How mathematics helped China create an empire


The first steps of the mathematical journey of man were given by the ancient cultures of Egypt, Mesopotamia, and Greece, cultures that created the basic language of number and calculation.

But when ancient Greece went into decay, mathematical progress stopped … in the west. In the east, it rose to new heights.

Much of this mathematical inheritance often does not receive the credit it deserves.

On BBC World, we started a recount of what history, something forgotten, of the development of mathematics in the East that transformed the West and gave birth to the modern world.

The distance

The Great Wall of China, spanning thousands of kilometers, has taken nearly 2,000 years of construction since it began in 220 BC. to protect the growing empire.

Section of the Great Wall of China

Never fails to surprise

The vast defensive wall is an incredible engineering feat built on rugged, high ground.

As they began to lift it, the ancient Chinese had to make calculations on distances, elevation angles, and quantities of material, so it is not surprising that it had inspired ingenious mathematical methods.

Its foundation was an incredibly simple numerical system which laid the foundations for the way we counted in the West today.

When they wanted to make a sum, they used small bamboo sticks.

O bars they were willing to represent the numbers from 1 to 9.

Numbers in bars

Then they put them columns so that each one represents units, tens, hundreds, thousands, and so on.

For example, if you wanted to represent the number 924, simply put the symbol 4 in the units column, the symbol 2 in the tens column and the 9 symbol in the hundreds column.

924 with bars

The way the ancient Chinese did their calculations is very similar to the way we learned today at school

The power of these bars is that they allow for very fast calculations.

This is what we call a system of decimal values, and it is very similar to what we use today: we use numbers from 1 to 9, and their position tells us whether they are units, tens, hundreds, or thousands.

The ancient Chinese were not only the first to use a system of decimal values, but they did so over a thousand years before adopting it in the West.

But they only used this by calculating with the rods.

When they wanted to write the numbersEverything was complicated.

Since they did not have the concept of 0, they needed to create special symbols to represent tens, hundreds, thousands, and so forth as they were written.

Then the number 924 would be written as 9 hundreds, 2 tens and 4.

924 when writing.

924 written

It is notfrog so efficient.

Without a zero, the number written was extremely limited.

However, this did not prevent the ancient Chinese from adopting gigantic mathematical measures.

Cosmic numbers

In ancient China, numbers were objects of great fascination.

According to legend, China's first ruler, the Yellow Emperor or Huangdi, had one of his deities creating mathematics in 2800 BC, believing that the numbers were cosmically important.

And to this day, the Chinese still believe in the mystical power of numbers.

1 to 10 in Chinese, starting in the upper left corner

There are dangerous numbers, like 4, and blessed, like 8 (1 to 10 in Chinese, starting with the upper left corner)

Odd numbers are seen as men, even numbers, and women. Number 4 should be avoided at all costs. Number 8 is good luck.

The Magic Square

In addition, the ancient Chinese were drawn by standards in numbers and developed a very old version of sudoku. It was called the magic square.

Legend has it that thousands of years ago, Emperor Yu was visited by a sacred turtle which came out of the depths of the Yellow River.

In the back were numbers arranged in a magic square.

In that square, considered of great religious significance, all the numbers in each line (horizontal, vertical and diagonal) sumban the same: 15.

The turtle with the magic photo.

Sum 15, in all directions

Although it may not be more than one puzzle funnyThe game shows the ancient Chinese fascination with mathematical patterns, and it did not take long for them to create even larger magical squares with greater magical and mathematical powers.

On court

Mathematics also played a vital role in the functioning of the emperor's court.

The calendar and motion of the planets were of the utmost importance to the ruler, influencing all his decisions, even in the way his day was planned, so that astronomers would become valued members of the imperial court, and astronomers were always mathematicians.

Everything in the life of the emperor was governed by the calendar, and he he handled his subjects with mathematical precision.

Everything, including your sex life.

A mathematical sexual problem

One of the tasks of the Imperial mathematical advisers was to create a system that allowed the emperor to lie down with as many women as possessed in his harem.

Homage to the Yellow Emperor

The legendary Yellow Emperor reigned, according to tradition, from 2698 to 2598 a. C. He is credited with the introduction of wooden houses, cars, boats, bow and arrow, writing and use of invented money. His wife is credited with the discovery of sericulture (silk production)

The legend says that in the space of 15 nights, the emperor had to have relations with 121 women:

  • lEmpress,
  • 3 high-ranking consorts or "ladies",
  • 9 wives or "ladies invited",
  • 27 concubines or "hereditary ladies" and
  • 81 slaves or "visiting ladies".

