**Andrei Petrovich Kiselev** wasa Russian mathematician known mainly for his textbooks.

- Kiselev attended the district school in Mtsensk and from there he went to the Gymnasium in Oryol, the main city in the region.
- It is worth recording at this point that at least two of the mathematics teachers who taught Kiselev during his school years taught from textbooks that they had written themselves.
- Perhaps this influenced Kiselev to become a writer of textbooks when he himself became a school teacher.
- At St Petersburg University, Kiselev was taught by a number of world-class mathematicians.
- Kiselev graduated in 1875 from the Physics and Mathematics Faculty of St Petersburg University with a degree which entitled him to teach in Gymnasia.
- Kiselev taught at the 'real school' in Voronezh until July 1891 when he spent a year teaching at a Gymnasium in Kursk before returning to Voronezh to teach at the Voronezh cadet corps.
- Here are the most important of Kiselev's textbooks: Systematic arithmetic course for secondary schools (1884); Elementary Algebra (1888); Elementary Geometry (1892-1893); Additional topics in algebra (a course of the 7th grade real schools) (1893); Quick arithmetic for urban schools (1895); A Brief algebra for girls' schools and seminaries (1896); An elementary physics for secondary schools with a number of exercises and problems (1902); Physics (two volumes) (1908); Elements of the differential and integral calculus (1908); The initial study of derivatives for the 7th grade real schools (1911); Graphical representation of some of the features discussed in elementary algebra (1911); On topics in elementary geometry, which are usually solved by means of limits (1916); Brief algebra (1917); Brief arithmetic for urban county schools (1918); Irrational numbers, considered as infinite non-periodic fractions (1923); and Elements of algebra and analysis (2 volumes) (1930-1931).
- This was clearly the case for, in the Preface to the first edition of this book, Kiselev quotes ten geometry courses in French and German published in the previous decade.
- The well-known Russian mathematics educator Ivan Andronov (1941) once wrote that Kiselev knew his strengths and did not undertake that for which his strengths might not have been sufficient.
- Kiselev's textbooks are well-organized and logical (later, they were found to contain not a few logical gaps, but all of these were beyond the understanding of the ordinary student).
- In the course in geometry - Kiselev's most popular course - practically all of the assertions are grounded and proved.
- But Kiselev never tried to offer a strict axiomatic course with complete indication of axioms and all of the references that a professional mathematician would have considered necessary.
- There were other reasons too which were not related to the quality of the texts but rather to Kiselev's skills as a salesman.
- These selling techniques are common today but in Kiselev's time these were new ways of selling books and they certainly added to the success of the books.
- However, success ultimately depends on having outstanding books and Kiselev seems to have produced books with just the right approach.
- Kiselev himself suggested that the properties required of a good textbook were precision, simplicity, and conciseness.
- When the Russian Revolution took place in 1917 it looked at first as if Kiselev's good life, living off a good pension and royalties, would be over.
- With food scarce and his pension and income from books taken away, Kiselev returned to Voronezh where he took up teaching again in the colleges there.
- Kiselev's books became irrelevant to the Communist ideas of education in the years following the Revolution where all textbooks were considered unnecessary.
- However, many teachers ignored the new ideas and continued to use Kiselev's books.
- Slowly they returned to full use after the Moscow Mathematical Society, at a meeting held on 9 April 1937, recommended that Kiselev's Geometry should be, for the time being, the book used by schools.
- By the 1950s the book was still in widespread use and most Russian mathematicians who were at school in the early 1960s said that they had used Kiselev's books.
- But consider then that Kiselev precedes the definition with a reasonably developed theory of limits.
- Kiselev rightly observes that to justify it one needs methods that would go beyond elementary mathematics.
- So, based on the theory of limits developed in the first part (Planimetry), Kiselev proves (although without ever employing the symbol lim) the principle for triangular pyramids and uses the occasion to mention Hilbert's third problem.
- Kiselev spoke about the various "aberrations" in the schools: the fact that classes were overcrowded, the fact that there was not enough time properly to interview and assess all of the students in a class, the fact that school schedules were poorly designed, as a result of which there were "empty" lessons at the end of the year, which students spent playing games.
- During his lifetime Kiselev was awarded the Order of St Anne 3rd degree (1894), the Order of St Stanislaus 2nd degree (1896), the Order of St Anne 2nd degree (1899), and the Order of the Red Banner of Labour (1934).
- For example Sergei Alekseevich Chaplygin was taught in Voronezh by Kiselev.
- A great many others, such as Iossif Vladimirovich Ostrovskii, were turned on to mathematics by reading Kiselev's books.
- After his death in Leningrad, Kiselev was buried in the Volkov cemetery, in an area reserved for academics.

Born 30 November 1852, Mtsensk, Oryol Gubernia, Russia. Died 8 November 1940, Leningrad, USSR (now St Petersburg, Russia).

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Origin Russia

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive