Vasily Yakovlevich Zinger


Quick Info

Born
30 January 1836
Moscow, Russia
Died
16 February 1907
Moscow, Russia

Summary
Vasily Zinger was a Russian mathematician who was a major figure in Moscow University in the 19th century. He wrote a number of works on geometry, mechanics and hydrodynamics, as well as on botany and philosophy. He was a founding member and later president of the Moscow Mathematical Society.

Biography

Vasily Yakovlevich Zinger was the son of Yakov Khristianovich Zinger and Anna Vasilievna Volkova. Before we continue with our biography let us note the following. The name Zinger is sometimes transliterated from the Russian as Ysinger. The dates of his birth and death that we give above are according to the calendar used in Russia at the time but, in terms of our present calendar, these dates are 11 February 1836 and 1 March 1907. One further comment on these dates. Zinger's obituary in the Moscow Mathematical Society gives his date of death as 17 February 1907 but we have used 16 February 1907 that appears on the official documents.

Yakov Khristianovich Zinger, the father of the subject of this biography, came from an aristocratic family. He trained as a mathematics teacher but he never took up a teaching position, although he did give private lessons. Anna Vasilievna Volkova, the mother of the subject of this biography, was the daughter of a merchant. Yakov Khristianovich and Anna Vasilievna had four children: Yulia Yakovlevna Zinger (born 8 July 1832); Vasily Yakovlevich Zinger (born 30 January 1836), the subject of this biography; Nikolai Yakovlevich Zinger (7 May 1837 - 26 August 1837); and Nikolai Yakovlevich Zinger (19 April 1842 - 3 October 1918). We note that after the death of their second son in 1837 when under a year old, they gave their next son, born in 1842, the same name. Nikolai Yakovlevich Zinger became an astronomer and geodesist, was appointed a professor and became a leading member of the Russian Geographical Society. He was elected a corresponding member of the Imperial St Petersburg Academy of Sciences.

Yakov Khristianovich died when his son Vasily Yakovlevich was eleven years old. Even before the death of his father, Vasily Yakovlevich had lived with his paternal grandfather Christian Ivanovich Zinger. He had been born in Germany but had lived in Moscow since the last years of the 18th century. He became the manager of the Golitsyn Hospital and was able to prevent the hospital from being looted during Napoleon's occupation of Moscow in September-October 1812. He had been awarded the title of hereditary nobleman for his service to Russia.

Vasily Yakovlevich studied at the First Moscow Gymnasium. He later spoke of his experiences at this school saying that he disliked the educational system which operated there that he considered formal and boring. This meant that, particularly in the lower grades, he performed poorly since he did not find any of the subjects interesting; he did not find any satisfaction in learning facts by rote. When he moved to the upper grades in the school things improved. The teaching became more interesting and after the age of fifteen he impressed his teachers with his excellent memory and his abilities to think quickly and logically. He graduated from the First Moscow Gymnasium in 1853 obtaining qualifications which allowed him to enter any Russian university without taking an entrance examination.

Zinger entered the Physics and Mathematics Department of Moscow University in 1853. His outstanding qualifications from the First Moscow Gymnasium meant he was able to live in a student residence funded with a government grant. The conditions in the residence did not come up to the living standards he was used to and he was unhappy living there. Since his mother was living in Moscow he left the student accommodation and lived with his mother. He also did some private mathematics tuition to earn some extra money to help with the family finances.

There were a number of first class professors in the Physics and Mathematics Department of Moscow University who influenced Zinger; we note that the three most important were: August Yulevich Davidov, professor of applied mathematics; Nikolai Dmetrievich Brashman who gave inspiring courses on analytical geometry; and Nikolai Efimovich Zernov (1804-1862). Nikolai Efimovich Zernov was the son of a postal officer. After taking his undergraduate degree at Moscow University in 1822, Zernov had studied for a master's degree in astronomy and, in 1832, had been appointed astronomer-observer at the university observatory. Passed over for the position of astronomer, Zernov succeeded in obtaining the appointment of professor of pure mathematics at Moscow University. In 1837 he had been the first to defend a doctoral thesis in Russia.

Zinger graduated from Moscow University in 1857 and then he continued to study at the university, aiming to gain qualifications to allow him to become a mathematics professor. In 1862, Zinger defended his dissertation for a Master's Degree on the topic of "The Method of Least Squares" (Russian), in the same year he was elected by the Council of Moscow University to the full-time position of associate professor of the Department of Pure Mathematics.

