The Little Brick That Tells a Big Story About Chinese Math
Today, we’ll talk about a 2,000-year-old pottery brick in Shenzhen that preserves an ancient multiplication table and offers a glimpse into how mathematical knowledge spread throughout China.
The Little Brick That Tells a Big Story About Chinese Math
Today, we’ll talk about a 2,000-year-old pottery brick in Shenzhen that preserves an ancient multiplication table and offers a glimpse into how mathematical knowledge spread throughout China.
On July 23, 2026, the International Congress of Mathematicians opened in Philadelphia, where the International Mathematical Union announced the winners of the latest Fields Medals, one of the highest honors in mathematics. Among the four recipients were two Chinese mathematicians, Deng Yu and Wang Hong. It was the first time Chinese mathematicians had received the Fields Medal, not to mention the first time two had received it in the same edition.
For Wang Hong, born in Guilin, Guangxi, in 1991, the moment represented an extraordinary journey. She became only the third woman in the history of the Fields Medal to receive the award. Her research includes major work in harmonic analysis and geometric measure theory, and in February 2025 she and her collaborator Zar resolved the three-dimensional Kakeya conjecture, a problem that had challenged mathematicians for more than a century.
Yet for generations of Chinese children, the starting point of mathematics has been something far more familiar and far less sophisticated: it’s a multiplication table known as the “Nine-Nine” table.
It may seem strange to connect an international mathematics prize with a simple exercise memorized by schoolchildren. But there’s a small pottery brick in Shenzhen that makes the connection tangible. Preserved in the Shenzhen Museum, the multiplication table was carved nearly 2,000 years ago, during the Eastern Han Dynasty, a.k.a. the Later Han, which ran from the year 25 to 220. Though the brick is a modest object, it offers an extraordinary glimpse into how mathematical knowledge reached ordinary people in ancient China.
The brick is only 4 centimeters high, 37 centimeters long and 17 centimeters wide. It was unearthed in 1981 at Honghuayuan in Nantou, Shenzhen, from an Eastern Han tomb. Han tomb bricks often bear stamped or carved inscriptions, including dates and auspicious phrases. But a complete multiplication table carved into a brick was something archaeologists had never encountered before.
At first sight, there is little to suggest that the object is particularly important. One side is worn and mottled, with diamond-shaped patterns covering about two-thirds of its surface. The remaining area was smoothed flat and carved with characters in Han clerical script. The inscription contains 40 numbers arranged in two columns. Among them are formulas such as “nine times nine is 81,” “eight times nine is 72,” and so on.
There is no signature and no indication of who carved it. The handwriting is not especially elegant either. One character for “seven” is visibly malformed, while the formulas in the second column are not arranged in the correct order. Yet these imperfections are precisely what make the brick so valuable. Archaeologists had found earlier multiplication formulas written on bamboo and wooden slips, but this was the earliest known example of a multiplication table carved on a pottery brick in China.
The object itself spent years unnoticed.
In August 1980, Shenzhen became a special economic zone and soon entered a period of rapid construction. Archaeological remains were repeatedly uncovered at construction sites, but the young city did not yet have its own museum or archaeological team. Consequently, the Guangdong provincial archaeological team was brought in to help.
In 1981, archaeologists discovered nine Han tombs at Honghuayuan, including one Western Han tomb and eight from the Eastern Han period. The brick came from a tomb called M3. After the excavation, many of the objects were placed in a warehouse, where they remained for seven years.
In 1988, as the Shenzhen Museum prepared to open, Yang Yaolin, then deputy director and later director of the museum, was sorting through Han bricks in storage. He noticed the crooked characters on one of them and realized that they formed the Nine-Nine multiplication table. In 1990, scholars published a study of the brick in the journal Cultural Relics, attracting considerable attention in archaeological circles. The object was later designated a national first-class cultural relic.
To understand why a simple multiplication table matters, it helps to look at the history of the formula itself.
The Nine-Nine table, also known as the Nine-Nine Song or Nine-Multiplication Song, provided basic rules for calculations involving multiplication, division and square roots. References to it appear in several pre-Qin texts, including the Xunzi, Guanzi, Huainanzi, and Strategies of the Warring States. These references indicate that the formula was already widely used during the Spring and Autumn and Warring States periods.
One story recorded in the Han Shi Waizhuan, a ten-volume work attributed to Han Ying, a scholar of the Han dynasty, offers a glimpse of how familiar the formula had become. Duke Huan of Qi once invited talented people to his court, but after a year, few had come. Eventually, a man from the countryside arrived and said that his only skill was reciting the Nine-Nine formula. The duke nevertheless treated him with respect, reasoning that if even such a basic skill could be valued, more accomplished people would be encouraged to come.
The story may not be historical, but it reflects an important point: as early as that time, the Nine-Nine formula was regarded as common knowledge.
