The most important contribution of the byzantines to the fields of mathematics and science was

The contribution of byzantine era in the field of mathematics was mainly involved in the practice of architecture and construction. During this era, byzantine mathematicians used complex mathematical equations in order to construct churches and large infrastructures.

Also in this era was when the byzantine empire Became the leading scholarship center in the region. The Byzantine Empire initially provided the medieval islamic world with ancient and early medieval Greek texts on astronomy, mathematics and philosophy, for translation into Arabic.

its b they wanted to be able to expand their trade..

in 1897, pershing became a tactical officer at west point, and that's where he was given the nickname "black jack." pershing's first name is "john," for which "jack" is a nickname, and he was a white man who commanded black troops. hence "black jack".