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China – A Dynasty Of Mathematical Genius
One of the most fascinating things about history is how much stuff was wiped out – on purpose. For example, in the 9th century CE, the largest library in the world, the Library of Alexandria, was burnt down in an act of war, and ever since then history buffs have been amused and tempted to guess the identity of some of them. those books that we will never see. From the burning of libraries to the destruction of presidential newspapers today, the idea of the lost book has a certain romantic, if frustrating, appeal.
People who have studied the history of mathematics have their own “lost library” to wonder about – the treasury of early Chinese mathematical treatises burned by the order of Emperor Qin Shi Huang in 212 BCE.
China has been at the forefront of mathematics for almost as long as civilization has existed. Evidence of a highly developed numeral system dates back to the period of the Shin Dynasty – 1600 to 1046 BC. This first Chinese numeral system also includes decimals, a major intellectual breakthrough in itself. To write the number 260, for example, you write the number two, followed by the hundred symbol, then six followed by the ten symbol – you get the idea. There is also evidence that Chinese mathematicians had been developing their own version of the abacus (an ancient calculating machine that used rods with moving counters) from very early times. So whatever was contained in those burnt math books of 212 BCE was probably important work.
A handful of ancient Chinese mathematical works survived this public purge (the reasons for which are unclear). As early as 1046 BCE we have the I Ching, a favorite of 60s hippies and mystics even today, and the Mo Jing, a compilation of geometry and physical science from around the fifth century BCE. . These two survivors exemplify the high level of intellectualism and imagination characteristic of ancient Chinese mathematics.
Writers of the Han dynasty period – a four hundred year period beginning in 202 BC. mathematicians were synthesizers, bringing together the best ideas of ancient thinkers, and their most important work was the nine chapters on the art of mathematics. This essential compilation illustrates the right way to use geometry to build a structurally sound dwelling; it also shows that Chinese mathematicians understood pi (the seemingly endless number by which we calculate the circumference of a circle) and various laws regarding right triangles. Perhaps most strikingly, he uses Cavalieri’s principle to determine the volume of a shape – but he does so over a thousand years before Cavalieri came up with the idea. In other words, Chinese mathematicians understood certain geometric ideas long before anyone in the West.
Elsewhere during the Han dynasty, other Chinese mathematicians “came first”, including Jing Fang (78-37 BCE), a music theorist who discovered principles of temperament that had to wait, in the West, until in the 17th century.
For a thousand years after the Han dynasty, Chinese mathematicians continued to come up with great ideas – all at a time when European mathematicians did not exist, to speak of. Chinese thinkers developed ideas such as negative numbers (the genius invention that helps us all keep our bank balances in order), the use of matrices to solve linear equations (an idea that continues to baffle Western students from eleventh to date) and elements of calculation and trigonometry. From prehistory to the Middle Ages, China produced some of the greatest mathematical reasoning ever found.
Yet you wonder what additional heights these brilliant thinkers could have reached if their foundation had not been partially destroyed. Just as today’s playwrights and poets lament the great tragedies and epics that were probably lost in the fire at the Library of Alexandria, so historians of human genius must ask what wonderful ideas fell victim to the pride of Emperor Qin Shi Huang. (His order, after all, was only for provinces of China outside of his own state of Qin – so presumably, though we don’t know for sure, he only wanted people from his own part of China can read for themselves.) On the other hand, maybe he did Chinese math a favor. By giving Han dynasty mathematicians the impetus to safeguard and consolidate every morsel of mathematical knowledge still available, he may have lit another fire – a fire he never wanted.
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