Kiselev's Systematic Course of Arithmetic: The Classic Russian Mathematics Textbook — A Complete English Translation

For over 70 years, this single textbook trained tens of millions of Russian and Soviet students in mathematics. Generations of scientists, engineers, and Fields Medal winners came up through the tradition that learned arithmetic from these pages. This is the new, definitive English edition of the complete work — expanded and fully verified. Originally published in 1884 by Andrey Kiselev, this legendary textbook became the standard mathematics text across the Russian Empire and, later, the Soviet Union. It remained in continuous classroom use until 1955 — one of the longest runs of any textbook in history. Governments changed; the mathematics did not. What makes Kiselev's Arithmetic different from every modern textbook: Every rule comes with a proof. Where modern textbooks say "memorize this," Kiselev says "here is why it works — and you are ten years old, so you can handle the proof." Students don't just learn that a number is divisible by 3 when its digits sum to a multiple of 3. They learn why. Euclid's proof of the infinitude of primes, in an elementary textbook. Most students don't meet this proof until university. Kiselev presents it to children, building mathematical reasoning from the ground up: if there were a greatest prime, multiply all the primes together and add 1, and you reach a contradiction. Limits of sequences, in an arithmetic book. Kiselev introduces the concept of a limit and uses it to prove that repeating decimals converge to specific fractions — showing, for instance, that 0.999... has the limit 1. This is mathematical rigor usually reserved for calculus courses. 207 pages. 264 numbered articles. Seven divisions covering: whole numbers; concrete (denominate) numbers and the metric system; the divisibility of numbers, primes, and factorisation; common fractions; decimal fractions (including limits and repeating decimals); ratio and proportion; and a full course of word problems on proportional quantities. This is a faithful translation from the Russian — no adaptation, no simplification. The article numbering, worked examples, and proofs follow the source edition used in Russian and Soviet classrooms. Every displayed calculation and answer in this edition was independently verified, with zero arithmetic errors in the final text. This is not a quick-reference workbook but a complete course meant to be worked through. It rewards the thorough reader and the adult returning to mathematics: every rule is there to be understood, not skimmed, and the understanding it builds is the kind drilling alone never provides. Pair with the companion problem book. Berezanskaya's Arithmetic — Problems and Exercises (first complete English edition) is the classical Soviet problem collection published as the exercise companion to Kiselev's Arithmetic. Chapter-aligned to Kiselev's exposition, it turned the same generations of Soviet schoolchildren from readers into fluent problem-solvers. Continue with Kiselev's Algebra, Part I — the natural next step in the same author's mathematical canon, available in the same English edition. Ideal for: serious and self-directed learners who want to understand mathematics rather than memorise it; adults rebuilding or revising their mathematical foundations from the ground up; students who want a proof-based command of arithmetic before moving on to algebra; homeschool families seeking a rigorous curriculum; math teachers looking for a proof-based approach; and anyone interested in the tradition that produced some of the greatest mathematicians of the twentieth century. Part of Russian Math Classics — English Editions. Translated by Valery Manokhin, PhD (Royal Holloway, University of London). Published by Northern Star Academic Press. Full catalogue at russianmathbooks.com.