Ancient Science · Part 25 · Late Alexandria · B1–B2
India and China: The Nine Chapters, Negative Numbers and the Zero
Part 25 of Ancient Science: while the Greeks proved theorems, Chinese mathematicians calculated with red and black rods and solved several equations at once, and Indian astronomers developed the numbers, with a zero, that the whole world now uses. Sophia shows what each tradition found, how Indian numbers reached Europe, and why the oldest zero is still argued about. Similar to, different from, both … and, neither … nor, with Philo, Sophia, Marcos and Demetria.
Tonight we leave the Greeks behind. All through this series I have shown you glimpses of India and China. Now let us look properly.
In some things more, in some things less, and in some things they simply did something different. The numbers you will use one day, with a zero, come from India. Negative numbers were first used regularly in China.
The Greeks thought a negative answer was absurd. Let me show you.
In China, the most important book of mathematics was the Nine Chapters on the Mathematical Art, put together from older material around the first century BCE or the first century CE. It contains 246 practical problems: measuring fields, sharing grain, digging canals, paying taxes, each with an answer and a method.
Chinese mathematicians calculated with counting rods, small sticks laid out on a board in columns, so that the position of a rod showed its value: units, tens, hundreds. An empty column meant nothing there. They used red rods for positive numbers and black rods for negative ones, and the Nine Chapters gives rules for adding and subtracting them.
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