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This article comes from the official account of Wechat: back to Park (ID:fanpu2019). Author: Chen Guanrong (City University of Hong Kong)

"Mathematics is part of culture, just like music, poetry and philosophy."

-- Israel Gale van der

Israel Gelvander (September 2, Israel Moiseevich Gelfand,1913-October 5, 2009) was born into an ordinary Jewish family in the town of Okny (now known as Krasni Okny) in southern Ukraine.

After graduating from junior high school, Gale van der entered a vocational and technical school to be trained as a chemical experimenter, but dropped out before graduating. In early 1930, at the age of 16, he came to Moscow alone from his hometown to seek his own livelihood. He works as a temp everywhere in Moscow, but he often loses his job. Later he found a job as a loan librarian in the Lenin library. There, he eagerly taught himself what he had not learned before. He became acquainted with several college students and often arranged time to follow them to attend lectures at Moscow University. The most rewarding thing for him was to attend the class on complex functions organized by mathematician Mikhail A. Lavrentyev,1900-1980.

In 1932, Gelvander, without a college degree, was admitted as a graduate student at Moscow State University because of his outstanding mathematical performance. He studied under the famous mathematician Andrey N. Kolmogorov,1903-1987. From then on, in Gale van der's own words, his academic career was "ordinary and formal, entering the usual track of mathematicians".

Fig. 1 Gale van der (1913-2009) 1. Before introducing how Gelvander "entered the usual orbit of mathematicians" and grew into "one of the greatest mathematicians of the 20th century", let's review how he studied mathematics when he was a child.

There is only one middle school in Gale van der's hometown of Okny. When he was in junior high school at the age of 12, he realized that some geometric problems could not be solved by algebraic methods. On one occasion, he calculated a chord length every five degrees and made a table for the figure of the sine curve. Later, of course, he understood that he had "created" a trigonometric function table. During that time, he finished an elementary algebra problem set without a corresponding algebra textbook. This small success made him understand and remember that he can enter a new field of mathematics by solving problems.

By the age of 13, he had a special interest in plane geometry. He noticed that some right triangles had sides of 3, 4, 5, or 5, 12, 13, and wanted to find all right triangles whose sides were integers. As a result, he "invented" the Pythagorean theorem.

At that time, his family was poor and often got sick. But whenever he fell ill in bed, especially when the school was on holiday, he studied math by himself, and the result was very rewarding. Many years later, he often let his son stay at home for a few more days after his illness, saying that capable students could do a lot of things at home when they were ill.

When Gale van der was a child, it was hard for others to imagine that his family was poor. For example, it was extravagant to ask his parents to buy an exercise book. Then he finally got an exercise book, so every page was filled with statements and proofs of mathematical theorems. It taught him how to write a math book, he later recalled.

For Gale van der, who is very talented in mathematics, the lack of mathematics books is a serious obstacle to his further development. He often sees advertisements for advanced mathematics books and guesses that higher mathematics is probably very interesting. Unfortunately, it is impossible for his poor parents to buy these books for him. At the age of 15, he had appendicitis and needed to go to the big city Odessite hospital for surgery. He took the opportunity to cheat on his parents, saying that I would not go to the hospital if you didn't buy me advanced math books. His parents had no choice but to buy him a Ukrainian course in Advanced Mathematics. Poor parents only had enough money to buy the first volume, which included plane analytic geometry and elementary calculus.

Gale van der felt lucky to have the opportunity to start studying advanced mathematics in a regular college course. From the third day after the operation, he couldn't wait to read the book, interspersed with a novel by the French writer Emile Zola,1840-1902. During his nine days in the hospital, he finished reading the first volume of higher mathematics. During this period, he also independently deduced the Euler-McLaughlin formula, the recurrence formula of Bernoulli numbers, and the summation formula of the p power of the first n natural numbers. For him, the biggest gain is to exercise the ability to solve problems independently and develop the good habit of continuing to explore further results after solving problems.

In 1930, the 16-year-old Gale van der said goodbye to his parents and went to Moscow to earn his own living.

2. The outstanding contribution of mathematicians in 1932, Gelvander became a graduate student at Moscow State University, studying under the great mathematician Kolmogorov.

