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How to use mathematical thinking to solve difficult problems scientifically after reading Liu Xuefeng's Know Well?
When using mathematical thinking to solve difficult problems scientifically, Zhixing put forward the principle of "using both hands". In The Doctrine of the Mean, "Use both ends at the same time for the people". The algorithm behind it is "least square estimation"; It means that when solving problems, don't go to extremes and avoid them, but grasp both ends and comprehensively find the middle solution.

Agile action and Excellence are important methods to solve problems. "Knowing the root and the bottom" mentioned two concepts in the algorithm: derivative method and numerical solution, which correspond to waterfall model and agile model respectively, and these two models correspond to two ways of solving problems step by step and Excellence.

According to the idea of "step by step", solving problems should be strict first, then divided into several steps and gradually completed; The idea of "Excellence" does not require every step to be optimal, but to complete one round quickly and then iterate for many rounds, each round trying to be better than the previous round, so as to get a good result after many rounds of iteration.

The most suitable way for young people is naturally the concept of "Excellence", that is to say, it doesn't care how perfect it is once, but pays more attention to the power of repetition and the rhythm of running in small steps. This is also the "agile mode" in software development.

Of course, no matter what you do, you have to do your best at the beginning. In this process, we need to keenly find good "positive feedback" and persevere. Sometimes you need some external force to help you take a good step and keep going. Once the flywheel turns, good results will naturally follow.

Just like in our life, it is impossible to complete the perfect 10 km in the first run, but we need to constantly motivate ourselves with a little luck in repeated training and iteration, from 1 km, 3 km to 10 km. You will be panting at first, but if you stick to it, you will be like a duck to water.

This also corresponds to everyone's growth process. We don't want quick success and instant benefit, and we don't expect it to happen overnight. We must take a long-term view and make ourselves more stable in order to go further.