Izrail Gelfand Mathematician, biologist, teacher and organizer of mathematics education Date of Birth: 02.09.1913 Country: USA

Biography of Israel Gelfand

Israel Moiseevich Gelfand was a mathematician, biologist, educator, and organizer of mathematical education. He was one of the greatest mathematicians of his time, working in the Soviet Union until 1989 and later in the United States. Gelfand authored over 800 scientific articles and around 30 monographs, and he was the head of a prominent scientific school. He was a professor at Rutgers University since 1990 and at Moscow State University (MGU) from 1941 to 1990. He held a doctorate in physical and mathematical sciences since 1940. Gelfand served as the president of the Moscow Mathematical Society (MMO) from 1966 to 1970. His major works are in functional analysis, algebra, and topology. He was one of the creators of the theory of normed rings (Banach algebras), which served as the starting point for his theory of rings with involution and the theory of infinite-dimensional unitary representations of continuous groups (known as Lie groups), which has significant importance in theoretical physics. Additionally, Gelfand made fundamental contributions to the theory of generalized functions, differential equations, the theory of topological linear spaces, inverse problems in spectral analysis, quantum mechanics, dynamical systems, probability theory, approximation and numerical methods, and other areas of mathematics. He also authored numerous works in neurophysiology of voluntary movements, cell migration in tissue cultures, proteomics (classification of protein tertiary structure), and algorithmization of clinical work for doctors. Gelfand was an honorary member of the Moscow Mathematical Society (1971) and an honorary doctor (Honoris Causa) of the universities of Oxford (1973), Sorbonne (1973), Harvard (1976), Princeton (1977), Uppsala (1977), Lyon (1984), and Pisa (1985). He was also an honorary foreign member of the American Academy of Arts and Sciences (Cambridge, Massachusetts, 1964), the American Mathematical Society (AMS, 1966), the London Mathematical Society (LMS, 1967), the National Academy of Sciences of the United States of America (NAS, 1970), the Royal Irish Academy (1970), the Royal Society of London (1977), the Royal Swedish Academy (1974), the Academies of Sciences of France (Académie des Sciences, 1976), Italy (Academia dei Lincei, 1988), and Japan (1989), the New York Academy of Sciences (Honorary Life Member since 1999), the European Academy of Sciences (fellow since 2004), and an academician of the USSR Academy of Sciences (1984, since 1991 a corresponding member). He was the first recipient of the Wolf Prize in Mathematics (1978), the Wigner Medal of the International Union of Pure and Applied Physics (1980), the Kyoto Prize (Japan, 1989), and the Leroy P. Steele Prize for Lifetime Achievement, the highest award of the American Mathematical Society, in 2005. Gelfand also received the MacArthur Fellowship (1994). He was awarded the Stalin Prizes (1951, 1953), the Lenin Prize (1961), the Order of Lenin (1954, 1956, 1973), the Order of the Red Banner of Labour (1963, 1983), the Order of Friendship of Peoples (1975), the Order of Honour (1953), and the State Prize of Russia (jointly with S.G. Gindikin and M.I. Graev, 1997). Gelfand is also known for becoming a leading scientist through self-education, without completing secondary education or attending university courses. Israel Moiseevich Gelfand was born into an accountant's family in the town of Okny in Transnistria (from 1920 - Krasnye Okny, later the district center of the Krasnooknyansk District of the Moldavian SSR and the Odessa Oblast of Ukraine). He studied at Jewish, Russian, and Ukrainian schools and showed a special interest in mathematics at a very young age. In 1923, his family moved to Olhopil in the Vinnytsia Oblast, where Gelfand attended secondary school and became friends with his classmate and future mathematician D.P. Milman. Due to difficult family circumstances, Gelfand was unable to complete his secondary education. In February 1930, he moved to Moscow to live with distant relatives. He was unemployed for some time and worked odd jobs, including as a controller at the Lenin Library, where he continued his self-education. In 1931, he started attending evening lectures on mathematics at several educational institutions, including Moscow State University, and soon became an assistant at the Mathematics Department of the Evening Chemical and Technological Institute. Despite not having a formal higher education, he was admitted as a graduate student in A.N. Kolmogorov's group in 1932 and began teaching at Moscow State University the same year. According to another student of Kolmogorov, V.I. Arnold, Kolmogorov said there were only two mathematicians with whom he felt the presence of higher intellect, and one of them was I.M. Gelfand. Gelfand cites the early death of mathematician L.G. Shnirelman as having