During the postgraduate study, under the guidance of his tutor, Gale van der entered the emerging field of functional analysis at that time. In 1935, Gale van der received an associate doctorate on abstract functions and linear operators. He proved many basic properties of functional analysis, especially complete normed spaces, and established some universal methods to transform many of these problems into classical analysis problems by continuous linear Functionals.

In 1940, Gale van der received a doctorate in physics and mathematical science from the Soviet Union. In his thesis, he founded the theory of commutative normed rings, which laid the foundation of Banach algebra. In this field, he later established a new representation theory and extended the spectral theory of linear operators in Hilbert spaces to normed algebra. An interesting example is that he applied the theory and technique of normed rings and used only five lines to deduce a famous theorem proved by Norbert Weiner (Norbert Wiener,1894-1964) in an earlier long article: if a function without zero can be expanded into an absolutely convergent Fourier series, then its reciprocal can also be expanded into an absolutely convergent Fourier series. Next, Gelfander initiated the study of C * algebra.

In 1943, Gelvander became a professor at Moscow State University and later worked at the Institute of Applied Mathematics of the Soviet Academy of Sciences. In the 1950s, Gelfander carried out a large number of fruitful studies in many branches of pure mathematics and applied mathematics. His main contributions include functional analysis, harmonic analysis, group representation theory, integral geometry, generalized functions, differential equations, mathematical physics and other fields. In addition, he carried out in-depth research on biology and physiology after 1958 and established and led an institute of biophysics at the Soviet Academy of Sciences. In the field of biomedicine, he studied the mathematical problems of X-ray and CT scanning, and improved the image transformation of Johann K. A. Radon,1887-1956, thus creating a new subject of integral geometry.

Gale van der published nearly 500 papers, of which 33 were published in his own name, accounting for only 7% of the total, while there were 206 co-authors, including Chinese mathematician Xia Daoxing. He also published 18 textbooks and monographs. At the end of 1980s, Springer Publishing House published three volumes of selected works of Gelvander, including 167 papers of the author's choice. From 1958 to 1966, Gelfander took the lead in editing and publishing the six-volume masterpiece Generalized function. Among them, the first volume discusses the definition, basic properties and Fourier transform of generalized functions and various special types of generalized functions; the second volume examines various types of basic function spaces and their generalized functions and the corresponding Fourier transforms; the third volume uses generalized functions to study the existence, uniqueness and well-posedness of solutions to the Cauchy problem for systems of partial differential equations and the expansion of self-adjoint differential operators according to eigenfunctions. The fourth volume studies the kernel space and its applications and introduces the equipment Hilbert space, as well as the measurement theory on positive definite generalized functions, generalized random processes and linear topological spaces. The fifth volume is based on integral geometry. The harmonic analysis of Lorentz groups and related homogeneous spaces is discussed. In the sixth volume, representation theory and automorphic functions are introduced. This set of monographs enjoys a high international reputation and has been translated into Chinese, English, French and German. It is the basic textbook and reference material for analytical mathematicians.

Fig. 2 the mathematical research of Gelvander (Moscow State University) is closely related to mathematics teaching. He often teaches junior undergraduates at Moscow State University and has held functional analysis discussion classes for young teachers and graduate students since 1944, followed by theoretical physics discussion classes. The discussion class organized and directed by Gelvander continued into his later years and became a major base for the Soviet Union to develop functional analysis and train new talents in mathematics. Gale van der has always been humorous and witty. He said many times: "this discussion class is for ordinary high school students, good undergraduates, excellent graduate students and outstanding professors." A group of young people who worked with him came successively from his discussion class, and many of them later became famous mathematicians, including F. Berezin, J. Bernstein, E. Dynkin, A. Goncharov, D. Kazhdan, A. Kirillov, M. Kontsevich, A. Zelevinsky, etc., especially the 1990 Wolf Mathematics Prize winner Llya Piatetski-Shapiro (1929-2009). According to Piazetsky-Shapiro, there were three great figures in Soviet mathematics at that time, namely, Kolmogorov, Gelvander and Igor Shafarevich (Igor R. Shafarevich,1923-2017). "Gelvander is the most outstanding," he said. He has both the profound mathematical attainments of Shafarevich and the extensive knowledge of Kolmogorov. In addition, Gelvander has a special talent: he can do research in several basic areas at the same time without effort.... in this respect, Gelfander is unparalleled. "

It is worth mentioning that, perhaps because his family was poor and dropped out of school when he was young, Gale van der paid special attention to the mathematics education of middle school students. He was one of the founders of the Mathematical Olympiad in Moscow in the 1930s and participated in the establishment of a distance mathematics correspondence school. Together with several mathematicians, he has written five books on basic mathematics for middle school students: "Algebra", "Geometry", "Trigonometric functions", "functions and Images" and "coordinate methods". The English version was published by Springer Publishing House in 2000s, and the Chinese translation was included in the Galvander Middle School students' Mathematical thinking Series.

