2000-yr-old brain teaser: was Pythagoras Chinese?

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THE PUZZLE OVER how China suddenly became a global leader in Artificial Intelligence has a simple, widely overlooked answer: mathematics. AI and other Big Data handling techniques are rooted in processes developed thousands of years ago by Chinese scholars. Numeracy has always remained high on educational priorities in the country for millennia, and that holds true today. More than three out of four Chinese doctoral graduates are in STEM disciplines. The stereotype of the Asian nerd who is good at math appears to be rooted in observation.

UNDER-REPORTED

Yet it is the developments in the cultural, historical development of mathematics that is a fascinating, under-reported story.

It’s becoming increasingly clear that many key developments in the history of mathematics were made in China, centuries or millennia before they were found by Europeans.

There’s no dispute about the birthplaces of the great mathematicians in the history books: Pythagoras was Greek, Blaise Pascal was French, Carl Gauss was German and W.G. Homer was British. But the equations bearing their names? That’s a different matter.

Yun Jiang, a scholar based in Australia, commented on Twitter on Saturday that she had recently learned that Gaussian elimination, a key mathematical technique, was developed in China more than 1600 years before Carl Gauss stumbled on it. She suspected there were many examples in the history of science. “Yet we still call them by their Western discoverer’s name,” she said.

She’s right. Another example is the math technique known as Pascal’s Triangle, now known to have existed in China 300 years before Pascal was born.

In some cases, the time gap is even wider. Homer’s root extraction algorithm is always credited to W.G. Homer, a British mathematician of the 1800s. Yet the same technique was used by Chinese mathematicians more than one and a half millennia earlier, about AD 250.

Even the work of the legendary Pythagoras (born 570 BC), one of the ancient fathers of mathematics, may have been pre-dated by the Chinese – or may have been developed in parallel, since the Han people had been working on similar mathematics as a discipline from 1100 BC.

At the end of this article is a brain-teaser that shows the Chinese knew about the maths involving triangles and squares for between two and three millennia.

UPSIDE DOWN

The history of mathematics was quietly turned on its head in 2011, when renowned scholar Roger Hart published an academic book called The Chinese Roots of Linear Algebra.

It showed, with meticulous evidence-based arguments, that many elements in a series of mathematical “discoveries” credited to European thinkers between 1500 and 1700 had been known to Chinese scholars for more than a thousand years.

PRACTICAL NOT THEORETICAL

Chinese mathematics was certainly different in character to that of Europe. It was very much “applied” math, not theoretical. Unlike the Greeks, who took a philosophical route, China’s mathematicians were practical, using their equations to solve problems involving the calendar, commerce, architecture, tax payments, the calculation of land sizes, and so on. Mathematical ability was embedded into normal trade or retail activities (see picture at the top).

Four hundred years before the birth of Christ, the Chinese had developed a unique visual system called the counting board, not seen anywhere else on earth. By mapping numbers onto a place-based system, this anticipated the decimal point based system that underpins modern mathematics.

BAMBOO STRIPS

The full story has come together relatively recently, over the past 40 years or so, through historical research. In 1984, a book found written on bamboo strips near Jiangling in Hubei province was discovered to be a mathematics book dating back to about 180 BC.

Since then, several other mathematics books, or fragments of books, or references to the existence of such books, have been found.

Several combine knowledge of star maps with mathematics, anticipating the strong link between physics and mathematics that would become apparent across the world much later. One Chinese word, pronounced “chouren” in English, is used for both mathematicians and astronomers.

In 2009, Beijing’s Tsinghua University in Beijing received a donation of nearly 2,500 mouldy, smelly, dirty strips of wood, found at a Hong Kong market (cleaned up, above).

Researchers suspected that they came from tomb robbers. But the good news is that they ended up with scholars who could work out what they were. It was a table for multiplying numbers, carbon-dated to 305 BC, as confirmed by Nature, the science journal.

BOOK BURNING

The most famous Chinese mathematics book is one called simply by its descriptive label, Nine Chapters on the Mathematical Art. Most historians think that the text originated about 200 BC, as an attempt to rebuild a store of useful knowledge after a notorious book-burning session by Qin ruler Shih Huang Ti.

The book is very practical, providing math techniques to help people calculate the width of their fields, the depths of trenches, the volume of goods sold, and so on.

Much of the writing is presented in a learn-by-solving-this-story-problem style, which is still the mainstay of modern mathematical teaching around the world.

2200-YR-OLD BRAIN TEASER

Fancy yourself as a Chinese scholar from two millennia ago?

Here is an example of a challenge from this ancient book.

Imagine a small, walled town. You know it is square in shape, but don’t know its dimensions. Twenty paces outside the North Gate is a tree. You walk out of the South Gate walk 14 paces, then walk to the West for 1775 paces and notice that the tree will come into view.

How big is the town?

The puzzle is easy to solve if you use Pythagoras’s theorem (see diagram below), so clearly readers knew how to make calculations using triangles and squares, whether they had got it from Pythagoras or, as is increasingly belived, from local scholars. 

(The answer is that each side of the town is 250 paces.)

It’s classic Pythagoras. But the person in China who wrote it, more than two millennia ago, may have learned his skills from local sources, rather than from a man who loved in Samos, Greece, on the other side of the world.

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Illustration at the top from public domain works by George Newenham and Thomas Allom

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Links: China’s mathematical education an advantage in AI

Ancient times table hidden in bamboo strips

Academic paper on history of Chinese mathematics

Was Pythagoras Chinese? Academic book