How important is mathematics?Look at the mathematics behind the mobile phone

Text ｜ Zong Chuanming (Professor of Chair at Tianjin University)

In recent years, under the importance of the country and media propaganda, people have formed consensus "mathematics". People have realized that mathematics plays an important role in every branch and link of science and technology.

It is difficult to imagine what astronomy and physics that do not have mathematics support is like, and it is even more difficult to imagine what will happen without mathematical protection.

In fact, today, when the state strongly advocates primitive innovation and seeks to break through the neck of the stuck, we should even realize that mathematics has played a decisive role in modern science and technology, but in some most critical scientific and technological processes.

Taking the most familiar high -tech product smartphones as an example, mobile phones are micro computers with communication functions: its intelligence is designed by mathematicians such as Alan Turing and von Neumanman. Claude Xiangnon's information theory, Nonberry Venna's control theory, and modern cryptographic guarantee.

The birth and development of computers, information theory, control theory, and modern cryptography are led by mathematics.

The birth of a computer

Electronic computers are the greatest invention of the last century. It not only brings tremendous changes to every field of science and technology, but also improves everyone's daily life, and even changes our way of thinking and profoundly affects the future development of human civilization.

Since ancient times, people have continuously explored and inventing high -efficiency computing tools to extend our ability to solve problems: more than 3,000 years ago, people invented the abacus; more than 400 years ago, British mathematician John Napier invented the number of pairs of pairs On this basis, people manufactured the calculation ruler; in 1642, French mathematician Blaise Pascal created an arithmetic aircraft that can be performed and subtracted; • Gottfried Wilhelm Leibniz created the multiplication machine that can be used for computing; Around 1833, British mathematician Charles Babbage designed and manufactured a differential computing program differential machine. And analysis machine.

In the early development of electronic computers, many scientists and engineers made outstanding contributions: in 1930, American scientist Vannevar Bush built the earliest simulation machine at Massachusetts Institute of Technology; in 1936, Britain, Britain Alan M. Turing (Alan M. Turing) proposed the theoretical framework of the computer on the basis of mathematical logic (a branch of mathematics), which not only affirmed the computer's calculation function, but also gave it the mission of logical reasoning; around 1940, German engineer Konrad Zuse proposed the concept of computer program control and built a model machine independently; in 1945, American mathematician John Von Neumann proposed according to the memory function of the brain. Electronic computer schemes with storage programs.

On the basis of these pioneers, electronic computers were born and developed rapidly in the UK and the United States around 1945.

Alan Turing was born in London in 1912. In 1931, he was admitted to the King's College of Cambridge to study mathematics. )Impact. In 1936, he published the "Application of Digital Calculation in Decisive Difficulties".

The paper describes a machine that can assist mathematics research, which was later called a Turing machine. The mission of the first assignment of the machine for symbolic logic reasoning was laid the foundation for later computers and artificial intelligence.

In 1938, Turing obtained a Ph.D. in Mathematics of Princeton University under the guidance of Qiu Qi. During World War II, he called to the British Intelligence Center Bla Cheli Park to engage in the work of deciphering the German password. He led the world's earliest electronic computers and successfully decoded the German password. For some time after the war, Turing has been participating in the development of electronic computer development at the University of Manchester.

In 1966, in order to commemorate his foundation in computer science, the Alan Turing Award was established by the American Computer Association (ACM).

Alan Turing

John von Neumanman

John von Neumanman was born in Budapest, Hungary in 1903. In 1926, he obtained a PhD in mathematics from the University of Budapest under the guidance of Leopold Fejer. Subsequently, he went to the University of Goshgen, Germany as the assistant of Hilbert, a major mathematician, and was deeply influenced by his mathematical logic theory. In 1930, he immigrated to the United States and served as a professor of mathematics at Princeton University and a professor of mathematics at the Princeton Higher Research Institute.

Based on mathematical logic theory, he began to study computer construction. In 1945, he proposed an electronic computer solution that can store programs on the basis of joint discussion, which specifically introduced the idea of ​​making electronic computers and programming. This solution clearly lays the composition of the computer: the operationer, the controller, the memory, the input and output equipment.

In 1999, in order to commemorate his foundation in computer science, the John von Norman Award was established. In the past 100 years, with the rapid development of science and technology, electronic computers have gradually developed from the initial electronic tube digital machine to transistor digital machines, integrated circuit digitals, until today's large -scale integrated circuit computers. The operating system has also undergone tremendous changes. However, regardless of the development of hardware and software, computers have always used the design ideas of Turing and von Norman.

