The Power of Mathematical Thinking in Life and Business

　　Everyone has their own way of understanding the laws of the world. These methods are not right or wrong, but they need to be effective for a long time. Mathematical thinking is a tool for understanding the world.
　　Never ignore negative numbers.
　　The famous physicist Professor Zhang Shoucheng gave a report in Silicon Valley before his death. The people who listened to the report were engineers, entrepreneurs and investors. As his friend, I also went to join him. In the report, Professor Zhang asked everyone a question: What number multiplied by itself equals 4? Everyone answered yes 2. Seeing me smiling and not saying a word, Professor Zhang asked me what the answer was, and I said -2.
　　The reason why Professor Zhang thought of the “-2” example is because everything has two opposite sides, which is an inherent characteristic of this world. Matter and energy are conserved, and what is gained is bound to be lost; electric charge is conserved, where there is positive charge, there is negative charge; elementary particles often correspond to antiparticles. When you understand this, you can think about the problem comprehensively.
　　With the concept of negative numbers, we must first understand that 0 is not the smallest number. Today almost everyone wants to have as much money as possible. If there is no money, the world will feel terrible and the sky will fall. In fact, in this world, there are worse things than having no money, that is, they owe a lot of debt, and their money is negative.
　　When a person’s net worth is negative, it is very difficult to turn around for a lifetime. For more than half of Americans, 20% of their pre-tax income is used to pay off various debts, such as interest on mortgages and credit cards. The income of these people is usually not high. After removing this 20%, they can only live a busy life every day and spend their time on dealing with debts. It is impossible for them to think about how to improve themselves, change their financial situation, and have no leisure to enjoy life.
　　Once you have the concept of negative numbers in your mind, you may be able to understand that every time we do something, the benefits we get may not necessarily be positive, and it may be negative. This is not only true of investment, but also of life.
　　People are constantly investing their time and life throughout their lives. Everything you do produces a result, either good or bad. Many people don’t have the concept of “negative numbers” in their minds, which causes them to always think of good results before starting to do something, and don’t want bad results.
　　For example, everyone says “make friends widely, many friends have multiple paths”, this sentence sounds fine, but the premise of this sentence is that this friend is a good friend rather than a bad friend. Many people make friends indiscriminately, and finally regard bad friends as good friends. If they make a mistake, they regret it too late, and bad friends are “negative numbers”. If you have negative thinking, you will screen a person before you contact him, and then choose whether you can continue the relationship.
　　Subtraction is more important than addition.
　　Addition is “I want, I want, and I want.” I keep adding, I can’t wait to do everything again, and every second is occupied; subtraction is “I don’t want to do this.” , don’t do this, let alone do that”, I only find out the most important one or two things, and then try my best to do it.
　　Which is better? Instinct makes us choose addition, because people like more than less, like gain but not lose. But in fact, subtraction is more efficient, and many things can only be done by subtraction. For example, before Jobs returned to Apple, Apple had a bunch of product lines, but almost none of them were profitable, so Jobs cut off most of them and concentrated resources on making profitable products. But many entrepreneurs don’t understand this truth. They always feel that there is so much money in the market, and it would be a pity if they don’t earn it.
　　Today, most startup founders talk about their plans as omnipotent, big business plans. What they talk about and what they do often comprehensively challenge the existing companies in the industry, and even want to disrupt the entire industry.
　　It’s good for an entrepreneur to be a little ambitious, but it usually backfires. A start-up company has limited resources in all aspects and no ready-made products and markets. Logically speaking, it should not do too many things. Almost without exception, those companies that started with a big spread ended in failure, and they failed very quickly. On the contrary, those start-ups that can focus on one point and solve a seemingly small problem to the extreme, even if they fail to go public in the end, will be acquired by large companies because of their own specific value. These ventures have a much higher success rate.
　　Therefore, almost all venture capitalists and institutions will require startups to simplify their task list as much as possible before investing, until it can no longer be reduced. Facts have proved that when the founders realize the significance of subtraction and can put their minds on making products with generational differences, they are close to success.
　　To give another example, the five companies with the largest market capitalization in the world today are Saudi Aramco (Saudi Arabian National Oil Company), Apple, Microsoft, Alphabet (Google’s parent company) and Amazon, and their market capitalization exceeds one trillion US dollars. , with an annual revenue of more than 200 billion U.S. dollars, but the product lines of these five companies are very short, and they can be counted with almost a slap.
　　In contrast, some companies have extremely long product lines and hold more than a dozen listed subsidiaries, but their annual income and market value are not as good as any of these five companies.
　　Multiplicative thinking: make good use of leverage to get twice the result with half the effort What does “leverage” mean
　　here ? For example, as long as a person can develop a skill to the extreme and excel in a field, many people will ask him to use his expertise to do things. Their efforts to solve a problem can be repeatedly used to solve similar problems without having to start all over again. This is the role of leverage.
　　People who are good at using leverage can use a skill repeatedly. In a popular saying, they can achieve “one fish, three meals”. People who are not good at using leverage have to start from scratch every time they do something. Everything is addition, and addition is naturally not as fast as multiplication.
　　Whether you can use leverage well depends on two factors: one is the thing itself, and the other is the person itself.
　　For example, if you studied mathematics or theoretical physics as an undergraduate, you can choose almost all science and engineering majors at the graduate level, and you only need to make up two or three professional courses. A large number of biologists engaged in biological research after World War II originally studied physics, but later turned to biological research because they saw the damage caused by the atomic bomb explosion to human beings.
　　Many people who are engaged in finance on Wall Street today have a background in mathematics and theoretical physics. That is to say, if you have a good foundation in mathematics or theoretical physics, you may do a lot of things in the future, because these two subjects teach people at the lowest level. logic.
　　In contrast, if you learn a certain major-specific skills in college, you will almost have to start from scratch if you change your major. This is what I have always emphasized. If conditions permit, general education should be done well in the foundation stage, because the knowledge acquired in general education has a particularly wide range of applications.
　　To give another example, in the computer industry, all courses or knowledge belong to one of the following three categories: system-related, algorithm-related, and application-related. The first two kinds of knowledge are more difficult to learn, but they have a leverage effect, and they can be mastered after they are mastered; the last kind of knowledge is the most practical, and they can work and earn money immediately after learning it.
　　Many people switch to computer science. In order to see the effect as soon as possible, they will learn the last kind of application-related knowledge, but the reusability of this knowledge is relatively poor. A person without a foundation in algorithms and systems will find that applied knowledge becomes obsolete very quickly.
　　People engaged in information technology today will have a “35-year-old middle-aged crisis”. The reason is not difficult to understand. The knowledge they have has no leverage effect, and its value is reduced by half every three to five years. On the contrary, some professionally trained practitioners with a solid foundation do not have this problem, because the basis of their knowledge is algorithms and systems.
　　Whether to do addition or multiplication when things happen reflects two different ways of thinking of people. Some people must emphasize the particularity of everything, and they are used to doing addition; some people can see the commonality between things, and they will greatly improve efficiency by doing multiplication.
　　We might as well make a list of the things we want to do and the things we have to do, delete all the things that have little relevance and importance to other things, and concentrate on doing things that can produce multiplicative effects.