After his studies in Kazan, he returned to Kiev and he taught at Kiev Cadet School from 1855 to 1862, receiving his Master's Degree in 1862 for a dissertation on the operational method and its application to solving linear differential equations. After receiving his Master's Degree, Vashchenko-Zakharchenko was appointed to the University of Kiev as a Privatdozent in 1863. He remained there for the rest of his life, being promoted to extraordinary professor in 1867 and to ordinary professor in the following year. He retired from teaching in 1902.
Vashchenko-Zakharchenko made contributions to several areas of mathematics. In particular he worked on the theory of linear differential equations, the theory of probability (see ) and non-euclidean geometry. He exerted great influence on a number of other mathematicians who joined him at Kiev, and his research interests strongly influenced others who taught there, particularly Boris Bukreev who was appointed as professor of mathematics at Kiev in 1889.
With wide ranging interests, it was natural for Vashchenko-Zakharchenko to write on a variety of topics and, indeed, his twelve textbooks cover many different topics. He published The Symbolic Calculus and its Application to the Integration of Linear Differential Equations in 1862. This book contained an extremely extensive development of the operational method. His book Riemann's theory of functions of a complex variable (1866) brought the Russian reader into contact with the most advanced ideas of the theory of functions at the time. Another important book was The theory of determinants and the theory of forms (1877). Taranovskaya looks at this work in  in the context of the development of the theory of determinants and the spreading of these ideas in Russia. We also mention Vashchenko-Zakharchenko's Analytic geometry which he published in 1887.
Ziwet, writing in 1884, four years after the publication of Vashchenko-Zakharchenko's The Elements of Euclid, with an explanatory introduction and annotations (1880), explains:
Besides numerous and extensive notes, and additions to the text, designed to render Euclid's treatment of geometry more palatable to modern taste, and to fill up some lacunae in the old work, the author has prefixed to his translation a valuable dissertation on the axioms and postulates and on the so-called non-Euclidean geometry of Bolyai and Lobachevsky, of which a sufficiently full sketch is presented. That a man so well acquainted with modern investigations of the principles of the science of space as Mr Vashchenko-Zakharchenko (a bibliography of this subject is also appended to the volume) should prove such an ardent adherent of Euclid, pure and simple, for the schools, is a truly remarkable fact.The article by Ziwet makes some interesting deductions from the data given in Vashchenko-Zakharchenko's Euclid where he lists 455 published editions of Euclid's Elements. What Vashchenko-Zakharchenko's list of editions shows is that by the middle of the 19th century Euclid's Elements was used as a textbook in Britain but in no other country in the world. In fact I [EFR] can confirm that 100 years later, in the 1950s, Euclid was still being used as a textbook in Britain for I was taught geometry from Euclid at secondary school. The difference between Britain and other European countries is marked in this respect. For example, the last edition of Euclid's Elements listed by Vashchenko-Zakharchenko as published in France appeared in 1778.
Vashchenko-Zakharchenko also wrote an important work on the history of mathematics in 1883 in which he discussed the history of mathematics up to the 15th century. The authors of  write:-
In 1880 Vashchenko-Zakharchenko professor of mathematics at the University of Kiev, and an active advocate of teaching geometry in Gymnasium according to Euclid, translated Euclid's 'Elements' into Russian with historical commentary. Three years later he published the first volume of 'History of Mathematics' which was devoted mainly to geometry from antiquity to the Renaissance. Despite the fact that Vashchenko-Zakharchenko's translation of Euclid was free and sometimes inaccurate, and that his 'History of Mathematics: Historical treatise on the development of geometry, Volume 1' was little more than a compilation of the works of Western European authors, especially Moritz Cantor, both work were of considerable importance. They marked the beginning of the history of mathematics in Russia as a discipline, and not simply as a field of sporadic research. In Russia (and later in the USSR), the history of mathematics was developed mainly by mathematicians and so was regarded as a mathematical discipline. This perception has persisted to the present ...Vashchenko-Zakharchenko wrote on other historical topics too; for example he wrote a history of the development of analytic geometry.
Article by: J J O'Connor and E F Robertson