What advances in mathematics were made under the tang and song how did these ideas spread?

During the Tang (618-907) and Song (960-1279) dynasties, significant advances in mathematics included developments in algebra, the invention of the decimal place value system, and the use of negative numbers. The mathematician Zhu Shijie made contributions to polynomial equations and the Chinese Remainder Theorem. These mathematical ideas spread through trade routes, the establishment of formal education systems, and the compilation of mathematical texts, which were shared and translated across Asia, influencing neighboring cultures. The advancements laid foundational concepts that would later impact mathematics globally.