the greatest influence on his creative development in mathematics. In addition to Shnirelman and Kolmogorov, other significant influences on the young mathematician included L.A. Lusternik, M.A. Lavrentiev, A.I. Plesner, and I.G. Petrovsky. Gelfand wrote his first scientific paper jointly with Kolmogorov. In 1935, he defended his candidate dissertation on "Abstract Functions and Linear Operators," which already contained important results and a methodology for using classical analysis to study functions in normed spaces. In 1938, Gelfand presented and defended his doctoral dissertation, in which he proposed his theory of commutative normed rings, establishing himself as one of the leading mathematicians of his time. The theory of normed rings by Gelfand revealed the close relationship between general Banach functional analysis and classical analysis for the first time. The use of maximal ideals not only gave impetus to the development of harmonic analysis but also to the development of algebraic geometry. This first creative period for Gelfand culminated in the monograph "Commutative Normed Rings" (co-authored with D.A. Raikov and G.E. Shilov), and Gelfand turned his attention to representation theory. In the early 1940s, in collaboration with M.A. Naimark, Gelfand developed the theory of non-commutative normed rings with involution, demonstrating that such rings could always be represented as rings of linear operators in a Hilbert space. This was a cornerstone of the modern theory of C*-algebras. During this time, Gelfand also worked on the representation theory of non-compact groups, which developed the theories of finite Frobenius and Schur groups, as well as compact Weyl groups. This led Gelfand to lay the foundations of integral geometry and to study the Radon transform. He also began working on generalized functions, inverse problems, numerical methods, mathematical physics, and generalized stochastic processes. During this period, he made important contributions to the field of geodesic flows on surfaces of negative curvature and made the first observation of the connection between automorphic forms and representations with S.V. Fomin. From 1958 to 1966, Gelfand published six volumes of the monographic series "Generalized Functions," which played a significant role in the development of 20th-century mathematics. In the 1960s, Gelfand worked on the topological classification of elliptic operators, based on the observation of the index as a homotopy invariant of the leading symbol. These discoveries led to the important Atiyah-Singer index theorem. He also worked with B.M. Levitan and L.A. Dikii on inverse spectral problems and scattering theory. Between 1968 and 1972, he wrote a series of significant works on the cohomology of infinite-dimensional Lie algebras (Gelfand-Fuks cohomology), including joint work with D.B. Fuks. This work led to a special class of foliations known as Gelfand-Fuks. In the field of differential equations, based on the works of S.L. Sobolev and L. Schwartz on generalized functions and distributions, Gelfand solved the inverse problem for Sturm-Liouville equations. He also worked on the representation theory of Lie groups, together with I.N. Bernstein and S.I. Gelfand. He continued to work in other areas such as integrable systems, combinatorics, the theory of hypergeometric functions, non-commutative mathematics, theory of multidimensional determinants, and developed the marching method for solving partial differential equations. Gelfand also explored the application of mathematical methodology in various fields of physics, seismology, and informatics. From 1935 to 1939, he worked as an associate professor at the Department of Mathematics at Moscow State University. From 1939, he became a senior research scientist at the Institute of Applied Mathematics of the USSR Academy of Sciences (IPM RAS) and worked there until 1990. From 1953, he was the head of the heat transfer department at the Institute of Applied Mathematics of the USSR Academy of Sciences. In 1967, Gelfand became the chief editor of the journal "Functional Analysis and Its Applications," which he founded. On October 23, 1953, he was elected a corresponding member of the USSR Academy of Sciences. The exclusion of Gelfand from international mathematical congresses and his non-election as a full member of the USSR Academy of Sciences for decades became one of the reasons for accusations of anti-Semitism against the Soviet mathematical establishment in the late 1970s. Immediately after the end of the Great Patriotic War, the "Gelfand Mathematical Seminar" was organized at Moscow State University, which met on Monday evenings for 45 years. The seminar invited both domestic and foreign mathematicians, such as P. MacPherson in 1981 and J.