The famous American mathematician Wiener has been a famous mathematical prodigy since he was a child, and at the doctoral conferment ceremony of Harvard University, when the principal saw his childish face, he asked him how old he was, and Wiener asked the audience a famous mathematical question about his age: "The cube of my age this year is a four-digit figure, the fourth power is a six-digit number, and these two numbers just use the ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9." Have you readers quickly guessed Wiener's age?
Wiener, who had a powerful talent, did indeed become a generation of masters, did not bury his own genius, and the story about him is now told.
<h1>From prodigies to mathematicians</h1>
Norbert Wiener (1894-1964) was a famous American mathematician of the twentieth century, who made outstanding achievements in both basic and applied mathematics, especially as the founder of "cybernetics", and Wiener was also one of the important contributors to the development of American mathematics.
Wiener's father was an immigrant from Russia, and he was also a language prodigy as a child, and later learned an astonishing forty languages through hard study, and later he came to Harvard University in the United States and became a professor of linguistics with his strong linguistic talent. Wiener's father was somewhat arrogant and wanted Wiener to excel, and Wiener grew up under the influence of his father.
Wiener's talent was so young that his father made many study plans for him, which he had to carry out whether he wanted to or not. But Wiener's talent makes it difficult for him to learn, and he doesn't get bored driven by curiosity. From literary fiction to physical chemistry, Wiener read everything and dabbled in a wide range of subjects, which laid a solid foundation for his future mathematical career. At the same time, at his father's request, language and mathematics remained Wiener's main subjects of study.
In order to avoid the talented Wiener drawing too much attention, Wiener's father did not let Wiener take the Harvard undergraduate entrance exam, but instead let him go to the mathematics department at Tufts College. The lower grade math course Wiener had already mastered, so he started directly from the Galois theory in abstract algebra. In addition to mathematics, Wiener was very interested in physics, especially the magical experiments, so he liked to fiddle with motors and radios. In the second grade, he abandoned physics and became fascinated with philosophy, reading and studying many philosophical works. Among the many philosophers throughout the ages, Wiener especially admired the versatile Leibniz and spinoza, who advocated high morality. Before long, the energetic Wiener fell in love with biology again, and in addition to studying the works of famous masters, he also liked to observe animal behavior and collect animal specimens. It turned out later that Wiener's extensive involvement did help him tremendously.
In 1909, at the age of fifteen, Wiener spent three years getting his undergraduate degree and, following his childhood interests, chose to pursue a doctorate in biology at Harvard University. His father, however, seemed less satisfied with this, and the following year arranged for Wiener to study philosophy at Cornell University, but it was not long before Wiener returned to Harvard, but studied mathematical logic instead. Eventually, at the age of eighteen, he easily got his Ph.D.
After graduation, Wiener, like many American students at the time, chose to study in Europe. He first came to Cambridge University because there were mathematical masters Russell and Hardy, and the former had a particularly great influence on him. Russell himself was a brilliant mathematical logician and mathematical philosopher, and his classes benefited Wiener greatly, and such cutting-edge knowledge could not be learned in the United States. Russell's scope was also extremely extensive, even going on to win the Nobel Prize in Literature, and his request to Wiener was to learn the latest physical theories developed by Einstein, Rutherford, and Bohr, because Russell was keenly aware of the enormous potential of these theories. At the same time, Wiener also learned a lot of basic mathematics, and in this regard, Hardy gave him great help, And Wiener later praised Hardy and said: "He is my ideal mentor and role model".
Since Russell was going to lecture in the United States the following year, he suggested that Wiener go to the University of Göttingen in Germany and study with German mathematicians such as Hilbert. After arriving in Göttingen, Wiener learned in-depth knowledge of algebra and differential equations, and gained a deeper understanding of the combination of physics and mathematics.
In 1913, Wiener published a paper on set theory in the Journal of the Cambridge Philosophical Society, marking the beginning of his mathematical career, and later, on the recommendation of TheodhIosgood, the head of the Harvard Department, Wiener went to work in the Department of Mathematics at MIT until his retirement. In particular, Wiener was invited to lecture at the Department of Mathematics at Tsinghua University in 1935, where Heiner discovered Hua Luogeng's mathematical potential. As we all know, Hua Luogeng later went to Cambridge University to study number theory with Hardy, and Wiener played a huge role in this.
Talking about a mathematician is necessary to mention his mathematical contributions, and we will introduce Wiener's main achievements from both basic mathematics and applied mathematics.
<h1>Achievements in basic mathematics</h1>
Anyone who has studied stochastic processes should know that brownian motion we are familiar with is often referred to as the "Wiener process", which is enough to see Wiener's influence on this field. At Russell's request, Wiener carefully read Einstein's paper on Brownian motion, and was inspired by this that Wiener became the first mathematician to examine Brownian motion mathematically. Wiener describes the path of motion of particles through functional space, and establishes powerful analytical tools such as Wiener measures and Wiener integrals, proving that the path of particle motion is continuous but almost everywhere is not different. Wiener's work was an important pioneering achievement in modern probability theory, and later the famous Japanese mathematician Kiyoshi Ito (1915-2008, Wolfe mathematician winner) developed the theory of random integrals on the basis of Wiener's work.
Studying at Cambridge made Wiener very interested in functional analysis, and for a while he even wanted to devote his life to the study of functional analysis. In 1920, Wiener generalized the French mathematician Fréché's generalized theory of limits and differentiation to general vector spaces and gave the axiomatic system. Wiener's results coincided with Barnach's, and mathematical ideas were almost the same, so these two works were once called Banach-Wiener space theory. But then Wiener's interest shifted and he faded out of the study of functional analysis. Today we all hail Barnach as the founder of functional analysis, but in fact, We should not forget Wiener's work in this regard.
Wiener borrowed functions from physics as objects of study for harmonic analysis, and then established a connection with communication theory through the powerful Fourier transform, and later obtained what is now called the spectral distribution state. To prove one of these key formulas, Wiener based on the work of Hardy and Littlewood to propose a powerful and original approach, the famous inversion theorem for non-zero absolute convergence Fourier series. Wiener's work in this area later became the basis of Barnach's algebra theory and was later even applied to the study of the prime number theorem.
In addition to these achievements, Wiener was also very successful in the potential theory of partial differential equations, and by defining the concept of capacitance of sets, Wiener established the Wiener criterion for the smoothness of the solutions of partial differential equations.
Unlike pure mathematicians, Wiener was very concerned about the application of mathematics, and in fact, Wiener's achievements in applied mathematics are more well known.
<h1>Achievements in applied mathematics</h1>
As we have already mentioned, Wiener is famous as the founder of cybernetics, and cybernetics can indeed be regarded as Wiener's most important achievement, and cybernetics is a combination of mathematics that links the study of common problems of common concern in disciplines such as autoregulation, communication engineering, computer and computational technology, and neurophysiology and pathology in the biological sciences.
In 1948, after a long period of thinking and research, Wiener published the epoch-making masterpiece "Cybernetics—or the Science of Control and Communication in Animals and Machines", which revealed the common laws of communication and control functions in machines and human nerve and sensory functions. As soon as this book came out, it shocked the scientific community like a stone, because such ideas completely broke through the traditional and mechanical scientific ideas, and it provided new blood not only mathematically, but also philosophically for the development of related sciences. Cybernetics has since developed rapidly and is now being applied in every way.
Wiener was also one of the pioneers of information theory, co-founder with Shannon (1916-2001). Unlike Shannon, Wiener introduced statistical methods based on systems that could be thought of as DC circuits. Wiener saw information as a time series of measurable events and communication as statistical problems, and thus could be studied mathematically as stationary stochastic processes and their transformations. Wiener clarified the principles and methods of information quantification, used "entropy" similar to "entropy" in physics to define the amount of information in continuous signals, and proposed the Shannon-Wiener formula that characterizes the amount of information.
Due to the needs of the war, Wiener was also actively involved in the study of filter wave theory, and the results of this can be directly applied to the problem of anti-aircraft fire control and radar noise filtering. Wiener's filtering model was later popularized, its application extended to more areas, and it is still one of the powerful tools for processing various dynamic data (such as meteorology, hydrology, earthquakes, etc.).
<h1>epilogue</h1>
Wiener's life experience is quite similar to that of von Neumann, who was a well-known prodigy from an early age, and both devoted the first half of their lives to the study of basic mathematics and the second half of their lives to the study of applied mathematics, and achieved great success in both aspects. Wiener received a mathematical education in the United States, and under the influence of the British and German schools of mathematics, winning the strengths of each family was the key to Wiener's success. But it has to be said that there is a huge gap between prodigies and masters, and Wiener is such a typical example of successfully crossing this gap.