Gelvander recalled the past at the age of 90 and was very grateful to his teachers at all stages of his life: "for me, the most important teacher was Schnirelman, a talented mathematician who died young. Then there are Kolmogorov, Lavrentyev, Plesner, Petrovsky, Pontriagin, Vinogradov, Lusternik, they are different... but they are all great mathematicians. I am very grateful to all of them. I have learned a lot from them."

Fig. 3 some of Gale van der's works 3, awards and honors Gale van der has given three plenary reports at the International Congress of mathematicians (1954, 1962, 1970), which is enough to show his important position in the development of contemporary mathematics. In fact, so far, only Vito Volterra (Vito Volterra,1860-1940) has given four plenary reports, and Erigadang (É lie Cartan,1869-1961), Lars Alfus (Lars Ahlfors,1907-1996) and Andre é Weil,1906-1998 have given three plenary reports.

Gelvander was elected Academician of Communications of the Soviet Academy of Sciences in 1953 and Academician in 1984. He was president of the Moscow Mathematical Society from 1968 to 1970. Later, he won the Lenin Medal three times (the first in 1973), the Kyoto Award, known as the "Japanese Nobel Prize" (1989), the highest honor in American culture, MacArthur Fellow (1994), and the Lifetime Achievement Award of the American Mathematical Association (2005 L. P. Steele Prize).

Gelvander is also a member of the Royal Society, the National Academy of Sciences, the American Academy of Arts and Sciences, the Paris Academy of Sciences and the Royal Swedish Academy of Sciences. He received honorary doctorates from Oxford University, Harvard University and the University of Paris.

In 1981, Gelvander and German mathematician Carl L. Siegel,1896-1978 shared the first Wolf Mathematics Prize established by the Wolf Foundation in Israel. However, because of his participation in an open letter signed by 99 Soviet mathematicians in 2016, demanding the release of mathematician Alexander Yesenin Wolpin (1968), a mathematician who had been locked up in a mental hospital for dissent, and because the Soviet Union had previously severed diplomatic relations with Israel, Gelfander was banned from attending the awards ceremony that year, embarrassing the Wolf Prize for the first time. It was not until 1988 that Gelvander was able to go to Israel to reclaim the medal he won ten years ago.

Incidentally, the only Chinese mathematicians who have won the Wolf Prize for Mathematics so far are Shiing-Shen Chern (1983) and S.T. Yau (2010).

Fig. 4 Gale van der lecturing at MIT 4. Unfinished Story in 1989, the 76-year-old Gale van der emigrated to the United States. After visiting Harvard University and Massachusetts Institute of Technology, he was hired as a tenured Distinguished visiting Professor at Rutgers University University.

Gale van der died on October 5, 2009, in New Brunswick, New Jersey, at the age of 96.

Gelvander and his first wife, Zorya Shapiro, had three sons, Sergei and Vladimir, but the youngest, Aleksandr, died of leukemia in 1958. The pain of that year became the main reason why he began to study biomedicine. He and his later wife, Tatiana, had a daughter, also named Tatiana.

In this way, the Ukrainian mathematician Gale van der spent his extraordinary life, leaving a large number of valuable mathematical wealth for mankind.

On September 2, 2003, Gelfander gave a brief speech at a dinner to celebrate his 90th birthday (see "speech at the 90th birthday party by Gelfand, a Ukrainian-born mathematician") on his views on mathematics and why he is still doing it at such an old age. At the end, he made a change of words and made a digression:

"finally, I would like to give an example other than mathematics. There is a short and incisive sentence that combines the features of simplicity and precision that I mentioned earlier. This is what Nobel Prize winner Isaac Bashevis Singer said:'as long as people still destroy the weak with knives and guns, there will be no justice.'"

Today, it seems, he foresaw an unfinished story.

Fig. 5 Gale van der lecturing at Rutgers

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