-P. Serre in 1984. Several generations of future mathematicians passed through this seminar. In the 1960s, Gelfand began working with two classes of the Moscow Second School, developing a series of lectures and seminars for students and organizing the first mathematics circle for schoolchildren at Moscow State University. Based on these activities, he created the Correspondence Mathematical School (later the All-Union Correspondence Mathematical School), which was attended by over 70,000 people over 30 years. Throughout these years, Gelfand served as the chair of its scientific council and developed educational materials for students. This school became the first institution of its kind, and similar schools were subsequently created in other scientific disciplines. In 1989, Gelfand settled in the United States and became a visiting professor at Harvard University (1989-1990) and the Massachusetts Institute of Technology (MIT) (1990). Since 1991, he was a professor in the departments of mathematics and biology at the Institute of Discrete Mathematics and Computer Science at Rutgers University in New Jersey. In 1992, he organized "The Gelfand Outreach Program" in the United States, an equivalent of the Correspondence Mathematical School for high school students, which he had previously led in Moscow (now known as the Gelfand Correspondence Program in Mathematics). The famous Gelfand seminar also continued at Rutgers University in Piscataway, New Jersey. In 1994, Gelfand was awarded the MacArthur Fellowship, also known as the "genius award," with a financial award of $500,000 for a period of five years. Since 1994, Gelfand and his family have been advocates of vegetarianism, and since 2000, veganism. Israel Moiseevich Gelfand founded a large scientific school, with his students including renowned mathematicians such as D.A. Kajdan, M.L. Konzovich, F.A. Berezin, I.N. Bernstein, E.B. Dynkin, I.I. Piatetski-Shapiro, A.A. Kirillov, and many others. Starting from his 50th birthday, international conferences have been held every 10 years in his honor. The last such conference was organized at Harvard University from August 31 to September 4, 2003, to celebrate his 90th birthday. From the late 1950s, Gelfand became interested in biology (biocybernetics) and later medicine (medical cybernetics), in part due to his student M.L. Tsetlin and possibly due to a family tragedy (the death of his youngest son Sasha from leukemia). In 1957, Gelfand and Tsetlin organized an interdisciplinary mathematical-physiological seminar, which met at the Burdenko Neurosurgery Institute of the USSR Academy of Medical Sciences until 1961. The medical part of the seminar was led by V.S. Gurfinke. The main topics of the seminar were the physiology of the heart and neurophysiology of motor movements. In 1960, Gelfand and the director of the Institute of Biophysics of the USSR Academy of Sciences (IBP RAS) G.M. Frank decided to create a permanent interdisciplinary department based on the participants of the seminar. This department, the Interfaculty Laboratory of Mathematical Methods in Biology, was established in the spring of 1961. In addition to Gelfand and Tsetlin from the mathematical side, it included V.S. Gurfinke and M.L. Shik from the medical side. In 1976, the laboratory became part of the A.N. Belozersky Institute of Physico-Chemical Biology at Moscow State University as the Department of Mathematical Methods in Biology. The department included groups on cellular biology (led by Yu.M. Vasiliev) and mathematics and medical diagnostics (led by I.M. Gelfand). Gelfand headed the department from its inception. Research on motor neurophysiology was conducted based on Laboratory No. 9 (neurobiology of motor control) of the Institute for Problems in Information Transmission of the Russian Academy of Sciences (IPPI RAS), in collaboration with Yu.I. Arshavsky. The result of this work was a series of publications on the neurocontrol of voluntary movements in cats and the mechanisms of synaptic information transmission in the cerebellum and descending spinal pathways. Initially, Gelfand worked on applying mathematical methods to describe the behavior of complex systems in the study of locomotor control mechanisms in mammals and the regulation of epithelial cell division in tissue culture. Together with his co-authors, he proposed the principle of least action and the concept of synergies in the control of elements in complex biological systems. Starting from the mid-1960s, Gelfand worked on the systematic description of cell proliferation and morphogenesis in epithelial and mesenchymal tissue cultures and modeling wound processes in these cultures (in collaboration with Yu.M. Vasiliev). Another area of research involved the mathematical description of mechanisms of tumor transformation and metastasis. All this research is now being carried out by the same scientific groups primarily at Rutgers University in New Jersey. Gelfand also worked in bioinformatics and algorithmization of surgical and therapeutic practices (medical cybernetics), for example, in prognostic issues and their application to emergency surgical tactics in gastroduodenal ulcer bleeding and predicting complications in myocardial infarction.