The ancient version, however, looked different from the multiplication table Chinese children learn today. It originally contained 36 formulas and did not include formulas beginning with one. It was also arranged in reverse order, starting with “nine times nine is 81” and ending with “two times two is four.” This ancient order helps explain why the table is still called the “Nine-Nine” table rather than the “One-One” table.
Archaeologists have found even earlier physical examples. In 2002, a wooden slip containing a multiplication table was discovered in a well at the Liye ancient city site in Hunan Province. The site yielded more than 38,000 Qin administrative slips, and the multiplication table is regarded by China’s national archival authorities as the earliest and most complete surviving physical record of its kind. Other multiplication formulas have also been found on Han bamboo slips from places such as Dunhuang and Juyan.
The table itself gradually evolved. Around the fourth century, formulas involving one, from “one times nine is nine” to “one times one is one,” were added, expanding the table from 36 formulas to 45. By the Song Dynasty, lasting from 960 to 1279, its order had changed to the form familiar today, beginning with one times one and ending with nine times nine.
The Shenzhen brick, therefore, preserves an older stage in that evolution. Its formulas still follow the ancient reverse order and contain none of the formulas involving one.
Museum experts suggest that the inscription may have been made by a brick worker. While the clay was still damp, he may have used a break from his work to practice the multiplication formulas involving nine, and because the surface was soft and difficult to write on, the characters ended up uneven and awkward.
That possibility makes the brick especially intriguing. The person who carved it was probably not a highly educated scholar. Yet he could recite the formulas from memory. The mistakes in his handwriting may tell us something about his education, but the fact that he knew the formulas at all reveals something even more important about the society in which he lived.
By the Eastern Han period, the Nine-Nine formula had apparently become deeply embedded in everyday life. It was not merely knowledge restricted to scholars or government officials. An ordinary craftsman in a southern frontier region of the Han empire knew it well enough to reproduce it from memory.
This is what makes the brick more than an archaeological curiosity. It is not a famous person’s inscription or an official text. It is the casual work of an anonymous laborer, and precisely because it is so ordinary, it provides a rare glimpse of how knowledge circulated among ordinary people.
Shenzhen was far from the political and cultural centers of ancient China. Yet mathematical knowledge had reached it. The multiplication table had traveled from bamboo and wooden slips to a pottery brick, and from learned traditions into the hands of someone making bricks.
Archaeologist Tang Jigen, a professor at Southern University of Science and Technology, has described the brick as an important witness to this historical process. Its discovery in what was then a frontier region suggests that mathematical education had already spread considerably.
This little brick also forms an unexpected bridge to the mathematics celebrated in Philadelphia in 2026.
Wang Hong’s research in geometric measure theory deals with fundamental questions about sets, dimensions and volume. The Kakeya conjecture, in simplified terms, asks how small a three-dimensional set can be while still containing a line segment that can point in every possible direction. Wang and her collaborator proved that in three dimensions, no matter how cleverly the trajectory of the line is arranged, the set containing it must have full three-dimensional dimension.
The proof drew on sophisticated areas of modern mathematics, including harmonic analysis and combinatorics. But beneath such advanced theories lies the same basic mathematical language that children first encounter in a multiplication table: numbers and the operations that connect them.
Deng Yu, another 2026 Fields Medalist, was born in Shenzhen in 1989. He and his collaborators made a major advance related to the sixth Hilbert problem, providing a rigorous mathematical connection between microscopic particle systems and the macroscopic Boltzmann equation.
His work belongs to a world unimaginably distant from that of the anonymous worker who carved multiplication formulas into wet clay nearly 2,000 years ago. Yet the two stories meet in the same city.
One of the world’s most advanced mathematical achievements is represented by a young mathematician born in modern Shenzhen. In the same city, a small brick preserves the work of someone whose name has been lost but whose knowledge has survived.
The multiplication table traveled from bamboo and wooden slips to pottery over centuries. From that pottery brick to the frontiers of modern mathematics, the journey spans nearly two millennia.
Visitors to the Shenzhen Museum may see only a weathered piece of pottery covered with crooked characters. But behind those 40 numbers lies a much larger story about how knowledge moves through society. It does not survive only in great books by famous scholars or from prestigious institutions. Sometimes, it survives in the memory of an ordinary worker and in a few uneven characters pressed into clay.
Every child who learns the Nine-Nine table today, in a small way, is continuing a tradition that reaches back across centuries. The numbers may be abstract, but their journey leaves traces. In Shenzhen, one of those traces is a little Eastern Han brick that quietly records how far mathematical knowledge had already traveled almost 2,000 years ago.
Well, that’s the end of our podcast. Our theme music is by the famous film score composer Roc Chen. We want to thank our writer Zhang Jin, translator Yu Shougang, and copy editor Pu Ren. And thank you for listening. We hope you enjoyed it, and if you did, please tell a friend so they, too, can understand The Context.