**Georgii Vasilovich Pfeiffer**'s date of birth is certainly in 1872 but there seems to be some uncertainty regarding the month. Some obituaries give the month as October, some give November, while others give December. The uncertainty of the day relates to the calendar in operation at the time so some give the 11th day of the month while others give the 23rd day or 24th day. The date of birth we have given, 24 October, is the date which is carved on his tombstone. Sokyryntsi, where he was born, is a small village in beautiful surroundings with a lake and parkland. He began his education there but to attend the Gymnasium he had to go to Pryluka, the regional centre of the Chernihiv region. This town, also known as Pryluky, is about 28 km west of Sokyryntsi and is about 120 km east of Kiev. Pfeiffer entered the Pryluka Gymnasium, a school which had been founded in 1874 and was directed by Feodosii Voronoy, the father of the mathematician Georgy Fedoseevich Voronoy. In fact, when Pfeiffer entered the Gymnasium Georgy Voronoy was still a pupil there showing his brilliance by publishing a paper while still at the Gymnasium.

After graduating from the Pryluka Gymnasium, Pfeiffer entered the Faculty of Physics and Mathematics of Kiev University. The university had been founded in 1834 and had, from its foundation, a strong school of mathematics. Among Pfeiffer's lecturers at Kiev University we mention Mikhail Egorovich Vashchenko-Zakharchenko, Boris Yakovlevic Bukreev and, in particular, Vasilii Petrovich Ermakov (1845-1922). Pfeiffer graduated from the University of Kiev in 1896 and was then appointed as a secondary school mathematics teacher in a Gymnasium in Kiev. He was appointed to the Kiev Polytechnic Institute in 1899 and he taught there until 1909. After this he spent two years 1909-1911 teaching at the University for Women in Kiev. He defended his doctoral thesis on problems of the theory of algebraic surfaces in 1911. While holding the appointment at Kiev Polytechnic Institute, he was also appointed as an assistant professor of mathematics at the University of Kiev in 1900 and he taught there until his death in 1946. At the University, he was promoted to extraordinary professor in 1909 and then to full professor in 1911. In the following year he was made chairman of the Department of Analysis and, also in 1912, he became chairman of the Academic Council of the Faculty of Physics and Mathematics. He continued to hold this latter post until he left Kiev in 1941. In Kiev, Pfeiffer lived in an apartment in a complex of residential buildings on Khmelnitsky Street. The building were built in an Art Nouveau style. He lived at number 59, in apartment number 5 on the third floor.

Elected to the Academy of Sciences of the Ukraine in 1920, Pfeiffer chaired the Commission on Pure Mathematics from that time. Pfeiffer was also attached to the Institute of Mathematics of the Academy of Sciences of the Ukraine in Kiev and served as Director during two periods, namely 1934 to 1941 and again from 1944 until his death in 1946. The gap in his working in Kiev was a result of World War II. The Molotov-Ribbentrop non-aggression pact between Germany and the Soviet Union meant that the initial years of the war had little effect on life in Kiev and Pfeiffer continued his work there. However, things changed dramatically on 22 June 1941 when Germany broke the non-aggression pact and invaded the Soviet Union. Kiev was soon threatened by the advancing German armies (they entered the city on 19 September 1941) and the Ukrainian Academy of Sciences was relocated to the city of Ufa. In the three years 1941-44, Pfeiffer was in Ufa, the capital of the Bashkortostan republic in western Russia. In Ufa, Pfeiffer was Director of the Institute of Mathematics and Physics. By the end of 1943 Soviet troops had liberated Kiev and in the following year Pfeiffer returned to the city when the Ukrainian Academy of Sciences returned. When he returned to Kiev he was made head of the Department of Ordinary Differential Equations at the University.

Pfeiffer's first research was on the problem of solving equations by radicals, and he next looked at algebraic geometry. V O Volkova describes Pfeiffer's papers in this area in [6] writing:-

Georgii Vasil'evich Pfeiffer(1872-1946), professor at Kiev University, is known as a specialist in the field of integration of differential equations and systems of partial differential equations. However, at the beginning of his career he was interested in algebraic geometry, especially in the study of singular points of algebraic curves and surfaces. This period of his activity is well known neither to specialists in geometry nor to historians of mathematics.

As this quote indicates, however, his most important contributions involve work on partial differential equations following on from the methods developed by Lie and Lagrange. Summarising this area of Pfeiffer's work in [3], Koval'chuk describes:-

... some work of the Ukrainian mathematician G V Pfeiffer , showing how to find integrals of a general system of partial differential equations by using sequential complete systems instead of passing to Jacobian systems. Pfeiffer also constructed all the infinitesimal operators of a system of equations.

Koval'chuk explains how Pfeiffer's methods greatly expanded the class of integrable systems, but have been neglected over the past half-century as functional-analytic methods have been in fashion. For example, he published three papers in 1946: *La réception et l'intégration par la méthode spéciale des équations, systèmes d'équations semi-Jacobiens, des équations, systèmes d'équations semi-Jacobiens généralisés aux dérivées partielles du premier ordre de plusieurs fonctions inconnues* Ⓣ; *Sur les équations, systèmes d'équations semi-jacobiens, semi-jacobiens généralisés aux dérivées partielles de premier ordre à plusieurs fonctions inconnues* Ⓣ; and *Sur les équations, systèmes d'équations semi-mixtes aux dérivées partielles du premier ordre à plusieurs fonctions inconnues* Ⓣ. The first of these was reviewed by Morris S Knebelman who writes:-

As the title indicates, the paper is concerned with a special method for solving semi-Jacobian systems of partial differential equations. Such a system arises from a linear partial differential equation of the first order containing one or more parameters whose elimination leads to the Jacobian system of equations which are nonlinear. Three illustrative examples are worked out, but the validity of the stated "rules'' is not clear.

Reviewing the third of these, Dirk Struik writes:-

The author sketches two rules for integration of systems of "semi-mixed'' partial differential equations of the first order with several unknown functions.

The second paper was also reviewed by Struik who writes:-

The author sketches two ways of applying his method of integration[first published in1923]to systems of generalized semi-Jacobian equations of the first order with several unknown functions.

In total, Pfeiffer published 250 scientific papers in several languages including Ukrainian, Russian, French and German. He also published books such as his 346-page 1937 book *Integration of differential equations*. He also used his language skills to translate books such as the 1891 French text by Édouard Goursat *Leçons sur l'intégration des équations aux dérivées partielles du premier ordre* Ⓣ which appeared in Ukrainian in 1940. He participated in the International Congress of Mathematicians in Rome (in April 1908), Bologna (in September 1928), and Zürich (in September 1932). He also attended a mathematical conference in Moscow (1929), the first All Union Congress of Mathematicians in Kharkov (July 1930) and the second All Union Congress of Mathematicians in Leningrad (June 1934).

Pfeiffer was a great connoisseur of mathematical literature in many different areas of mathematics showing himself to be a scholar with deep feelings and high standards in everything he did. After his death he was buried in the Lukyanovsky cemetery in Kiev. In 2006, sixty years after his death, commemorative events were held.

**Article by:** *J J O'Connor* and *E F Robertson*

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