In 1865 Zinger married Magdalena Ivanovna Raevskaya (1838-1888). They had four children: Nikolai Vasilyevich Zinger (11 May 1866 - 18 May 1923), who became a botanist and professor at the Novo-Alexandria Institute of Agriculture and Forestry; Alexander Vasilyevich Zinger (16 May 1870 - 24 December 1934), who became a physicist and teacher and wrote many textbooks; Elizaveta Vasilyevna Zinger (dates unknown); and Ivan Vasilyevich Zinger (dates unknown).

Zinger was one of the founders of the Moscow Mathematical Society in 1864 and he became its first secretary. In 1866 the first president Nikolai Dmetrievich Brashman died and August Yulevich Davidov, who had been vice-president, became president. Zinger was elected as vice-president at this time. The Society began publishing its journal Matematicheskii Sbornik in 1866 and Zinger began publishing papers in the journal. He published the paper Relative motion of thrown mass (Russian) in 1866 in the first part of volume 1 of Matematicheskii Sbornik. The paper begins:-
In determining relative motions, one usually uses general differential equations, which are obtained from the equations of absolute motion through a transformation of coordinates. For solving particular problems, such a method in most cases turns out to be insufficient, because integration of the equations of relative motion is rarely accessible. The complex form of these equations presents another inconvenience, that the meaning of the heterogeneous terms entering into them is not always sufficiently clear; and this circumstance can easily be the cause of inaccuracy or obscurity of exposition.

But the connection between absolute and relative coordinates, which is expressed by the transformation formulas and which serves to obtain differential equations, can obviously lead us directly to the integrals of relative motion, and precisely in those cases when the absolute motion is known.
In 1867, he defended his doctoral dissertation with the title On the Motion of a Free Liquid Mass (Russian). Here is a short extract from the paper of the same name which he published in Volume 2 of Matematicheskii Sbornik in 1867:-
Lacking the ability to integrate the general equations of hydrodynamics, we are forced to resort to an indirect method, the verification method, to solve problems about the motion of a fluid; we can, for example, make some assumption about the motion of the particles of the fluid, give the function p a certain form, and then, using the general equations, draw conclusions about the conditions under which the assumptions made take place. Obviously, for lack of anything better, this method can lead us to the solution of many problems of hydrodynamics; but even in this direction, little has been done; in the simplest case, when the movement of a homogeneous and completely free liquid mass is considered, only one question is developed about the uniform rotational movement of the liquid without changing the relative position of its particles and, consequently, without changing the appearance of the surface.
Zinger began lecturing at Moscow University in 1862. One of the students he taught near the start of his career was Nikolai Egorovich Zhukovsky who is famed for his pioneering work on aerodynamics and is best known today for the so-called Joukowski aerofoil. Zhukovsky was a student at Moscow University from 1864 to 1868 and during these years he attended lectures on mechanics from both Zinger and Fyodor Alekseevich Sludsky (1841-1897) who had been a student of Brashman and Davidov. Zhukovsky spoke of the contrasting styles of these two lecturers; Zinger's teaching of the subject was visual, geometrically clear, while Sludsky's presentation of the material was exclusively abstract, consisting only of formulas, without any geometric illustrations. Zhukovsky also said that he chose to follow Zinger's style when he himself became a lecturer and became a follower of the visual method. After Zinger's death, Zhukovsky spoke about the influence Zinger style had on him (see for example [19]):-
With his love for figurative geometric thinking, Zinger captivated young mechanics, directing their work along the path followed by the great geometers Newton, Poinsot, Poncelet, and Chasles.
In both teaching and research Zinger had broad mathematical interests. In addition to mechanics, he taught higher algebra, differential calculus, analytical geometry, projective geometry, etc. His lectures were original, visual, carefully thought out and always attracted a large number of listeners. In [20] his teaching is described as follows:-
The elegance of his presentation and the depth of his scientific ideas attracted many students to Zinger... One of the most significant features of Zinger's lectures was that in them he drew the attention of his listeners ... to the guiding ideas and forced them to clearly grasp the difference between the inner meaning of each question or method and those established ... techniques and transformations that constitute, as it were, the outer shell of pure speculation.
On 19 February 1869 he delivered the talk On the fundamental theorem of higher geometry to the annual meeting of the Moscow Mathematical Society. He explained that he had chosen the topic because of its:-
... special interest and deserves attention in many respects. Higher geometry, unfortunately still very little widespread, especially among us, is one of the sciences that has arisen and developed only in recent times: it is also called new geometry; and yet, both in content and in its fundamental principles, and especially in its method, it stands closer than all other sciences to the geometry of the ancients.
You can read an English translation of his talk at THIS LINK.

