Final answer:
Chinese mathematics is believed to have developed independently due to China's historical periods of isolationism and the cultural and political factors unique to the region. In contrast, Indian and Greek mathematics had significant interactions and exchanges with other cultures, which facilitated the sharing and transformation of mathematical knowledge.
Step-by-step explanation:
The development of Chinese mathematics is widely believed to have developed independently from other civilizations due to several factors. Chinese civilization during different periods of its long history demonstrated various degrees of isolationism, influenced by philosophical and political reasons. Complex mathematical knowledge in China grew out of a combination of practical needs and cultural factors unique to the region, and this is reflected in the degree of sophistication reached in areas such as geometry and algebra.
For instance, the spirit of isolationism that 'penetrated the Court' is one of the factors historians suggest contributed to this independent development of Chinese mathematics. Due to a variety of reasons, including possibly superstition and the extravagances of the emperor, China restricted its exchanges with other countries at different times in its history, focusing on its own technological and cultural advancements.
In contrast, Indian mathematics emerged as a separate field of study and had significant exchanges with Greek mathematicians. Indian scholars were the first to use decimals and the number zero, significantly influencing the mathematical education and advancements elsewhere, including the Arab world and eventually Europe. Furthermore, the Buddhist and Jain cultures in India contributed to the notions of zero and infinity, interweaving religious philosophies with mathematical concepts.
Therefore, in the cases of Indian and Greek mathematics, there were clear influences and exchanges with other cultures, as evident from the transmission of ideas and knowledge through trade and conquest. The independent development of Chinese mathematics, in contrast, seems to have occurred in a more isolated context possibly due to a combination of cultural, philosophical, and political factors, including a period of Chinese expansionism followed by a retrenchment from international exchanges.