The mathematical consultants found the solution based on an idea called geometric progression.

They noticed that it was a series of numbers in which one passes from one number to the other, multiplying the same number each time, in this case, 3.

Each group of women is three times larger than the previous group, so they could organize a rotation that would guarantee this, In space out of 15 nightsthe emperor will sleep with all the women of the harem.

The first night was reserved for the Empress. The next, for the top 3 consorts. The 9 wives came later, and then the 27 concubines, in groups of 9 each night.

Finally, during a period of 9 nights, the 81 slaves passed through their beds in groups of 9.

Broken bed

There is no denying that ser emperor required in very resistance.

In addition, the rotation ensured that the emperor slept with the tallest women on nights closest to the full moon, when yin-the female force-was at its highest level and able to match yangor male strength.

The goal was clear and imperative: to seek the best possible imperial succession.

  • The mathematicians who helped Einstein and without whom the theory of relativity would not work

9 chapters

Of course, mathematics was also fundamental to the functioning of the state.

Ancient China was a vast and growing empire with strict legal code, generalized taxes, and a standardized system of weights, measures, and money.

The empire needed a civil service highly qualified, competent in mathematics. And to educate these officials, there was a manual written around 200 BC: "The nine chapters on mathematical art."

Emperor of the Han Dynasty with scholars translating classical texts.

Emperor of the Han Dynasty with scholars translating classical texts

The book is a compilation of 246 problems in practical areas such as trade, payroll, and taxes.

And at the heart of these problems lies one of the central themes of mathematics: how to solve equations.

The equations are rather like enigmatic puzzles. You get a certain amount of information about some unknown numbers, and from that information, you need to figure out the unknown numbers.

For example…

Plums and peaches in groups and their weights

If you know that:

  • 1 plum with 3 peaches weighs a total of 15 grams
  • 2 prunes with 1 peach weigh a total of 10 grams …

… you can deduce how much a single plum weighs and a single peach.


If you take the first set – 1 plum and 3 peaches weighing 15 grams – and fold, you will have:

  • 2 plums and 6 peaches weighing 30 grams.

If subtracting the second set -2 plums and 1 peach weighing 10 grams-, the result is interesting: you not only know you get 20 grams, but now there are no plums.

So if the remaining 5 peaches weigh 20 grams, a single peach weighs 4 gbouquetsand from this you can deduce that each plum weighs 3 gbouquets.

The explained operation with images

… until you deduce that each peach weighs 4 grams


The ancient Chinese continued to apply methods similar to a growing number of unknowns, using it to solve increasingly complicated equations.

The extraordinary thing is that this particular system of solving equations did not appear in the West until the beginning of the 19th century.

In 1809, when analyzing a rock called Pallas in the asteroid belt, Carl Friedrich Gauss, who would be known as "the prince of mathematics", rediscovered this method that had been formulated in ancient China centuries earlier.

  • The genius of Carl Gauss, the prince of mathematics

The importance of the rest

The Chinese solved even more complicated equations involving much larger numbers.

In what is known as The Chinese rest theorem, they came up with a new kind of problem.

In this, we know the number that remains when the unknown number of the equation is divided by a certain number, for example, 3, 5 or 7.

Although it is an abstract mathematical problem, the ancient Chinese expressed in practical terms.

For example…

A woman at the market does not know how many eggs she has. What he knows is …

  • if you fix them 3 in 3, 1 egg left;
  • if you put them 5 out of 5, 2 eggs left over;
  • if you organize them in rows of 7find out that Do you have 3 eggs left over?
Eggs in groups of 5

If you organize them into groups of 5, you have 2 eggs …

The ancient Chinese have discovered a systematic way of calculating that the smallest number of eggs they could have on the tray is 52.

Most surprising is that you can capture as large a number as 52 using small numbers like 3, 5 and 7.

In the sixth century AD, the Chinese rest theorem was being used in ancient Chinese astronomy to measure planetary motion.

And today it still has practical uses.

Internet Encryption code numbers using mathematics that have their origins in the Chinese rest theorem.

Chinese abacus

The best was yet to come …

In the thirteenth century, mathematics had long been established in China's curriculum, with more than 30 math schools scattered throughout the country.

O ANDin Oof Mmathematics Whina had arrived And his most important mathematician was called Qin Jiushao.

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