Zinger continued to publish in Matematicheskii Sbornik with papers such as: Construction of a curve of the third order from nine given points (Russian) (1868); Rotational motion of a fluid ellipsoid with change of form (Russian) (1872); On a case of equilibrium of a liquid (Russian) (1873); and On the geometrical significance of inequalities (Russian) (1875).

Today Zinger is remembered both as a mathematician and as a botanist. We have looked at some of his mathematical contributions but so far have not mentioned his achievements in botany. He had been brought up in Moscow and for many years had no cause to become interested in the countryside. This changed in 1865 when he married Magdalena Ivanovna since her family lived on an estate in the village of Melekhovka in the Tula region about 170 km south of Moscow. Zinger would spend free time there with his family and he often went for walks with Nikolay Nikolayevich Kaufman, a professor of botany at Moscow University. Zinger said [22]:-
When I watched Kaufman collect and study plants, when I listened to his stories, my eyes were opened: the grass, the forest, and the soil appeared to me in a completely new light, full of the deepest interest.
Although botany began as a hobby for Zinger, it steadily grew into a serious scientific study. He became friends with Dmitry Aleksandrovich Kozhevnikov who was a student in natural sciences in the Physics and Mathematics Department of Moscow University, graduating in 1878. Zinger and Kozhevnikov began a systematic study of the flora of the Tula region in 1877 and in 1880 published a joint work Essay on the Flora of the Tula Province (Russian). In July 1882, together with the botanist Dmitry Ivanovich Litvinov, Zinger explored Galichya Gora in the Zadonsky District, where there are limestone cliffs on the right bank of the Don River. They returned several times over the following years and discovered plants that were not typical for the East European Plain. The area has become a nature reserve. Zinger also undertook investigations of plants with the botanist Rudolf Ernestovich Trautfetter of the University of Dorpat.

In total Zinger wrote five botanical works, the most famous being the 500-page work Collection of Information on the Flora of Central Russia published in the "Scientific Notes of Moscow University" in 1885. He wrote in the Preface [23]:-
There is no need to be a specialist to study our native flora successfully and profitably; what is needed is that love for the work and desire which transforms the considerable and not always easy work of collecting and identifying plants into a familiar favourite pastime and little by little turns a simple amateur into an experienced connoisseur. Unfortunately, our circumstances are such that of the many amateurs, very few manage to cope with the various difficulties that are inevitable for any beginner. In most cases, an amateur, interested and enthusiastic about the matter, from the very beginning gets lost in a heap of errors, contradictions, difficulties and cannot find not only advice or instructions from an experienced guide, but even a satisfactory book, so much as applicable to his needs. Involuntarily, despite his enthusiasm and desire, he has to abandon the matter and stop at the first step. On the other hand, there can be no good guides to local flora until the necessary factual material is collected with the help of the same amateur work. We believe that in the activities of our learned societies one of the most important duties and essential tasks should consist in encouraging and developing amateur work and in attracting to it the greatest possible number of people, because only with their assistance can we obtain from a multitude of unexplored places those factual data of which we are still so poor and which we have needed for so long.
In addition to his works on mathematics and botany, Zinger wrote two articles of a more philosophical nature, namely Exact Sciences and Positivism (Russian) (1874) and Misunderstandings in Views on the Fundamentals of geometry (Russian) (1894). L M Lopatin writes [7]:-
His few articles devoted to philosophical issues are always distinguished by the clarity of the author's fundamental views and the unique depth of his conclusions. One may not agree with his views, but even the harshest critic must give credit to the serious thoughtfulness and independent firmness of his philosophical convictions.
You can read some information about these two articles, including a number of quotes from the articles, at THIS LINK.

