| 1925-1930 | Student of Tbilisi State University Faculty of Physics and Mathematics |
| 1930-1933 | Post-Graduate Student of USSR Academy of Sciences |
| 1937 | Cand.Sci.(Phys.& MAth.) |
| 1940 | Dr.Sci.(Phys.& Math.) |
| 1929-1933 | Observer of Georgian Geophysics observatory |
| 1933-1937 | Junior researcher of Tbilisi State University, Faculty of Physics and Mathamatics |
| 1933-1940 | Scientific secretary of Mathematical Institute of the Georgian Branch of the USSR Academy of Sciences |
| 1936-1938 | Head of the theoretical geophysics department at the Geophysics Institute of the Georgian Branch of the USSR Academy of Sciences. |
| 1937-1940 | Docent of Tbilisi State University |
| 1940 | Full professor of Tbilisi State University. |
| 1939-1946 | Head of the theoretical mechanics chair at the Transcaucasian Institute of Means of Communication |
| 1940-1941 | Deputy director of the Mathematical Institute of the Georgian Academy of Sciences |
| 1940-1944 | Dean of the faculty of physics and mathematics |
| 1940-1947 | Head of the chairs of geometry of Tbilisi state University |
| 1941-1944 | Senior researcher of the Mathematical Institute of the Georgian Academy of Sciences |
| 1943-1951 | Head of the applied mathematics department at the Tbilisi Mathematical Institute |
| 1939-1946 | Head of the theoretical mechanics chair at the Transcaucasian Institute of Means of Communication |
| 1944-1947 | Prorector of Tbilisi State University |
| 1947-1950 | Head of the mathematics and natural science departmant of the Georgian Academy of Sciences. |
| 1947-1951 | Academician secretary of the Georgian Academy of Sciences |
| 1951-1952 | Head of department at N.E. Zhukovski Central Aerodynamical Institute |
| 1952-1953 | Deputy director of the Institute of Precise Mechanics and Computer Hardware of the USSR Academy of Sciences |
| 1951-1954 | Head of the theoretical mechanics chair at Moscow Institute of Physics and Engineering |
| 1954-1959 | Deputy-director of V.A. Steklov Mathematical Institute of the USSR Academy of Sciences |
| 1954-1959 | Member of the bureau of the physics and mathematics department of the USSR Academy of Sciences |
| 1959-1964 | Rector of Novosibirsk University |
| 1959-1961 | Head the theoretical department at the Hydrodynamics Institute of the Siberian Brabch of the USSR Academy of Sciences |
| 1959-1964 | Head of the mathematical physics chair of Novosibirsk University |
| 1964 | Member of Presidium of Academy of Sciences of the USSR |
| 1964-1965 | Vice-president of the Georgian Academy of Sciences |
| 1966-1972 | Head of the higher mathematics chair at Tbilisi State University Rector of Tbilisi State University |
| 1969 | Member of the Polish Society of Theoiretical and Applied Mechanics Honorary Senator of Jena University Honorary Doctor of Halle University |
| 1968-1977 | Director of the Applied Mathematics Institute at the Tbilisi State University |
| 1972-1977 | President of the Georgian Academy of Sciences |
| 1959-1965 | Member of Novosibirsk regional committee |
| 1959-1963 | Member of Novosibirsk city committee |
| 1961-1963 | Deputy of Novosibirsk City Soviet of Working People |
| 1963-1965 | Deputy of Novosibirsk regional soviet of deputies of working people, member of Novosibirsk regional committee |
| 1966 | Deputy of Supreme Soviet of the USSR (and further of all convocations) |
| 1944 | Corresponding Member of the Georgian Academy of Sciences |
| 1946 | Corresponding member of the USSR Academy of Sciences Academician of Academy of Sciences of the Georgian SSR |
| 1958 | Academician of the USSR Academy of Sciences |
| 1968 | Foreign member of German Academy of Sciences |
| 1969 | Foreign member of the Academy of Natural Sciences "Leopoldina" (Halle) |
| 1976 | Foreign member of Academy of Sciences of Literature and Art (Sicilian Academy of Sciences) |
| 1950 | Stalin Prize of the second degree for research work "New methods of solution of elliptic equations". (Russian),published in 1948. |
| 1975 | Order of Lenin for scientific work "Generalized analytic functions".(Russian), published in 1959. |
| 1984 | State Prize for research work " Some general methods of constructing various versions of the shell theory". (Russian), published in 1982. |