Chinese Legacy

Chinese Legacy to the World

People in China were using written numbers by about 1500 BC, in the Shang Dynasty. This is about two thousand years later than people began to write numbers in West Asia, and more than a thousand years later than people began to write numbers in India. Nobody knows whether people in China thought of the idea to write numbers for themselves or learned it from people in West Asia or India. Chinese people counted in base ten, likepeople in India. But the Chinese system was more efficient. In China, people wrote the number 465 like this: 4 times the symbol for hundreds plus 6 times the symbol for ten plus 5. This way of writing numbers made it easier to do addition and multiplication than theWest Asian system, which used base 60. For calculating, Chinese people used number rods: they arranged short bamboo rods in patterns, with the numbers from 1-10 represented by horizontal rods, while the tens place had vertical rods, and the hundreds were horizontal again (6-9 are upside-down versions rather than really horizontal). There was no mark for zero, but you left a space, and having two horizontal or two vertical places next to each other showed that there was a space left.

People in China were probably using this method of calculating with rods by about500 BC, in the time of Lao Tzu. When traders started traveling on the Silk Road toCentral Asia and India, about 200 BC, they brought this method of calculating with them to Samarkand and Benares.

About this time, in the early Han Dynasty, Chinese scholars began to write math textbooks that were used by these merchants, and also by government administrators who needed to know how to keep accounts, survey land, and generally run the government. The earliest Chinese mathematical textbook is called the Nine Chapters; it includes a chapter on how to solve simultaneous equations (more than one algebraic equation at the same time). After the fall of the Han Dynasty in the 200s AD, the Chinese mathematician Liu Hui calculated the volume of a cylinder. By 450 AD, Zu Chongzhi built on Liu Hui's work to figure out what pi was to seven decimal places, and to calculate the volume of a sphere (as Archimedes had done 700 years earlier).

Under the Song Dynasty, there were many math colleges or institutes in China. In the 1200s, the mathematician Qin Jiushao worked on solving quadratic equations like x2 + 2xy + y2, cubic equations with x3 and on up to tenth order (x10) (which again had been done by Euclid about 1400 years earlier, or maybe even earlier by Pythagoras). Qin Jiushao also brought the use of zero to China, just about the same time that it first reached Europe.

But mathematical ideas traveled in both directions on the Silk Road. Traders brought back the abacus, another way of doing calculations that people were already using in Persia. The abacus was very fast, almost like a modern calculator. Eventually most people in China stopped using the counting rods and started to use the abacus instead. In school, teachers only taught kids how to use the abacus. This may be why mathematics stopped moving forward in China after a while.

Inventions of the Great Ancient Chinese Empire

Once people in West Asia figured out how to write down numbers, about 3500 BC, they quickly began to want to use cuneiform to write down other mathematical ideas. The earliest example of this that we have is from about 2700 BC. It shows a multiplication table to help people figure out the area of a space by multiplying width by length. The first column is the width, the second is the length, and the third column is the area. It uses a system for writing down large numbers in base 60 (the way our clocks work today).

This tablet, from about 2000 BC, was a school math book for teaching kids how to calculate inheritance. The problem asks how much each of seven boys would get when their father died, according to Babylonian law. Apparently the law said they should each get a different proportion, with the oldest getting the most and the younger kids less and less. Whoever did the math worked up from the bottom (which was not normal), and also made a mistake in his or her calculations! Here's a Babylonian math problem you could try to solve yourself. Are you as smart as Babylonian kids?

By the time of the Babylonians, mathematicians were working out quadratic equations like the Pythagorean Theorem, computing square roots and cube roots, and the factors of sixty (because they often worked in base 60).

After the Assyrians formed their empire, mathematical developments seem to have slowed down after this initial rush. But mathematicians continued to work on new ideas. Assyrian mathematicians, working around 1000 BC, first had the idea of dividing the circle into 360 degrees (still working in base 60, so 360=6x60). During the Persian Empire, around 500 BC, people first began to use the abacus (nobody knows whether the abacus was invented in Persia or China, or both about the same time). An abacus is a way of calculating large numbers quickly by moving pebbles along grooves, or beads along wires.

When Alexander conquered the Persian Empire in 331 BC, Greek mathematicians were able to talk to Persian and Indian mathematicians much more easily than before. A lot of new ideas came out of these conversations. The most important was the development by men like Aristotle and Euclid of the idea of the logical proof: that you could start from a few accepted axioms (basic facts) and work gradually by logical steps to show that more complicated ideas also had to be true (or could not be true).

Under Parthian and Sassanian rule, scholars concentrated on bringing together knowledge from the countries around them - India, China, and the Roman Empire. There doesn't seem to have been much independent thinking going on, but we really don't know much about it. In the 600s AD, the Arabs conquered West Asia and established the Islamic Empire. Around the same time, Indian numbers revolutionized mathematics. You can read about that here.