat to a problem that you can solve, and enlighten your thinking by thinking and solving the "special" to achieve the purpose of solving the "general".

The significance of mathematics

Mathematics is closely related to many fields of national economy. Internet, computer software, HDTV, mobile phone, portable computer, game machine, animation, fingerprint scanner, Chinese character printing, display, etc. It occupies a considerable proportion in the national economy and has become an important pillar industry of the world economy.

Among them, Internet, computer core algorithm, image processing, speech recognition, cloud computing, artificial intelligence, 3G and other major R&D fields in IT industry are all based on mathematics. So the information industry may be one of the industries that employ the most mathematicians.