The birth of information theory

Since there are human activities, people have to face the problem of reliable information transmission: gestures, sounds, text, telegrams, telephones, Internet, etc.

In 1837, British inventor Charles Wheatstone and William CookE and American inventor Samuel F. MORSE almost invented the telegrams. In 1860 and 1876, Antonio Meucci, the inventor of Italy, and Alexander G. Bell, Alexander, the inventor of the United States, respectively. In 1895, the Italian inventor Guglielmo Marconi successfully received and sent the radio newspaper for the first time.

These new technologies provide a means for large -scale and long -distance information transmission. However, how to ensure accurate and efficient transmission has ushered in challenges. In 1924, Harry Nyquist, a scientist at Bell Lab, began to study the factors affecting the speed of telegram transmission, and for the first time, the information transmission speed was given quantitative portrayal. In 1928, Ralph v. Hartley, who was in Bell Lab, further quantitatively studied the ability of communication system transmission information and tried to measure the channel capacity of the system.

Based on the work of Naquist and Hartley, in 1948, Claude Shannon published epoch -making papers "communication theory of communication", thereby announcing the birth of information theory. This paper laid the foundation for modern information theory with another paper published in 1949.

For the first time, Xiangnon's work has established a mathematical model for the communication process on the basis of probability statistics and geometric space and derives some of the most important quantitative principles (three theorems of information theory) through mathematical models. These models and principles not only guide the theoretical research of information theory, but also ensure all aspects of communication engineering technology.

Claude Xiangnon

Claude Xiangnon was born in Michigan, USA in 1916. He obtained a PhD in Massachusetts Institute of Technology under the guidance of Frank L. Hitchcock, Frank L. Hitchcock, 1940.

In 1941, he joined Bell Lab Mathematics and worked until 1972.

Since 1956, he has also been a professor at MIT and has become a honorary professor in 1978. In 1972, the foundation of the IEEE Information Society set up the Claude Fragrant Award for the foundation of his foundation for information theory.

In the past century, with the rapid development of computer technology, information communication has become part of everyone's daily life through mobile phones and the Internet.

In this development process, mathematical disciplines such as mathematics, map theory, and digital theory have played an extremely critical role. For example, many famous mathematicians have made outstanding contributions.

The birth of control theory

The birth of control is one of the greatest scientific achievements in the 20th century. The theory of control is a product of multi -disciplines such as mathematics, computer technology, radio communications, neurophysiology, and language.

It is subject to the characteristics of the communication and control of various systems as the object to study the laws of their own movements based on some changes in the surrounding environment.

The idea of ​​automatic control has a long history. Around 1760, James Watt installed a speedler on his steam engine to automatically adjust the running speed of the steam engine.

In 1858, Alfred R. Wallace made a research and explanation of this.

In 1868, James C. Maxwell, a well -known physicist and mathematician, studied the automatic speed regulator and discussed this self -regulating device for the first time.

In 1927, Harold S. Black, an engineer in Bell Lab, began to explore the use of negative feedback information to control the amplifier.

In 1932, Nequist discovered the stability conditions of negative feedback amplifiers.

In 1943, Arturo Rosenblueth, Norbert Wiener, and Julian Bigelow used mathematical models to study the control of feedback information.

In 1945, Wina promoted the concept of feedback to the general control system, and understood the feedback as the process of extraction from the output of the controlled object as the next step, thereby affecting the process of re -output.

In 1948, Nobot Venna published the famous "Control theory -Science on Control and Communication in Animals and Machines", marking the birth of control theory as a discipline. Wina regards control theory as a general law that studies machines, life and society. More specifically, it is a science that studys how to maintain a balanced or stable state under the environmental conditions of the dynamic system under the environmental conditions of the changes.

The basis of control is information, all information transmission is to control, and any control depends on information feedback to achieve. Establishing mathematical models for quantitative research on the basis of micro -division equations, optimization, probability statistics, and blurming mathematics.

Nobot Venna

Nobot Venna was born in Missouri, USA in 1894. In 1913, he obtained a PhD in Harvard University under the guidance of Karl Schmidt and Josiah Royce. Subsequently, he studied at the University of Cambridge and the University of Gosteen in Germany in the United Kingdom. Essence

Since then, he has been teaching at Massachusetts Institute of Technology. From August 1935 to May 1936, he taught mathematics at Tsinghua University, which had a great impact and help on Hua Luogeng. In 1967, the foundation of the American Industry and Applied Mathematics Society (SIAM) set up the Nogt Virgin Award for his foundability contribution to control theory.