In addition to his teaching, his mathematical research and his botanical research, Zinger held important roles in Moscow University. He was elected secretary of the Physics and Mathematics Faculty three times in the years between 1870 and 1876. During these years, 1870-1876, he was also a member of the university court. From June 1876 to February 1878, Zinger was the dean of the Physics and Mathematics Faculty. From February 1878 to March 1880, he held the position of vice-rector of Moscow University, but in March 1880, he resigned from that role. In June 1880, Zinger was elected for a second time as dean of the Physics and Mathematics Faculty and held this position until October 1885.

Zinger also made an important contribution to Russian mathematics through translating works by Michel Chasles. Natalia Vasilievna Lokot writes [6]:-
The translation by V Ya Zinger of the work of Michel Chasles (1793-1880) devoted to the history of geometry was a landmark in the period of infancy of the Russian history of mathematics. ... Neither the translator's nor the editor's name was provided on the cover of the Russian publication. However, it is common knowledge that Vasily Yakovlevich Zinger was the translator and the editor of this publication. ... His student, Konstantin Alekseevich Andreev (1848-1921), stated that "as a young man Vasily Yakovlevich was very passionate about Chasles' works and closely scrutinised them. . . He translated one of Chasles' fundamental works ... into Russian in full, however, he did not do it diligently, he did not pursue editing details; instead, he did it as quickly as he was reading and speaking, because he always had a ready-to-use clear and precise phrase for each established or accepted idea." Thus, owing to the efforts of Moscow Society of Mathematics and V Ya Zinger, Russian historians of science were able to read the work of M Chasles, the acknowledged leader of French school of geometry of that time, in their native language.
In 1888 Zinger's wife Magdalena Ivanovna died suddenly. Soon after her death, he married for the second time. He had for a long time been friends with Alexey Vasilyevich Letnikov (1837-1888), a mathematician who worked on analytic geometry and the theory of differential equations. Zinger's second marriage was to Letnikov's daughter, Ekaterina Alekseyevna Letnikova. They had several children including Alexey Vasilyevich Zinger (1892-1945), who became a Russian naval officer and a teacher of naval astronomy but lived in exile in France after the civil war; Natalya Vasilievna Zinger (1897-1977), a professor of botany; and Vera Vasilievna Zinger (1900-1993), who married Evgeny Alekseevich Chudakov (1890-1953) and their son Alexander Evgenyevich Chudakov (1921-2001) became a leading physicist.

When Zinger reached the age of 62 in 1898, he gave up lecturing at Moscow University and with his wife Ekaterina Alekseyevna and their children, moved to Melehovka. There they had an elementary school built which provided education for peasant children from the surrounding villages. During the Christmas holidays, the Zingers had a Christmas tree in their home which they invited the local children to visit; they gave the children who came presents and books to read. Ekaterina Alekseyevna was often ill with heart problems and she died in 1903. On 30 August 1904, Zinger married for the third time to 25-year-old Anna-Maria-Elizaveta Aboling and the went to live in Moscow to bring up Zinger's young family. During the winter of 1906-07 Zinger became ill with pneumonia and died in February 1907. The funeral service took place in the university church of Saint Tatiana on Mokhovaya and he was buried in the Vagankovskoye Cemetery in Moscow.

Zinger received several honours. In 1900 he was elected a corresponding member of the St Petersburg Academy of Sciences. He was awarded the title of Honorary Doctor of Botany by the University of Dorpat. In 1888 be became an honorary professor of pure mathematics at Moscow University. He was elected president of the Moscow Mathematical Society in 1886 and served in this role until 1891. He is remembered today by botanists since at least two species of plants are named for Zinger.

Eleven days after his death a meeting of the Moscow Mathematical Society was held at which a minute's silence was observed in memory of Vasily Yakovlevich. The Society decided to commission a portrait of Zinger to be hung in the meeting room of the Society, and asked for various articles on Zinger and his work to be prepared for a meeting on 4 April 1908. The articles which were presented on that occasion were printed in the Mathematical Collection in 1911; see [1], [3], [7], [8] and [17].

Let us end this biography with a quote from the speech Nikolai Egorovich Zhukovsky made at an evening dedicated to the memory of Zinger on 4 April 1908 (see [17]):-
Professor Zinger did not gain fame by the abundance of his scholarly works, but by the nature of these works. Everything he wrote, with its depth of content, was distinguished by clarity, completeness and concreteness of form. There are mathematical works which, once read, are remembered forever, just as a painting by a famous artist, briefly seen in an art gallery, is then clearly depicted in the imagination. The works of V Ya Zinger belong to this kind of works... His students, both mathematicians and mechanics, also tried to work in this direction... We honour the memory of a mathematician who can rightly be called the head of the Russian geometric school.


