Kiselev's Arithmetic

For over 70 years, this single textbook trained 80 million Soviet students in mathematics. Generations of scientists, engineers, and Fields Medal winners learned arithmetic from these pages. Now, for the first time, the complete English translation is available.

Originally published in 1884 by Alexander 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.

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 10 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 infinite primes - in an elementary textbook. Most American students don't encounter this proof until college. Kiselev presents it to children, building mathematical reasoning from the ground up.

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. This is mathematical rigor typically reserved for calculus courses.

191 pages. 214 sections. 7 parts covering: whole numbers, divisibility, fractions, decimals, ratios and proportions, limits, and word problems.

This translation preserves Kiselev's original pedagogical approach: concepts introduced gradually, problems carefully sequenced, abstraction built step by step, and reasoning emphasized over memorization.

Ideal for: homeschool families seeking a rigorous arithmetic curriculum, parents supplementing their children's math education, math teachers looking for a proof-based approach, adults who want to rebuild their mathematical foundations, and anyone interested in the tradition that produced some of the greatest mathematicians of the 20th century.

Translated by Valery Manokhin, PhD - mathematician, data scientist, and advocate for rigorous mathematical education.