MediumThe multiplication method Russian peasants used for a thousand years — and why every computer in the world still uses it today | by Valeriy Manokhin, PhD, MBA, CQF | Jul, 2026 | MediumSitemapOpen in appSign up<br>Sign in

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Math

Arithmetic

The multiplication method Russian peasants used for a thousand years — and why every computer in the world still uses it today

Valeriy Manokhin, PhD, MBA, CQF

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A folk algorithm that turns out to be Egyptian, and turns out to be binary.<br>I spent some time translating Yakov Perelman’s Entertaining Arithmetic into English for the first time. Perelman was, in his lifetime, the most-read popular-science writer in the Russian language — forty books, thirteen million copies, translated into dozens of languages. He was the Martin Gardner of the Soviet century. In English, almost none of him exists.<br>One of the passages that stopped me during translation is a short section in Chapter 3, “The Russian Method of Multiplication.” Perelman quotes an 18th-century Russian arithmetic textbook — Magnitsky’s — which insists in verse that you cannot multiply without memorising the multiplication table. Then, quietly, Perelman notes that Magnitsky was wrong. There is a method for multiplying two numbers that requires no multiplication table at all. Only halving, doubling, and adding. Russian peasants used it. They inherited it, as Perelman puts it, “from deep antiquity.”<br>Here is the method. Suppose you want to multiply 32 × 13. Write the two numbers side by side. Halve the left number; double the right. Repeat until the left number reaches 1.<br>32 × 13<br>16 × 26<br>8 × 52<br>4 × 104<br>2 × 208<br>1 × 416The answer is the last number on the right: 416. Verify: 32 × 13 = 416. ✓<br>The reason this works is disarming. Halving one factor and doubling the other preserves the product. So after six operations, we’ve reduced 32 × 13 to the equivalent 1 × 416 — which requires no multiplication at all.<br>What happens when the left number is odd? Halve after dropping the remainder — but on those rows, add the right-hand number back at the end. Example: 19 × 17.<br>19 × 17 (odd — keep 17)<br>9 × 34 (odd — keep 34)<br>4 × 68 (even — cross out)<br>2 × 136 (even — cross out)<br>1 × 272 (odd — keep 272)Sum the kept rows: 17 + 34 + 272 = 323. And 19 × 17 = 323. ✓<br>Two things about this method are worth pausing on.<br>One: it isn’t Russian. Perelman traces it, in the following section, to Ancient Egypt. Scribes on the Rhind Mathematical Papyrus, around 1550 BC, were multiplying by exactly this method — successive doubling, tallying the powers of two that sum to the multiplier. The “Russian peasant” name comes from a British journal called Knowledge, which christened it that way just before the First World War. The method had migrated from the pharaohs’ land, along some unrecorded route, into the Great Russian village.<br>Two: it’s binary. Look at the odd/even column when you multiply 19 × 17. The odd rows are 19, 9, 1. In binary, 19 = 10011. Reading the odd/even pattern from the top: 1 (odd), 0 (even), 0 (even), 1 (odd — wait, that’s the crossed-out row) — no, let me realign. Halving 19 gives 9 remainder 1; halving 9 gives 4 remainder 1; halving 4 gives 2 remainder 0; halving 2 gives 1 remainder 0; halving 1 gives 0 remainder 1. Reading those remainders bottom-to-top: 10011 = 19. The peasant method is binary multiplication. It’s what every arithmetic-logic unit inside every modern computer chip does — shift left (double), shift right (halve), add when the bit is set. The Russian peasant and the Intel Core i9 are executing the same algorithm.<br>The reason I want to publish Perelman in English is that this is what he does on every page. Take a piece of folk knowledge that looks trivial. Unpack it, honestly. Show that it connects to something deep. Never sacrifice accuracy for showmanship. He did this for arithmetic, algebra, geometry, mechanics, astronomy — across forty books.<br>None of his mathematics books were in English until this month.<br>Entertaining Arithmetic — Yakov Perelman, translated by Valery Manokhin (Northern Star Academic Press, 2026). 151 pages, 66 problems with full solutions, 54 figures from the source edition.<br>Amazon (paperback + Kindle): https://www.amazon.com/dp/B0H8ZZLLGT<br>Gumroad (PDF): https://valeman.gumroad.com/l/perelman_arithmetic

Math

Arithmetic

Written by Valeriy Manokhin, PhD, MBA, CQF

3.8K followers<br>·339 following

PhD in Machine Learning, creator of Awesome Conformal Prediction 👍Tip: hold down the Clap icon for up x50

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