The Chinese invented gunpowder and began using it for warfare over 1,000 years ago. How is it the people who were clever enough to invent it fell so far behind European firearms technology from the period of roughly the Renaissance through the 20th century?
It took a long time for cannon to be useful for anything except as siege warfare, and even longer for firearms to be a better alternative to bows for infantry. It was only at that point firearms became the world-conquering (by some definition of the term, its pretty uncontroversial that efficient personal firearms were part of the reason the armies of Europe were so dominant for so long) weapon, and that required a lot of other non-military social factors that did not exist in China.
Building firearms that function reliably and don’t blow up in your face requires advanced steel metallurgy and machining ability that the pre-15th Century Chinese didn’t have. The Chinese built and used the fire lance and later heavy cast bronze “hand cannon” but these were more intimidation devices than effective ranged weapons the way the Turkish and European musket was.
Stranger
One random factoid I just learned (on the excellent History of England podcast) that shows how late it was before firearms were really better than the alternatives. The men accompanying the famous Tudor explorers such as Francis Drake primarily relied on bows not muskets.
What you’re asking is (part of) a problem which, under the name “the Great Divergence” (Wiki link), has puzzled historians for a long time: How come a middle-sized peninsula on the Western edge of Eurasia came to overtake and ultimately dominate other powers that had been much more advanced at earlier stages of history?
As with so many debates in history, theories to explain this one vary greatly. One hypothesis is that Europe was, for most of its history, made up of almost constantly warring comparatively small (by the standards of China) states. This constant state of conflict put pressure on European rules to constantly improve their weapon technology and tactics. China, on the other hand, was a centralised state under a unified government without major external enemies; even where invasions occurred, they did not lead to a fragmentation of the country but simply to a takeover of the continued imperial throne by the invaders.
My understanding is that Europeans invented those heavy bronze cannon. It was an adaptation of the already developed tech of casting cathedral bells. So that gave the Europeans a head start on making lighter and smaller gunpowder weapons. Although it took about three centuries for the art of iron working to come up with strong enough steel for muskets and cannon.
On top of metallurgical issues, Chinese gunpowder was barely suitable even for cannons. They were pulverizing the ingredients, not very selective about the ingredients used or all that good at refining them, and didn’t use the same proportions of components the Europeans later refined. It took a large amount of powder to use with small simple cannon and was not very effective. The early Chinese gunpowder was ideal for making rockets that did not blow up but could never have been used to make a practical gun. The Europeans eventually discovered effective gunpowder had a structure, it was not simply a chemical mix.
Further to the difference between the Chinese empire and fragmented Europe - the Chinese empire had no problem throwing massive manpower at any problem, whether building a big wall or sending an overwhelming army to trounce pesky rebels or invading minor hordes. As a result, comparative arms capabilities were less of an issue.
It’s not just firepower. As I understand, the real arms race before that was between metal armour and crossbows. Metal armour of any degree required large horses, which could be a food drain on an overpopulated empire. Metal work in volume required a lot of firewood and charcoal. Plus, a man in armour on horseback can be relatively useless against a big enough horde of archers and pikemen, as was demonstrated many times in Europe too. They were only useful against smaller defenders and other armoured horsemen. (Or as Joan of Arc demonstrated, a crossbow vs. a woman in armour)