Since the founding control theory, Von Nomanman, Lev S. Pontryagin, Jacques-Louis Lions, etc. This theory.

Today, the theory of control has been widely used in high -tech industries such as aerospace, robot systems, and artificial intelligence. In fact, without scientific control theory, there is no today's aerospace achievements.

The foundation of mathematics lays the foundation of modern cryptography

In 1969, the Internet was born in western United States. These computer networks are connected by a set of general protocols to form a logical unified computer system. Using the Internet can send information to thousands of kilometers in an instant, it is the basis of the information society.

With the advent of the information age, information security has become a prominent issue. In military communication, the enemy always wants to intercept and decipher the other party's communication instructions. During World War II, passwords used to be the decisive factor of some wars, such as Sicily's landing, the Battle of Alaman, the naval battle and shot down the fifty -sixth generals of Yamamoto. In ordinary communication, from senior hackers to low -level scammers want to steal information about others. Therefore, modern cryptography came into being.

In 1976, Whitfield Diffie and Martin E. Hellman, the American cryptist, proposed the idea of ​​public key password system.

This system is different from the traditional password system. It requires the key to appear. One is the encryption key (public key), the other is the decryption key (private key), and the private key cannot be derived from the public key. In this way, even though the stealing party knows the encryption key, it is difficult to crack the password.

Due to this revolutionary solution, Diffei and Herman won the 2015 Turing Award.

Herman and Difei

Levist, Samil and Adman

In 1977, Ronald L. Rivest, a three -digit mathematician at the Massachusetts Institute of Technology, ADI Shamir and Leonard M. ADleman -based in mathematics For the first time, the problem of large -scale decomposition realizes this idea and proposes the RSA encryption solution.

As early as the ancient Greek period, Eu Jilin had proven that each positive integer could be uniquely decomposed into a product. However, when the integer is large, how to find a specific decomposition method is a very difficult mathematical problem.

It is precisely because of the complexity of this problem that the security of the RSA password system is guaranteed. Due to this plan, Levest, Shamir and Ademan won the 2002 Turing Award.

Since 1976, mathematicians and cryptologists have established a variety of cipher system based on basic mathematical difficulties. For example, the encryption system based on discrete numbers, an encryption system based on the oval curve, and so on. The application of these password systems has greatly promoted the development of information science and industry, and provided guarantee for information security in the Internet age. Since then, the basic mathematics that was originally considered useless has directly entered the core areas of high -tech.

Mathematics escort quantum technology

In the past 30 years, quantum science and technology have developed rapidly. Although in the experimental exploration phase, quantum computers have been widely considered to be the next technological revolution engine.

In the era of quantum computers, the intelligence and computing speed of computers will greatly increase. This will bring hope and dawn to the resolution of many scientific issues.

In 1994, Peter SHOR, a mathematician in Bell Laboratory in the United States, proposed quantum algorithms and applied to cryptography.

His work shows that in the era of quantum computers, the public key password system based on integer decomposition will be broken. In other words, the RSA password system will no longer be safe under quantum attacks. Samal received a doctorate in Mathematics at Massachusetts Institute of Technology in 1985 and was a world -renowned contemporary mathematician.

On the basis of Sarl's pioneer work, people further prove that in the era of quantum computer, a variety of extensive -application -based password systems such as discrete -of -numbers -based password systems and elliptical curve systems will be broken. Quantum science has brought severe challenges and crisis to the current practical password system.

Peter Sael

As early as 1840, the great mathematician Carl Friedrich Gauss proposed the concept of grid.

Nearly two hundred years have passed, and under the efforts of many mathematicians, the theory has developed into an important mathematical branch.

In 1996, American mathematician Miklós Ajtai, based on the theory, constructed a set of password encryption systems. Ajette received a PhD in mathematics at the University of Budapest, Hungary in 1976, and worked at the IBM Research Institute in the United States since 1991.

More than 20 years have passed, and people have not found quantum algorithms that break through this password system.

Crocodists generally believe that the style of the style can resist quantum algorithm attacks. At the same time, people are constantly exploring the new anti -quantum attack password system to escort the technology of the quantum era.

The development of science and technology is endless. Therefore, we must recognize the source of scientific and technological innovation, layout talents, and work hard to seize the opportunity.

In the past century, mathematics has proven that it has an irreplaceable intelligent role in the scientific and technological revolution. In the future scientific and technological revolution, mathematics will not be absent.

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