Science and technology of the Song dynasty in the context of "Chinese mathematics"

A cannon (plural either cannons or cannon) is a large-caliber gun classified as a type of artillery, which usually launches a projectile using explosive chemical propellant. Gunpowder ("black powder") was the primary propellant before the invention of smokeless powder during the late 19th century. Cannons vary in gauge, effective range, mobility, rate of fire, angle of fire and firepower; different forms of cannon combine and balance these attributes in varying degrees, depending on their intended use on the battlefield. A cannon is a type of heavy artillery weapon. The word cannon is derived from several languages, in which the original definition can usually be translated as tube, cane, or reed.

The earliest known depiction of cannons may have appeared in Song dynasty China as early as the 12th century; however, solid archaeological and documentary evidence of cannons do not appear until the 13th century. In 1288, Yuan dynasty troops are recorded to have used hand cannons in combat, and the earliest extant cannon bearing a date of production comes from the same period. By the end of the 14th century, cannons were widespread throughout Eurasia.

During the Manchu–led Qing dynasty, the economy was significantly developed and markets continued to expand especially in the High Qing era, and imperial China experienced a second commercial revolution in the economic history of China from the mid-16th century to the end of the 18th century. But akin to the other major non-European powers around the world at that time like the Islamic gunpowder empires and Tokugawa Japan, such economic development did not keep pace with the economies of European countries in the Industrial Revolution occurring by the early 19th century, which resulted in a dramatic change described by the 19th-century Qing official Li Hongzhang (who promoted the Self-Strengthening Movement) as "the biggest change in more than three thousand years" (三千年未有之大變局).

Critics of the Qing, some of whom may be motivated by Chinese nationalism and anti-Qing sentiment, argue that the specific actions and policies of the Qing dynasty held the nation-state of China back during its rule, when the Industrial Revolution which occurred in Europe by the 19th century led to a Great Divergence in which China lost its early modern economic and industrial lead over the West which it had previously held for more than a millennium. According to the critics, the advances in science and technology and economic development in the preceding Song and Ming dynasties moved China toward a modern age, but the restrictions placed on commerce and industry and the persecution of non-orthodox thought after the transition from Ming to Qing in the 17th century caused China to gradually stagnate and fall behind the West and led to the century of humiliation.