References (show)

  1. K A Andreev, Vasily Yakovlevich Zinger, his life and work (Russian), Mathematical Collection 28 (1) (1911).
  2. A E Godin, Development of the Ideas of the Moscow Philosophical and Mathematical School (Russian) (Krasny Svet, Moscow, 2006).
  3. M I Golenkin, Botanical works of V Ya Zinger (Russian), Mathematical Collection 28 (1) (1911).
  4. A Yu Gribov, V Ya Zinger as a philosopher, mathematician and teacher (on the 175th anniversary of his birth) (Russian), Yaroslavl Pedagogical Bulletin 3 (3) (2011), 148-152.
  5. L V Levshin, Deans of the Physics Department of Moscow University (Russian) (Physics Department, Moscow State University, Moscow, 2002).
  6. N V Lokot, Russian Translations and Translators of Western European works (XVIII - early twentieth century) devoted to the history of mathematics, Antiquitates Mathematicae 13 (1) (2-19), 67-111.
  7. L M Lopatin, Philosophical views of V Ya Zinger (Russian), Mathematical Collection 28 (1) (1911).
  8. B K Mlodzeevsky, Works of V Ya Zinger on mathematics (Russian), Mathematical Collection 28 (1) (1911).
  9. P A Nekrasov Moscow Philosophical and Mathematical School and Its Founders (Russian), Matematicheskii sbornik 25 (1) (1904), 3-249.
  10. V Rudenko, "What a fine fellow Zinger was!" The flora of the Tula province was best described by a mathematician (Russian), MKRU (18 March 2015).
    https://tula.mk.ru/articles/2015/03/18/cingerto-kakoy-molodec.html
  11. Vasily Yakovlevich Zinger (Russian), Russian wikiquote (2025).
    https://ru.wikiquote.org/wiki/Василий_Яковлевич_Цингер
  12. Vasily Yakovlevich Zinger (Russian), Chronicle of Moscow University (2025).
    http://letopis.msu.ru/peoples/1055
  13. Vasily Yakovlevich Zinger (Russian), Local History Museum, Museum of Military Glory (28 March 2020).
    https://eletsmuseum.ru/znakomimsya-s-issledovatelyami-vnesshimi-bolshoj-vklad-v-izuchenie-zapovednika-galichya-gora-2/
  14. Vasily Yakovlevich Zinger. Publications in the Math-Net.Ru database (Russian), Math-Net.Ru (2025).
    https://www.mathnet.ru/rus/person39915
  15. Vasilij Jakovlevich Zinger (1836 - 1907), geni.com (025).
    https://www.geni.com/people/Vasilij-Zinger/6000000021662387562
  16. T Votintseva, Vasily Yakovlevich Zinger: a mathematician passionate about botany and philosophy (Russian), Yasnogorsk Museum of Art and Local History (2025).
    https://vk.com/wall-150061300_3114
  17. N E Zhukovsky, On the works of V Ya Zinger on mechanics (Russian), Mathematical Collection 28 (1) (1911).
  18. Zinger, Vasily Yakovlevich (Russian), Library of Russian Religious-Philosophical and Fictional Literature (2025).
    http://www.vehi.net/brokgauz/all/112/112274.shtml
  19. Zinger, Vasily Yakovlevich (Russian), Russian wikipedia (2025).
    https://ru.wikipedia.org/wiki/Цингер,_Василий_Яковлевич
  20. Zinger, Vasily Yakovlevich (Russian), in Brockhaus and Efron Encyclopaedic Dictionary (St Petersburg, 1890-1907).
  21. Zinger, Vasily Yakovlevich (Russian), Great Russian People (2025).
    https://greatrussianpeople.ru/info13694.html
  22. A V Zinger, Entertaining botany (Russian) (State Publishing House "Soviet Science", Moscow, 1951).
  23. V Ya Zinger, Collection of Information on the Flora of Central Russia (Russian) (University Printing House, Moscow, 1885).

Additional Resources (show)


Written by J J O'Connor and E F Robertson
Last Update June 2025