Professor Andrea Razmadze

(August 12, 1889, vil. Chkhenishi, Georgia - October 2, 1929,
Tbilisi, Georgia)


The well-known Georgian mathematician, one of the founders of Tbilisi State University, A. Razmadze was born on August 12, 1889 in the village of Chkhenishi (Samtredia region, Georgia). In 1906 he finished the real school in Kutaisi, and in 1910 he graduated from the Moscow State University. The first A. Razmadze's scientific work dealing with the basic problem of variational calculus with free ends was published in 1914 in the journal "Matematische Annalen". The lemma belonging to A. Razmadze allows one to get easily Euler's differential equation; the same lemma results, as particular cases, in lemmas due to Dubois-Reymond and Lagrange. The work "Sur les exstremales discontinues dans le calcul des variations" published in 1925 won him wide recognition and popularity. Later A. Razmadze used this work for his Doctoral Thesis which he defended in Sorbonne University (France). A. Razmadze's theory of discontinuous extremals has found reflection and further development in the works of many scientists. In 1924, A. Razmadze participated in the work of the International Congress of Mathematicians (Toronto, Canada). Up to his dying day, A. Razmadze kept close scientific contacts with C. Carathéodory and L. Tonelli. The last A. Razmadze's work "Sur les solutions périodiques et les extrémales fermées du calcul de variations" was estimated by C. Carathéodory as follows: "The theory of closed extremals on a plane is brought by A. Razmadze to perfection". Later, the results obtained by A. Razmadze in the above-mentioned work, C. Carathéodory included in one of the sections of his book "Variationrechnung und partielle differentialgleichungen, Lpz.-B., 1935" under the title "The Hadamard and Razmadze Theory". Text-books in mathematics in Georgian language for the first time were published under A. Razmadze's authorship.

A. Razmadze passed away in 1929 in the age of 40. The Georgian Mathematical Society announced with deep regret the untimely death of professor A. Razmadze, founder and president of the Society, first Georgian mathematician, founder of higher mathematical education in Georgia. Italian mathematician L. Tonelli wrote: "Mathematics in the person of A. Razmadze has lost one of its outstanding scientists, researcher with lucid mentality and keen intellect".



1906 finished Kutaisi nonclassical secondary school
1906-1910 studies at Moscow University
1910 was granted Diploma in Mathematics, Moscow University
1917 was granted Master of Pure Mathemtics degree by Moscow University
1925 was granted Diplome de Docteur ès Sciences Mathématiques, Faculté des Sciences de Paris, Academie de Paris.


1910-1916 mathematics teacher at schools in towns located in vicinity of Moscow, in particular, at Mtsensk and Murom classical schools and Podolsk nonclassical secondary school
1917 privat-docent at Moscow University
1918-1929 professor at Tbilisi State University


Calculus of variations


(i) Papers

  1. Deux propositions du calcul des variations. Bulletin de l'Université de Tiflis 1(1919-1920), 157-172.
  2. Über das Fundamentallemma der Variationsrechnung. Math. Ann. 84(1921), 115-116.
  3. Über unstetige Lösungen mit einem Unstetigkeitspunkt in der Variationsrechnung. Bulletin de l'Université de Tiflis 2(1922-1923), 282-312.
  4. Sur une condition de minimum nécessaire pour les solutions anguleuses dans le calcul des variations. Bull. Soc. Math. 51(1923), 223-235.
  5. Sur les solutions discontinues dans le calcul des variations. Math. Ann. 94(1925), 1-52.
  6. Sur un théoréme de la théorie des surfaces minima. Bull. Sci. Math. 49 (1925).
  7. On the conditions of the existence of a lower limit of an integral in calculus of variation when an extremum does not exist. (Russian) Trans. All-Russian Math. Congr., Moscow (1927), 180-181.
  8. Sur les solutions périodiques et les extrémales fermées du calcul des variations. Math. Ann. 110(1935), 63-96.
  9. Selected works. (Georgian) Publ. House Georgian Acad. Sci., Tbilisi, 1952.

    (ii) Text-books

  10. Course on mathematical analysis, v. 1 (Introduction to analysis). (Georgian) Tphilisi University Press, Tphilisi, 1920.
  11. Course on integral calculus. Part I. Indefinite integrals. (Georgian) Tphilisi University Press, Tphilisi, 1922; 2nd ed., 1956.
  12. Calculus of variations (Lectures delivered by A. Razmadze prepared for publication by L. Gokieli). (Georgian) Sakhelgami, Tphilisi, 1933.

Bibliography on A. Razmadze

  1. L. Gokieli, Andrea Razmadze. (Georgian and Russian) Tbilisis Mat. Inst. Shromebi [Russian title: Trudy Tbiliss. Mat. Inst. (Proc. Tbilisi Math. Inst.)] 1(1937), 1-5, 6-10.
  2. L. Tonelli, Andrea Razmadze. (Italian) Tbilisis Mat. Inst. Shromebi [Russian title: Trudy Tbiliss. Mat. Inst. (Proc. Tbilisi Mat. Inst.)] 1(1937), 11-13.
  3. Papers communicated to the session dedicated to the memory of A. Razmadze, October 24, 1944. (Georgian) Tbilisi, 1945.
  4. T. Ebanoidze, Letters about Georgian mathematicians. (Georgian) Metsniereba, Tbilisi, 1981.
  5. A. Razmadze. (Collection of papers compiled and edited by G. Chogoshvili and V. Parkadze). (Georgian) Tsodna Soc. Publ., Tbilisi, 1985.
  6. Recollections and letters about A. Razmadze. (Compiled by T. Vashakmadze). (Georgian) Tbilisi University Press, 1993.
  7. A. Razmadze's lectures on probability theory (based on lectures delivered by A. Razmadze and recorded by D. Vashakidze; edited and supplied with comments by T. Shervashidze). (Georgian with Russian and English summaries) Metsniereba, Tbilisi, 1991.