Wu Jun, a graduate of Tsinghua University and Johns Hopkins University, has many identities.

Silicon Valley investor, founding partner of Fengyuan Capital, famous natural language processing expert and search expert, and manager of "getting" App column letter in Silicon Valley. He was one of the early employees of Google. During his tenure at Google, he led and participated in many R&D projects, and was the inventor of Google search algorithm in China, Japan and Korea. At the same time, he is also a best-selling author. In addition to the beauty of mathematics, he also wrote many bestsellers, such as Light of Civilization, Intelligent Age and Top of the Tide.

About this book

In this book, according to his own personal experience, Wu Jun introduced us to various applications of mathematics in the field of information science, as well as the mathematical wisdom of two famous masters of mathematical information science. Through these practical cases, he showed us the close connection between mathematics and our present life, and the simple beauty behind mathematical thought.

Core content

The core idea of this book is that mathematics is closely related to our life, and many unexpected problems in life can actually be solved by mathematical methods. Mathematics can help us to jump out of the superficial phenomenon of problems and grasp the logic behind the development of things, so as to solve complex problems skillfully; At the same time, because mathematics has simple consistency, we can often solve different kinds of problems with one idea. The beauty of mathematics lies in its practicality and simplicity.

1. Mathematics can help us jump out of appearances and grasp the logic behind things.

Making computers capable of processing human language is the basis of many of our work today, so scientists have been studying this problem for a long time.

In fact, when computers were first asked to process languages, scientists insisted that if machines want to learn translation or language recognition, they must let computers learn grammar first, just like people. But later people found that there were too many grammatical rules to exhaust. This method was gradually proved to be infeasible in the 1970s.

At the same time, Jarinik, a famous computer scientist, and his laboratory invented the method of processing natural language by statistics, which greatly improved the recognition rate and scale of speech recognition. Their method mainly uses the "Markov hypothesis", that is, it is assumed that the probability of each word in a sentence is only related to the previous word, just as the word "daily limit" is most likely to appear after "stock". Then, as long as the computer is given enough machine-readable text, the computer can calculate the probability that a word appears after a particular word. In this way, as long as the probability of all the words appearing in a sentence is multiplied, it is the probability of the sentence appearing. The most probable sentence is the correct sentence we need.

When solving problems, paying too much attention to imitation but being inflexible is also an important reason for failure. Just like when people made airplanes, they always wanted to design the wings of airplanes into the wings of birds, but in the end, the first airplane made by the Wright brothers relied on aerodynamics, not bionics. Therefore, it is a very important ability not to be confused by the superficial phenomena of things, and mathematics can help us jump out of appearances and grasp the logic behind the development of things.

Secondly, the consistency of mathematics embodies the beauty of mathematics.

Cosine theorem is an important mathematical theorem to reveal the relationship between the angles of a triangle. Using cosine theorem, the included angle between two sides of a triangle can be calculated only by the vectors of these two sides. In order for the computer to process human language, scientists should first turn the words in news into a set of computable numbers, and then design an algorithm to let the computer calculate the similarity of any two news by cosine theorem, so as to determine the classification of news.

Words in news can be divided into content words and content words. The notional words "whatever is right" are not helpful to judge the news classification, so we will not consider them, while the notional words "stock" and "interest" are very helpful to judge the news classification and are the focus of our attention. We will use these notional words to calculate the feature vectors of news. As long as the unique feature vector is calculated for each news, then the classification of any news can be judged according to the characteristics of words that often appear in each kind of news.

In the work of news classification, the computer does not need to understand every news, but only needs to find the similarities of similar news, so it can be solved by cosine theorem, which proves the consistency of mathematics. Although things are ever-changing, the mathematical models for dealing with them are similar or even the same. This consistency is a kind of "mathematical beauty".

Third, the beauty of mathematics is that a good method is often the simplest and clearest method.

Now each of us uses search engines almost every day. It can search a large number of web pages you need in a short time. The key behind this is mathematics.

The basic mathematical principle behind search engines is actually very simple. Binary is the simplest counting method in the world, because binary only has two numbers, 0 and 1, and binary can also mean "yes" and "no" logically. Boolean operation is a binary operation, which was invented by a British mathematician named Boolean in the19th century. There are only three basic operations: and or no, very simple.

The search engine will convert the sentences queried by users into Boolean expressions to see if the search keywords appear on this webpage. 1 means yes, 0 means no ... in this way, each page will be converted into a number. Finally, just take out the webpage displayed as 1, and this is the search result you want. Computers can perform Boolean operations very quickly, so search engines can easily search a large number of web pages in a short time.

Newton once said, "Truth is always simple in form, not complicated and ambiguous". The beauty of mathematics is also reflected here. If you can solve problems with mathematical tools, the basic idea should be simple no matter how complicated your method is.

Fourth, the mathematical thoughts of two masters of mathematical information science

Wu Jun, the author of this book, thinks that there are actually two kinds of technologies, namely "technique" and "Tao". "Skill" refers to the specific skills and methods of doing things, and "Tao" refers to the principles and principles of doing things.

The purpose of this book is to preach, not how specific it is. Because many specific technologies will soon become obsolete. People who pursue "art" will have a hard life. Only by mastering the essence and essence of technology can we do things with ease.

The first master was amit Singh. He is an academician of the American Academy of Engineering and a technical god of Google. Singh's philosophy of doing things is to help users solve 80% of the problems first, and then slowly solve the remaining 20%, which makes him always solve problems better in a short time. Amit Singh also pursues a simple philosophy. He thinks that the simplest things are often the best. Because he thinks that the simpler things are, the easier it is to explain the truth, and the easier it is to find mistakes.

The second master is Michael collins, who is good at using mathematics to do his work to the extreme. Collins' philosophy is the pursuit of perfection and perfection. For example, he once designed an analyzer to help computers process natural languages, not to test any theories, but to make the best analyzer in the world. Collins' characteristic is to do things to the extreme. He didn't deliberately pursue triviality and complexity, nor did he completely oppose amit Singh. He is just pursuing mathematical rigor and perfection.

Both amit Singh's simple philosophy and Michael collins's perfect philosophy have brought the power of mathematics to the extreme, allowing mathematics to solve complex problems in the best way. These two philosophies are not two sides of the same coin, but complement each other.

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1. In fact, excessive imitation without flexibility is also an important reason for failure when solving problems. Just like when people made airplanes, they always wanted to design the wings of airplanes into the wings of birds and swing them up and down to take off. But in the end, the first plane made by the Wright brothers relied not on bionics, but on aerodynamics.

2. Although things are ever-changing, the mathematical models for dealing with them are similar or even the same. This consistency is a kind of "mathematical beauty".

Newton once said, "Truth is always simple in form, not complicated and ambiguous", and the beauty of mathematics is also reflected here. If you can solve problems with mathematical tools, the basic idea should be simple no matter how complicated your method is.

Those who pursue "skills" will work hard all their lives. Only by mastering the essence and essence of technology can they do things with ease.

Many people fail not because they are not excellent, but because they have the wrong methods. If you pursue "Gao Daquan" from the beginning, but you can't solve the problem for a long time, the final result will be very poor.