The Chinese side of the equation
One of the more perplexing questions of history asks why China - the birthplace of many technological discoveries at the heart of civilisation - took so long to achieve industrial revolution, centuries after it had come and gone in the West.
Perhaps we should blame Emperor Kangxi. As China's longest serving leader - his 61-year rule ended in 1722 - Kangxi was politically astute and also a deeply curious man. For hours every day, he would discuss the latest advances in maths and sciences developing in Europe with visiting Jesuit missionaries, moving deftly between affairs of state and the life of the mind.
At the turn of the 18th century, China's own mathematics was languishing in the shadow of the all-important state examinations, which emphasised scholars' ability to write literary and political essays. Had Kangxi decided to make the Jesuits' knowledge central to the national education system, China's progress would likely have come much faster.
That is the argument of Siu Man-keung, a maths professor retired from the University of Hong Kong. Siu's theory is more than just an indulgence in the burgeoning 'what if' trend of alternate history. He argues the story of China can't be told fully without grasping the role maths played across the centuries, and conversely, maths cannot be taught to Chinese pupils today without putting it in the historical context.
'If China had truly harnessed maths and science in Emperor Kangxi's time, then it wouldn't have suffered the humiliation at the hands of the West a few centuries later,' Siu told an audience recently at an open lecture at the university. But Kangxi restricted the learning to a small private circle at the imperial court, and his many sons did not show any inclination towards the subjects.
Siu argues that Kangxi's motivation was partly Machiavellian. As the saying goes, knowledge is power, and the emperor equated his grasp of maths and science with political control. As a Manchurian lording over Han Chinese, Kangxi felt his rule was justified by his 'superior' mind, one that could move freely between Western thinking and traditional ideas.
'He had to convince the Han Chinese that he was the one who deserved to rule them - to show them he had vast knowledge,' Siu said. As to why he did not share this learning with others, Siu argues, 'If you promote it outside the imperial courts, then everybody learns it, and somebody is better than you.'
But Kangxi's political motives for keeping the masses ignorant were of course later forgotten. 'It's a sad thing,' Siu said.
'A missed opportunity.'
When China returned its attention to math and sciences, it was because it had no other choice: in the second half of the 19th century, at the heel of foreign gunboats and humiliating defeats in the Opium war, technology became essential. But by then, there was 'no more time to learn'.
Siu likes to integrate these bits of history into his teaching of even theoretical maths: at once making maths more human, by portraying it against regime changes, wars and famine.
He has spent decades trying to convince others of the importance of incorporating history into mathematics teaching.
'When I was a boy, you just learned what you're taught. You don't know what's behind it'. But Siu argues that knowing the history of maths is crucial to appreciating mathematics itself. He hopes to provide local teachers with a Chinese textbook of maths lessons put into historical context.
Only in recent decades have academics turned their attention to China's contribution to maths.
Take the Pythagorean theorem. Even if you have forgotten what it is (that the square of a right-angle triangle's longest side is equal to the sum of the squares of the other two sides), the name probably sounds familiar. But few people are likely to call the theorem by its Chinese name - the Gougu theorem.
Professor Wong Ngai-ying, a mathematician at Chinese University, thinks the Chinese version of the theorem may have arisen independently of the Greeks around the same time in the 1st century BC. But few, including the Chinese themselves, know this.
Today, Chinese maths and science textbooks follow not only Western names, but Western prescriptions and historical figures, even though innovations flourished in the Han and Song dynasties. Some discoveries in medieval China were more advanced than their western counterparts, Wong said.
Looking at Tang dynasty records and curricula, he concludes that exam questions would have tested critical thinking, and that 'mathematical proofs were not monopolised by the Greeks ... it's just that the [Chinese] presentation was different.'
Wong did not discover China's role in the development of mathematics until he took a then emerging course at the University of Hong Kong as an undergraduate in the 1970s - a course Siu was teaching. 'Brought up under the English system ... people thought the Chinese did not have mathematics,' Wong said. 'Chinese scholars knew the facts, but as a colony, [we] did not know about it back then.'
As for Kangxi's culpability, we will give him the last word in his own defence: 'How can a person who lacks knowledge judge who is right or wrong?'