Skip to main content

no historical likeness exists

c. 220 – 280China (Cao Wei state)

Liu Hui

Why the column-by-column algorithms work: proved, not just stated.

A short story

A Chinese mathematician who, more than seventeen hundred years ago, wrote a careful commentary on the Nine Chapters on the Mathematical Art. He explained, step by step, in writing, why the column-by-column way of multiplying and adding big numbers works. His commentary is the earliest surviving justification of arithmetic algorithms a child still uses in school today.

In their own words

If you split a number into pieces (hundreds, tens, ones) and combine those pieces one at a time, the totals add up to the right answer.

Paraphrased: from Liu Hui's commentary on the Nine Chapters on the Mathematical Art, c. 263 CE.

The lab their idea turned into

Forge Lab

Stack two numbers in columns. Forge the answer one column at a time.

Open Forge Lab